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Transcript 
1.
Define electric field strength at a point in space.
.................................................................................................................................
.................................................................................................................................
[Total 1 marks]
2.
Ionic solids consist of a regular arrangement of positive and negative ions. The figure
below shows two neighbouring ions in a particular ionic solid. The ions A and B may be
considered as two point charges of equal magnitude, 1.6 × 10–19 C, and opposite sign,
with a separation of 2.0 × 10–10 m. The ion A is positive.
2.0 × 10–10 m
(i)
+
–
A
B
On the figure above, draw electric field lines to represent the field in the region
around the two charges.
[3]
(ii)
Calculate the magnitude of the electric field strength at the mid point between the
charges.
electric field strength =...................................
[3]
Wilson's School
1
(iii)
State and explain a factor that might affect the tensile strength of an ionic
material.
........................................................................................................................
[1]
[Total 7 marks]
3.
Fig.1 shows two capacitors, A of capacitance 2μF, and B of capacitance 4μF,
connected in parallel. Fig. 2 shows them connected in series. A two-way switch S can
connect the capacitors either to a d.c. supply, of e.m.f. 6 V, or to a voltmeter.
S
S
V
V
V
A
V
A
B
B
Fig. 1
(a)
Fig. 2
Calculate the total capacitance of the capacitors
(i)
when connected as in Fig. 1
capacitance = .......................................... μF
[1]
Wilson's School
2
(ii)
when connected as in Fig. 2
capacitance = .......................................... μF
[2]
(b)
The switch in the circuit shown in Fig. 1 is then connected to the battery.
Calculate
(i)
the potential difference across capacitor A
potential difference = ................................. V
[1]
(ii)
the total charge stored on the capacitors.
charge = ................................................. .μC
[2]
(c)
The switch in the circuit shown in Fig.2 is then connected to the battery. Calculate
the total energy stored in the two capacitors.
energy = ................................................... . J
[2]
Wilson's School
3
(d)
The switch S in the circuit of Fig. 1 is moved to connect the charged capacitors to
the voltmeter. The voltmeter has an internal resistance of 12 MΩ.
(i)
Explain why the capacitors will discharge, although very slowly.
...............................................................................................................
...............................................................................................................
...............................................................................................................
[1]
(ii)
Calculate the time t taken for the voltmeter reading to fall to a quarter of its
initial reading.
t = .................................................... s
[3]
[Total 12 marks]
Wilson's School
4
4.
Describe briefly one scattering experiment to investigate the size of the nucleus of the
atom.
Include a description of the properties of the incident radiation which makes it suitable
for this experiment.
In your answer, you should make clear how evidence for the size of the nucleus follows
from your description.
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[Total 8 marks]
5.
(a)
Complete the table below for the three types of ionising radiation.
radiation
nature
range in air
α
β
γ
penetration ability
0.2 mm of paper
electron
several km
[3]
Wilson's School
5
(b)
Describe briefly, with the aid of a sketch, an absorption experiment to distinguish
between the three radiations listed above.
........................................................................................................................
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[3]
[Total 6 marks]
6.
Fig. 1 shows a square flat coil of insulated wire placed in a region of a uniform
magnetic field of flux density B. The direction of the field is vertically out of the paper.
The coil of side x has N turns.
x
x
region of uniform
magnetic field
Wilson's School
6
(a)
(i)
Define the term magnetic flux.
...............................................................................................................
...............................................................................................................
...............................................................................................................
[1]
Show that the magnetic flux linkage of the coil in Fig. 1 is NBx2.
(ii)
[2]
(b)
The coil of side x = 0.020 m is placed at position Y in Fig. 2 The ends of the 1250
turn coil are connected to a voltmeter. The coil moves sideways steadily through
the region of magnetic field of flux density 0.032 T at a speed of 0.10 m s–1 until it
reaches position Z. The motion takes 1.0 s.
0.0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10
distance / m
0.020m
Y
Z
0.10 m s –1
region of uniform magnetic
field B = 0.032 T
V
V
coil position at t = 0
coil position at t = 1.0s
Fig. 2
Wilson's School
7
(i)
Show that the voltmeter reading as the coil enters the field region, after t =
0.20s, is 80 mV. Explain your reasoning fully.
[3]
(ii)
On Fig. 3, draw a graph of the voltmeter reading against time for the motion
of the coil from Y to Z. Label the y-axis with a suitable scale.
voltmeter
reading
t/s
0
0.2
0.4
0.6
0.8
1.0
Fig. 3
[4]
[Total 10 marks]
7.
State the Cosmological Principle.
.................................................................................................................................
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[Total 2 marks]
Wilson's School
8
8.
Describe the important properties of the cosmic microwave background radiation and
how the standard model of the Universe explains these properties. Explain their
significance as evidence for the past evolution of the Universe.
In your answer, you should make clear how your explanation links with the evidence.
.................................................................................................................................
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[Total 5 marks]
9.
Explain why our understanding of the very earliest moments of the Universe is
unreliable.
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[Total 2 marks]
Wilson's School
9
10.
The future of the Universe may be open, closed or flat. Explain the meaning of the
terms in italics, using a graph to illustrate your answer.
‘size measure’
of Universe
age of Universe
.................................................................................................................................
.................................................................................................................................
.................................................................................................................................
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[Total 4 marks]
11.
The mean density of the Universe, ρ0, is thought to be approximately 1 × 10–26 kg m–3.
Calculate a value for the Hubble constant H0.
H0 =......................................................... s–1
[Total 2 marks]
Wilson's School
10
12.
The quality of ultrasound images in increasing at a phenomenal pace, thanks to
advances in computerised imaging techniques. The computer technology is
sophisticated enough to monitor and display tiny ultrasound signals from a patient.
The ratio of reflected intensity to incident intensity for ultrasound reflected at a
boundary is related to the acoustic impedance Z1 of the medium on one side of the
boundary and the acoustic impedance Z2 of the medium on the other side of the
boundary by the following equation.
reflected intensity (Z 2  Z1 ) 2

incident intensity (Z 2  Z1 ) 2
(a)
State two factors that determine the value of the acoustic impedance.
........................................................................................................................
........................................................................................................................
[2]
(b)
An ultrasound investigation was used to identify a small volume of substance in a
patient. It is suspected that this substance is either blood or muscle.
During the ultrasound investigation, an ultrasound pulse of frequency of
3.5 × 106 Hz passed through soft tissue and then into the small volume of
unidentified substance. A pulse of ultrasound reflected from the front surface of
the volume was detected 26.5 μs later. The ratio of the reflected intensity to the
incident intensity, for the ultrasound pulse reflected at this boundary was found to
be 4.42 × 10–4. The table below shows data for the acoustic impedances of
various materials found in a human body.
medium
air
blood
water
brain tissue
soft tissue
bone
muscle
Wilson's School
acoustic impedance Z/ kg m–2 s–1
4.29 × 102
1.59 × 106
1.50 × 106
1.58 × 106
1.63 × 106
7.78 × 106
1.70 × 106
11
(i)
Use appropriate data from the table above to identify the unknown medium.
You must show your reasoning.
medium = .....................................................
[4]
(ii)
Calculate the depth at which the ultrasound pulse was reflected if the speed
of ultrasound in soft tissue is 1.54 km s–1.
depth = .................................................. cm
[2]
(iii)
Calculate the wavelength of the ultrasound in the soft tissue.
wavelength = ............................................m
[2]
[Total 10 marks]
Wilson's School
12
13.
An average person in the UK will have at least 30 X-ray photographs taken in their
lifetime.
In order to take an X-ray photograph, the X-ray beam is passed through an aluminium
filter to safely remove low energy X-ray photons before reaching the patient.
(a)
Suggest why it is necessary to remove these low energy X-rays.
........................................................................................................................
........................................................................................................................
[1]
(b)
The average linear attenuation coefficient for X-rays that penetrate the aluminium
is 250 m–1.
The intensity of an X-ray beam after travelling through 2.5 cm of aluminium is
347 W m–2.
Show that the intensity incident on the aluminium is about 2 × 105 W m–2.
[3]
Wilson's School
13
(c)
The X-ray beam at the filter has a circular cross-section of diameter 0.20 cm.
Calculate the power of the X-ray beam from the aluminium filter. Assume that the
beam penetrates the aluminium filter as a parallel beam.
power = .................................................... W
[2]
[Total 6 marks]
14.
In an X-ray tube, the efficiency of conversion of the kinetic energy of the electrons into
X-rays is 0.15%.
(i)
Calculate the power required in the electron beam in order to produce X-rays of
power 18 W.
power =..................................................... W
[2]
Wilson's School
14
(ii)
Calculate the velocity of the electrons if the rate of arrival of electrons is
7.5 × 1017 s–1.
Relativistic effects may be ignored.
velocity =............................................. . m s–1
[2]
(iii)
Calculate the p.d. across the X-ray tube required to give the electrons the velocity
calculated in (ii).
p.d. = ........................................................ V
[3]
[Total 7 marks]
Wilson's School
15
15.
Discuss briefly the advantages and disadvantages of scanning using MRI techniques.
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[Total 6 marks]
16.
The figure below shows the variation with nucleon number (mass number) of the
binding energy per nucleon for various nuclides.
10
9
8
binding energy
per nucleon 7
/ MeV
6
5
4
3
2
1
0
0
Wilson's School
50
100
150
200
300
250
mass number
16
(a)
(i)
State the number of nucleons in the nucleus of
(ii)
State the number of protons in the nucleus of
(iii)
State the number of neutrons in the nucleus of
94
37 Rb .
........................
142
55 Cs .
.........................
235
92 U .
.........................
[2]
(b)
Use the figure above to calculate the energy released when a
undergoes fission, producing nuclei of
94
37 Rb
and
235
92 U
nucleus
142
55 Cs .
energy = .............................................. MeV
[4]
[Total 6 marks]
Wilson's School
17
17.
Discuss two advantages and two disadvantages of producing electrical power by
nuclear fission.
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[Total 6 marks]
18.
This question is about an alpha particle making a head on collision with a gold nucleus.
(a)
(i)
When the alpha particle is at a large distance from the gold nucleus it has a
kinetic energy of 7.6 × 10–13 J. Show that its speed is about
1.5 × 107 m s–1.
mass of alpha particle = 6.6 × 10–27 kg
[2]
Wilson's School
18
(ii)
As the alpha particle approaches the gold nucleus, it slows down and the
gold nucleus starts to move, Fig. 1.
gold nucleus
alpha particle
Fig.1
Explain this and explain how it is possible to calculate the speed of the gold
nucleus.
...............................................................................................................
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...............................................................................................................
...............................................................................................................
...............................................................................................................
[3]
(iii)
Fig.2 shows the alpha particle and the gold nucleus at the distance of
closest approach. At this instant the gold nucleus is moving with speed V
and the alpha particle is stationary.
V
gold nucleus
alpha particle
Fig. 2
Calculate the speed V of the gold nucleus.
mass of gold nucleus = 3.0 × 10–25 kg
V = ......................m s–1
[2]
Wilson's School
19
(iv)
The alpha particle bounces back. Its final speed approximately equals its
initial speed of approach. Assume that the mean force on the nucleus is 9.0
N during the interaction.
Estimate the time of the collision.
time = ….…………… s
[2]
(b)
15
F/N
10
5
0
0
5
10
15
20
r / 10 –14 m
Fig. 3
Wilson's School
20
(i)
Fig. 3 shows two points on the graph of the electrostatic repulsive force F
between the alpha particle and nucleus against their separation r. The
particle and the nucleus are being treated as point charges. Use data from
the graph to calculate the values of the force at distances r = 10 × 10–14 m
and 15 × 10–14 m.
F at 10 × 10–14 m =…………….N
F at 15 × 10–14 m =…………….N
[3]
(ii)
Plot the two points on the graph and draw the curve.
[1]
[Total 13 marks]
19.
The electric motor in a washing machine rotates the drum containing the clothes by
means of a rubber belt stretched around two pulleys, one on the motor shaft and the
other on the drum shaft, as shown in Fig. 1.
X
machine
casing
motor
belt
drum
Fig. 1
Wilson's School
21
(a)
The motor pulley of radius 15 mm rotates at 50 revolutions per second. Calculate
(i)
the speed of the belt
speed = ………………. m s–1
[2]
(ii)
the centripetal acceleration of the belt at point X.
acceleration = ………………m s–2
[2]
(iii)
When the motor speed is increased, the belt can start to slip on the motor
pulley. Explain why the belt slips.
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[2]
Wilson's School
22
(b)
When the drum is rotated at one particular speed, a metal side panel of the
machine casing vibrates loudly. Explain why this happens.
........................................................................................................................
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........................................................................................................................
[2]
(c)
A fault develops in the motor, causing the coil to stop rotating. Magnetic flux from
the electromagnet of the motor still links with the now stationary coil. Fig. 2 shows
how the flux linkage of the coil varies with time.
3
flux linkage /
2
Wb turns
1
0 0
5
10
15
20
–1
25
30
time/ms
–2
–3
Fig. 2
(i)
Using Fig. 2 state a time at which the e.m.f. induced across the ends of the
coil is
1
zero
……………………………… ms
2
a maximum.
………………………………. ms
[2]
Wilson's School
23
(ii)
Use the graph of Fig. 2 to calculate the peak value of the e.m.f. across the
ends of the coil.
peak e.m.f. = …………………….. V
[2]
[Total 12 marks]
20.
Fig. 1 shows a football balanced above a metal bench on a length of plastic drain pipe.
The surface of the ball is coated with a smooth layer of an electrically conducting paint.
The pipe insulates the ball from the bench.
A
+
5000 V
_
ball
pipe
bench
Fig. 1
(a)
The ball is charged by touching it momentarily with a wire A connected to the
positive terminal of a 5000 V power supply. The capacitance C of the ball is
1.2 × 10–11 F. Calculate the charge Qo on the ball. Give a suitable unit for your
answer.
Qo = ………..….unit …..…
[3]
Wilson's School
24
(b)
The charge on the ball leaks slowly to the bench through the plastic pipe, which
has a resistance R of 1.2 × 1015 .
(i)
Show that the time constant for the ball to discharge through the pipe is
about 1.5 × 104 s.
[1]
(ii)
Show that the initial value of the leakage current is about 4 × 10–12 A.
[1]
(iii)
Suppose that the ball continues to discharge at the constant rate calculated
in (ii). Show that the charge Qo would leak away in a time equal to the time
constant.
[2]
Wilson's School
25
(iv)
Using the equation for the charge Q at time t
Q = Qoe–t/RC
show that, in practice, the ball only loses about 2/3 of its charge in a time
equal to one time constant.
[2]
(c)
The ball is recharged to 5000 V by touching it momentarily with wire A. The ball is
now connected in parallel via wire B to an uncharged capacitor of capacitance
1.2 × 10–8 F and a voltmeter as shown in Fig. 2.
A
+
5000 _V
B
V
1.2 × 10 –8 F
Fig. 2
(i)
The ball and the uncharged capacitor act as two capacitors in parallel. The
total charge Qo is shared instantly between the two capacitors. Explain why
the charge left on the ball is Qo/1000.
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[3]
Wilson's School
26
(ii)
Hence or otherwise calculate the initial reading V on the voltmeter.
V = ………… V
[2]
[Total 14 marks]
21.
This question is about the electron beam inside a television tube.
Fig. 1
(a)
Fig. 2
Fig. 1 shows a section through a simplified model of an electron gun in an
evacuated TV tube.
(i)
On Fig. 1 draw electric field lines to represent the field between the cathode
and the anode.
[2]
Wilson's School
27
(ii)
The electrons, emitted at negligible speed from the cathode, are
accelerated through a p.d. of 7.0 kV. Show that the speed of the electrons
at the anode is about 5.0 × 107 m s–1.
[2]
(b)
Some electrons pass through a small hole in the anode. They enter a region of
uniform magnetic field shown by the shaded area in Fig. 2. They follow a circular
arc in this region before continuing to the TV screen.
(i)
Draw an arrow through the point labelled P to show the direction of the
force on the electrons at this point.
[1]
(ii)
State the direction of the magnetic field in the shaded area. Explain how
you arrived at your answer.
...............................................................................................................
...............................................................................................................
...............................................................................................................
[2]
Wilson's School
28
(iii)
Calculate the radius of the arc of the path of the electron beam when the
value of the magnetic flux density is 3.0 × 10–3 T.
radius = ……………….m
[4]
(c)
The region of uniform magnetic field is created by the electric current in an
arrangement of coils. Suggest how the end of the electron beam is swept up and
down the TV screen.
.................................................................................................................................
[2]
[Total 13 marks]
Wilson's School
29
22.
This question is about the decay of an isotope of bismuth,
212
83 Bi .
(a)
130
129
128
n
127
126
125
80
81
82
83
p
84
85
Fig. 1
Fig. 1 shows a small region of the chart of neutron number n against proton
number p. An isotope of bismuth, Bi, decays to an isotope of lead, Pb, in two
stages along the path shown by the two arrows on Fig. 1.
Complete the nuclear equations which describe these two decays.
(i)
212 Bi
83

....... Po  .......... ..
84
[2]
(ii)
..... Po
84

....... Pb  .......... ..
82
[2]
Wilson's School
30
(b)
Imagine that you are given a sample of 212
83 Bi mounted on a stand. You are
asked to verify experimentally that the two decays in (a)(i) and (ii) occur. Outline
briefly the experiment that you would perform.
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[4]
(c)
The decay constant for
(i)
212
83 Bi
is 0.0115 min–1.
Show that the initial activity of a sample containing 1.00 × 10–9 g of the
isotope is about 3 × 1010 min–1.
[3]
Wilson's School
31
(ii)
Calculate the half-life of the isotope.
half-life = ………….min
[1]
(iii)
Assume that only one decay in a million is detected in an experiment to
measure the half-life. Draw a graph on the axes of Fig. 2 of the count rate
against time that you would expect to observe.
count rate / 10 3 min –1
30
20
10
0
0
20
40
60
80
100
120
140
time / min
Fig. 2
[1]
[Total 13 marks]
Wilson's School
32
23.
In this question, two marks are available for the quality of written communication.
Describe the processes of fission and fusion of nuclei. Distinguish clearly between
them by highlighting one similarity and one difference between the two processes.
State the conditions required for each process to occur in a sustained manner.
(Allow one lined page).
[7]
Quality of Written Communication [2]
[Total 9 marks]
Wilson's School
33
24.
In this question, two marks are available for the quality of written communication.
The fission of a uranium-235 nucleus releases about 200 MeV of energy, whereas the
fusion of four hydrogen-1 nuclei releases about 28 MeV. However the energy released
in the fission of one kilogramme of uranium-235 is less than the energy released in the
fusion of one kilogramme of hydrogen-1. Explain this by considering the number of
particles in one kilogramme of each.
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[4]
Quality of Written Communication [2]
[Total 6 marks]
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25.
(a)
A student makes a transformer by winding coils of copper wire around a solid
hard iron core.
He carries out an experiment to show how the efficiency of the transformer varies
with the frequency of the supply. Describe the experiment, including the following
aspects in your answer
•
•
•
•
•
a sketch of the apparatus
the quantities which are kept constant
the procedure followed
the readings taken
how the efficiency is calculated.
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[10]
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(b)
The student concludes that the efficiency of the transformer decreases with
increasing frequency. Explain why this decrease takes place.
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[4]
[Total 14 marks]
26.
Explain what is meant by the statement that the strong interaction is a short-range
force and explain what this implies about the densities of nuclei of various sizes.
.................................................................................................................................
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[Total 3 marks]
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27.
A fuel rod inside a nuclear reactor contains uranium-238. When a 238
92 U nucleus is
exposed to free neutrons it can absorb a neutron. The resulting nucleus decays, first to
239
neptunium-239 239
93 Np (decay 1) and then to plutonium-239 94Pu (decay 2).
(a)
Write nuclear equations for these two decay reactions.
decay 1 ..........................................................................................................
decay 2 ..........................................................................................................
[2]
Wilson's School
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(b)
In the fuel rod,
239
93 Np
nuclei are produced at a constant rate of 1.80 × 107 s–1.
On the figure below, draw a graph to show how the number of 239
93 Np nuclei
produced varies with time.
Label this graph X. Assume that initially there are no 239
93 Np nuclei.
12
10
8
number of nuclei/
10 12
6
4
2
0
0.0
1.0
2.0
3.0
4.0
5.0
6.0
time / 10 5 s
[1]
(c)
(i)
State and explain, without calculation, how the number of
decaying per second varies with time.
239
93 Np
nuclei
...............................................................................................................
...............................................................................................................
...............................................................................................................
[2]
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(ii)
State why the number of
constant.
239
93 Np
nuclei present eventually becomes
...............................................................................................................
...............................................................................................................
[1]
(iii)
Calculate this constant number of
half-life of
239
93 Np
239
93 Np
nuclei.
= 2.04 × 105 s
number = .........................................................
[3]
(iv)
Sketch a graph on the figure above to show how the number of
nuclei present varies with time. Label this graph Y.
239
93 Np
[1]
[Total 10 marks]
28.
This question is about the possibility of fusion between a tritium nucleus and a
deuterium nucleus.
A tritium nucleus 31 H and a deuterium nucleus 21H approach each other along the
same line with the same speed u.
Each nucleus decelerates, comes to rest and then accelerates in the reverse direction.
(a)
(i)
Wilson's School
By considering conservation of momentum, explain why both nuclei cannot
come to rest at the same time.
39
...............................................................................................................
...............................................................................................................
...............................................................................................................
...............................................................................................................
[1]
(ii)
When the nuclei are closest together they have the same velocity. Show
that this velocity is u / 5.
[2]
(b)
(i)
Energy is conserved during the interaction.
Write a word equation relating the initial energy of the two nuclei when they
are far apart, to their energy when they are closest together. Your equation
should make clear the kind(s) of energy involved.
...............................................................................................................
...............................................................................................................
[1]
(ii)
Show that the total initial kinetic energy of the two nuclei is equal to
4.18 × 10–27 u2 joule where u is in m s–1.
[3]
(iii)
Wilson's School
The potential energy E of two charges Q1 and Q2, separated by a distance r
is given by
40
E=
For
3
1H
Q1Q 2
4π 0 r
0 = permittivity of free space
and 21H to fuse, their separation must be no more than
1.50 × 10–15 m.
Calculate the minimum value of u for fusion to take place.
minimum value of u = ................................................ m s–1
[4]
[Total 11 marks]
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29.
State and explain two possible advantages of using nuclear fusion rather than nuclear
fission for generating useful energy on a large scale.
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[Total 4 marks]
30.
236
92 U , undergoes
tellurium-131, 131
52 Te .
A uranium-236 nucleus,
fission, producing nuclei of zirconium-100,
100
40 Zr
, and
(a)
Write a nuclear equation to represent this fission reaction.
........................................................................................................................
[1]
(b)
Each of the product nuclei is a – emitter.
(i)
State the change, if any, in the nucleon number and the proton number
caused by a – emission.
nucleon number ....................................................................................
proton number ......................................................................................
[1]
Wilson's School
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(ii)
The – decay of zirconium-100 is followed by three more – decays before
the product nucleus is stable.
State the nucleon number and the proton number of the resulting stable
nucleus.
nucleon number ....................................................................................
proton number ......................................................................................
[1]
(iii)
On the figure below, use crosses to represent each of the nuclei involved in
the series of decays by which zirconium-100 changes to a stable nucleus.
Add arrows to show the direction of each reaction.
62
60
58
neutron
number
56
54
52
50
38
40
42
44
46
48
50
proton number
[2]
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43
(iv)
On a graph of neutron number against proton number, stable nuclei all lie
close to a line. On the figure above, sketch this line.
[1]
(c)
Zirconium-100 decays initially to niobium-100.
data:
(i)
nuclear masses:
zirconium-100
niobium-100
electron mass
99.895 808 u
99.891 679 u
0.000 549 u
Calculate the mass defect for this decay reaction.
mass defect = ...................................................... u
[2]
(ii)
Show that this mass defect is equivalent to about 5 × 10–13 J.
[2]
Wilson's School
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(iii)
When a particular zirconium-100 nucleus decays, the emitted – particle
has only about 2 × 10–13 J. Suggest why this is less than the energy
calculated in (ii).
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[2]
[Total 12 marks]
31.
This question is about the energy stored in a capacitor.
(a)
(i)
One expression for the energy W stored on a capacitor is
W=
1
QV
2
where Q is the charge stored and V is the potential difference across the
capacitor.
Show that another suitable expression for the energy stored is
W=
1
CV2
2
where C is the capacitance of the capacitor.
[2]
Wilson's School
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(ii)
Draw a graph on the axes of Fig. 1 to show how the energy W stored on a
2.2 F capacitor varies with the potential difference V across the capacitor.
30
W/J
20
10
0
0
1
2
3
4
V/V
5
Fig. 1
[2]
(b)
The 2.2 F capacitor is connected in parallel with the power supply to a digital
display for a video/DVD recorder. The purpose of the capacitor is to keep the
display working during any disruptions to the electrical power supply. Fig. 2
shows the 5.0 V power supply, the capacitor and the display. The input to the
display behaves as a 6.8 k resistor. The display will light up as long as the
voltage across it is at or above 4.0 V.
+
5.0V
–
2.2F
6.8k
display
Fig. 2
Suppose the power supply is disrupted.
(i)
Show that the time constant of the circuit of Fig. 2 is more than 4 hours.
[2]
Wilson's School
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(ii)
Find the energy lost by the capacitor as it discharges from 5.0 V to 4.0 V.
energy lost = .......................................................J
[2]
(iii)
The voltage V across the capacitor varies with time t according to the
equation
V = Voe–t/RC.
Calculate the time that it takes for the voltage to fall to 4.0 V.
time = ...................................................... s
[2]
(iv)
Calculate the mean power consumption of the display during this time.
mean power = .................................................... W
[1]
[Total 11 marks]
Wilson's School
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32.
This question is about a simple model of a hydrogen iodide molecule.
Fig. 1 shows a simple representation of the hydrogen iodide molecule. It consists of

two ions, 11 H  and 127
53 I , held together by electric forces.
I–
H+
Fig. 1
(a)
(i)
Draw on Fig. 1 lines to represent the resultant electric field between the
two ions.
[2]
(ii)
Calculate the electrical force F of attraction between the ions.
Treat the ions as point charges a distance 5.0 × 10–10 m apart. Each ion
has a charge of magnitude 1.6 × 10–19 C.
F = ..................................................... N
[4]
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(b)
The electrical attraction is balanced by a repulsive force so that the two ions are
in equilibrium.
When disturbed the ions oscillate in simple harmonic motion. Fig. 2 shows a
simple mechanical model of the molecule consisting of two unequal masses
connected by a spring of negligible mass.
mH
mI
Fig. 2
Use Newton’s laws of motion and the definition of simple harmonic motion to
explain why the amplitude of oscillation of the hydrogen ion is 127 times the
amplitude of oscillation of the iodine ion.
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[4]
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(c)
The natural frequency of oscillation of the hydrogen ion is 6.7 × 1013 Hz. Take the
amplitude of oscillation to be 8.0 × 10–12 m.
(i)
Sketch on Fig. 3 a displacement against time graph for the hydrogen ion.
15
10
displacement
/ 10–12 m 5
0
0.5
1.0
1.5
–5
2.0
2.5
3.0
time / 10–14s
–10
–15
Fig .3
[3]
(ii)
It is found that infra-red radiation of frequency close to 6.7 × 1013 Hz,
incident on the molecules, can cause this oscillation, but other frequencies
of infra-red do not. Suggest how this result can be explained.
...............................................................................................................
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[2]
[Total 15 marks]
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33.
The activity A of a sample of a radioactive nuclide is given by the equation
A = N
Define each of the terms in the equation.
A ..............................................................................................................................
.................................................................................................................................
 ..............................................................................................................................
.................................................................................................................................
N ..............................................................................................................................
.................................................................................................................................
[Total 3 marks]
34.
A 1000 MW coal-fired power station burns 7.0 × 106 kg of coal in one day. Two parts
per million of the mass of the coal is 238
92 U . The uranium remains in the residue left
after the coal is burnt.
9
The uranium nuclide 238
92 U decays by -particle emission with a half-life of 4.5 × 10
years to an isotope of thorium.
(i)
Write down
1
the proton number Z of thorium ...........................................................
2
the nucleon number A for this isotope of thorium ................................
[1]
(ii)
Calculate the mass of uranium produced in the residue in one day.
mass = ..................................................... kg
[1]
Wilson's School
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(iii)
Hence show that the number of uranium atoms in this mass of uranium is
3.5 × 1025.
[1]
(iv)
Calculate the activity of this mass of uranium. Give a suitable unit with your
answer.
1 year = 3.2 × 107 s
activity = ......................... unit .........................
[3]
[Total 6 marks]
35.
In this question, two marks are available for the quality of written communication.
Faraday invented the concept of a field of force. Starting from the definitions of electric,
gravitational and magnetic field strengths, discuss the similarities and differences
between the three force fields.
(Allow one lined page).
[7]
Quality of Written Communication [2]
[Total 9 marks]
Wilson's School
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36.
In this question, two marks are available for the quality of written communication.
To explain the laws of electromagnetic induction (Faraday’s law and Lenz’s law)
Faraday introduced the concept of magnetic flux. Describe how the flux model is used
in these laws.
Start by defining magnetic flux and magnetic flux linkage.
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[5]
Quality of Written Communication [2]
[Total 7 marks]
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37.
Full-body CT scans produce detailed 3-D information about a patient and can identify
cancers at an early stage in their development.
(a)
Describe how a CT scan image is produced, referring to the physics principles
involved.
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[7]
(b)
State and explain two reasons why full-body CT scans are not offered for regular
checking of healthy patients.
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[3]
[Total 10 marks]
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38.
Describe the principles of the production of a short pulse of ultrasound using a
piezoelectric transducer.
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[Total 5 marks]
39.
The diagram below shows a trace on a cathode-ray oscilloscope (CRO) of an
ultrasound reflection from the front edge and rear edge of a foetal head.
20 s
The CRO timebase is set to 20 s cm–1. The speed of ultrasound in the foetal head is
1.5 × 103 m s–1.
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(i)
Calculate the size of the foetal head.
size = ................................................... cm
[4]
(ii)
State and explain what would be seen on the CRO screen if gel had not been
applied between the ultrasound transducer and the skin of the mother.
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[3]
[Total 7 marks]
40.
This question is about nuclear fission of uranium-235.
(i)
State what is meant by a thermal neutron.
........................................................................................................................
........................................................................................................................
[1]
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(ii)
State the importance of thermal neutrons in relation to the fission of uranium-235.
........................................................................................................................
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[1]
[Total 2 marks]
41.
A uranium-235 nucleus
146
57 La
and bromine-87
shown below.
Wilson's School
235
92 U
87
35 Br .
undergoes fission, producing nuclei of lanthanum-146
The binding energies per nucleon of these nuclides are
nuclide
binding energy per
nucleon / MeV
235
92 U
7.6
146
57 La
8.2
87
35 Br
8.6
57
(i)
Plot these values on the grid below.
10.0
8.0
binding energy
per nucleon
/ MeV
6.0
4.0
2.0
0
0
50
100
150
200
nucleon number
250
[1]
(ii)
Sketch a graph on the grid above, to show how the binding energy per nucleon
varies with nucleon number for all nuclei.
[2]
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(iii)
Use information from the table to calculate how much energy in MeV is released
when a 235
92 U nucleus undergoes fission.
energy = ................................................ MeV
[3]
[Total 6 marks]
42.
This question is about nuclear fusion reactions inside the Sun.
Explain the importance of gravity in making fusion reactions possible inside the Sun.
.................................................................................................................................
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[Total 3 marks]
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43.
This question is about nuclear fusion reactions inside the Sun.
Two hydrogen nuclei 11 H , which are initially a long way apart, approach each other
along the same straight line.
1
1H
1
1H
x
Fig .1
The repulsive force Fe between them varies with their separation x as shown in Fig. 2.
Fe
0
0
x0
x
Fig. 2
The nuclei fuse if their separation becomes equal to or less than a critical separation
x0. What is the physical significance of the shaded area?
.................................................................................................................................
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[Total 2 marks]
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44.
The hydrogen cycle of fusion reactions is responsible for most of the energy generated
inside the Sun. In one of these reactions two 11 H nuclei fuse to make a deuterium
nucleus
2
1H
thus:
1
1H
(i)
 11H 
2
1H

0
1H

0
1e

0
0

Calculate the energy in joule generated by this reaction.
mass / u
1
1H
nucleus
1.007 276
2
1H
nucleus
2.013 553
0
1e
0.000 549
energy = ...................................................... J
[3]
(ii)
State how the positron
generation of energy.
0
1e
created in the reaction will result in further
........................................................................................................................
........................................................................................................................
........................................................................................................................
[1]
[Total 4 marks]
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45.
Uranium-238
238
92 U
One nucleus of
decays to lead-206
238
92 U
206
82 Pb
by means of a series of decays.
decays eventually to one nucleus of
206
82 Pb .
This means that, over time, the ratio of lead-206 atoms to uranium-238 atoms
increases. This ratio may be used to determine the age of a sample of rock.
In a particular sample of rock, the ratio
number of lead - 206 atoms
1
 .
number of uranium - 238 atoms 2
(a)
Show that the ratio
number of uranium - 238 atoms left
2
 .
number of uranium - 238 atoms initially 3
Assume that the sample initially contained only uranium-238 atoms and
subsequently it contained only uranium-238 atoms and lead-206 atoms.
[2]
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(b)
Calculate the age of the rock sample.
The half-life of
238
92 U
is 4.47 × 109 years.
age = ................................................ years
[3]
(c)
The rock sample initially contained 5.00 g of uranium-238. Calculate the initial
number N0 of atoms of uranium-238 in this sample.
number = .........................................................
[2]
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(d)
On the figure below, sketch graphs to show how the number of atoms of
uranium-238 and the number of atoms of lead-206 vary with time over a period of
several half-lives.
Label your graphs ‘U’ and ‘Pb’ respectively.
N0
number
of atoms
0
0
time
[3]
[Total 10 marks]
46.
(i)
Name the group of particles of which the electron and the positron are members.
........................................................................................................................
[1]
(ii)
Name another member of this group.
........................................................................................................................
[1]
[Total 2 marks]
47.
(i)
State the quark composition of the neutron.
........................................................................................................................
[1]
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64
(ii)
Complete the table to show the charge Q, baryon number B and strangeness S
for the quarks in the neutron.
quark
Q
B
S
[2]
(iii)
Hence deduce the values of Q, B and S for the neutron.
Q …………… B …………… S ……………
[1]
[Total 4 marks]
48.
Many televisions are now produced with flat panel screens. One type of flat panel
screen is the plasma screen. In a plasma screen millions of tiny cells are sandwiched
between two glass plates which enclose low pressure gas. In order to make a cell emit
light a voltage is applied across the cell between two electrodes. This ionises the gas
and ultra-violet radiation is emitted. This radiation falls on a phosphor which then emits
light. One third of all the phosphors emit red light, one third emit green light and one
third emit blue light. Three of the cells, one for each colour, are shown in the figure
below.
front glass plate
low
pressure
gas
electrode
red
phosphor
green
phosphor
blue
phosphor
cell wall
rear glass plate
electrode
(a)
Explain the meaning of the word ionise.
........................................................................................................................
........................................................................................................................
[1]
Wilson's School
65
(b)
Calculate the photon energy of ultra-violet radiation of wavelength 238 nm.
energy = ....................................................... J
[3]
(c)
Explain why it is possible to use ultra-violet photons to create photons of visible
light in a phosphor, but it would not be possible to create ultra-violet photons
from any photons of visible light.
........................................................................................................................
........................................................................................................................
........................................................................................................................
........................................................................................................................
[2]
(d)
A cell will emit light when a voltage of +15 V is applied to its positive electrode
and a voltage of −15 V to its negative electrode. The electrode separation is
0.20 mm. Calculate the value of the uniform electric field causing the ionisation.
State the SI unit for electric field.
electric field = ................................... unit ……….
[3]
[Total 9 marks]
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49.
This question is about electric forces.
A very small negatively-charged conducting sphere is suspended by an insulating
thread from support S. It is placed close to a vertical metal plate carrying a positive
charge. The sphere is attracted towards the plate and hangs with the thread at an
angle of 20° to the vertical as shown in Fig. 1.
S
20°
Fig. 1
(a)
Draw at least five electric field lines on Fig. 1 to show the pattern of the field
between the plate and the sphere.
[3]
(b)
The sphere of weight 1.0 × 10–5 N carries a charge of –1.2 × 10–9 C.
(i)
Show that the magnitude of the attractive force between the sphere and the
plate is about 3.6 × 10–6 N.
[3]
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(ii)
Hence show that the value of the electric field strength at the sphere,
treated as a point charge, is 3.0 × 103 in SI units. State the unit.
unit for electric field strength is ...................
[3]
(c)
The plate is removed. Fig. 2 shows an identical sphere carrying a charge of
+1.2 × 10–9 C, mounted on an insulating stand. It is placed so that the hanging
sphere remains at 20° to the vertical.
S
20°
Fig. 2
Treating the spheres as point charges, calculate the distance r between their
centres.
r = .............................. m
[3]
Wilson's School
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(d)
On Fig. 2, sketch the electric field pattern between the two charges. By
comparing this sketch with your answer to (a), suggest why the distance between
the plate and the sphere in Fig. 1 is half of the distance between the two spheres
in Fig. 2.
........................................................................................................................
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........................................................................................................................
[2]
[Total 14 marks]
50.
The radioactive nickel nuclide
120 years.
(a)
63
28 Ni
decays by beta-particle emission with a half-life of
A copper nucleus is produced as the result of this decay. State the number of
nucleons in the copper nucleus which are
protons ...........................................................................................................
neutrons .........................................................................................................
[2]
(b)
Show that the decay constant of the nickel nuclide is 1.8 × 10–10 s–1.
1 year = 3.2 × 107 s
[1]
Wilson's School
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(c)
A student designs an electronic clock, powered by the decay of nuclei of
63
28 Ni .
One plate of a capacitor of capacitance 1.2 × 10–12 F is to be coated with this
isotope. As a result of this decay, the capacitor becomes charged. The capacitor
is connected across the terminals of a small neon lamp. See Fig. 1. When the
capacitor is charged to 90 V, the neon gas inside the lamp becomes conducting,
causing it to emit a brief flash of light and discharging the capacitor. The charging
starts again. Fig. 2 is a graph showing how the voltage V across the capacitor
varies with time.
100
–12
1.2 × 10
V
F
neon
lamp
V/V
50
0
0
Fig. 1
(i)
1.0
2.0
3.0
time / s
Fig. 2
Show that the maximum charge stored on the capacitor is 1.1 × 10–10 C.
[2]
(ii)
When a nickel atom emits a beta-particle, a positive charge of 1.6 × 10–19 C
is added to the capacitor plate. Show that the number of nickel nuclei that
must decay to produce 1.1 × 10–10 C is about 7 × 108.
[2]
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(iii)
The neon lamp is to flash once every 1.0 s. Using your answer to (b),
calculate the number of nickel atoms needed in the coating on the plate.
number = .......................
[3]
(iv)
State, giving a reason, whether or not you would expect the clock to be
accurate to within 1% one year after manufacture.
...............................................................................................................
...............................................................................................................
...............................................................................................................
[1]
[Total 11 marks]
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51.
This question is about forcing a liquid metal, such as molten sodium, through a tube.
(a)
The liquid metal is in a tube of square cross-section, side w, made of electrically
insulating material. See Fig. 1. Two electrodes are mounted on opposite sides of
the tube and a magnetic field of flux density B fills the region between the
electrodes. An electric current I passes across the tube between the electrodes,
perpendicular to the magnetic field. The interaction between the current and the
field provides the force to move the liquid.
B
square tube
containing
flowing liquid
w
B
w
Fig. 1
(i)
Draw on Fig. 1 an arrow labelled F to indicate the direction of the force on
the liquid metal. Explain how you determined the direction.
...............................................................................................................
...............................................................................................................
[2]
(ii)
State a relationship for the force F in terms of the current I, the magnetic
field B and the width w of the tube.
...............................................................................................................
[1]
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(iii)
Data for this device are shown below.
B = 0.15 T
I = 800 A
w = 25mm
Calculate the force on the liquid metal in the tube.
force = ...................... N
[2]
(b)
To monitor the speed of flow of the liquid metal, a similar arrangement of
electrodes and magnetic field is set up further down the tube. See Fig. 2. A
voltmeter is connected across the electrodes instead of a power supply.
B
B
V
Fig. 2
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(i)
Explain, using the law of electromagnetic induction, why the voltmeter will
register a reading which is proportional to the speed of flow of the metal.
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[3]
(ii)
State how and explain why the voltmeter reading changes when the
magnetic flux density across the tube is doubled.
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[2]
[Total 10 marks]
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52.
In this question, two marks are available for the quality of written communication.
This question is about helium nuclei.
Describe the nature of alpha-particles and the main features of alpha-particle decay.
Describe one experiment where alpha-particles have been used to learn about atomic
structure. Explain how the experiment led to the discovery of the nucleus.
A space has been left for you to draw suitable diagram(s), if you wish to illustrate your
answer.
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[7]
Quality of Written Communication [2]
[Total 9 marks]
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53.
In this question, two marks are available for the quality of written communication.
A method of producing helium nuclei is shown by the following nuclear equation.
411 H  42 He  2 01 e
Describe this process of fusion giving as much detail as you can.
Compare the energy release in this process with the energy released in alpha-particle
decay.
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[5]
Quality of Written Communication [2]
[Total 7 marks]
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54.
The average orbital radius of Jupiter is approximately 5.2 AU.
Calculate the orbital radius of Jupiter in metres.
radius = ...................... m
[Total 1 mark]
55.
Describe and explain the stages which take place in the birth of a Main Sequence star.
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[Total 5 marks]
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56.
State Hubble’s law and define any symbols used.
.................................................................................................................................
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[Total 2 marks]
57.
Describe Olbers’ paradox and explain how the work of Edwin Hubble provides an
answer.
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[Total 5 marks]
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58.
(i)
Describe the shape and structure of our galaxy. Illustrate your answer with a
sketch.
........................................................................................................................
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........................................................................................................................
[2]
(ii)
Mark X on your sketch at the approximate position of the Sun within the galaxy.
[1]
[Total 3 marks]
59.
Some Cosmologists have estimated that as much as 90% of the total mass of a galaxy
is made up of gas, referred to as dark matter.
(i)
Suggest the nature and origin of this gas.
........................................................................................................................
........................................................................................................................
........................................................................................................................
[2]
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(ii)
The precise amount of dark matter in the Universe is unknown. Explain how the
presence of dark matter affects the average density of the Universe and thus has
a role in determining the ultimate fate of the Universe itself.
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[4]
[Total 6 marks]
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60.
Describe the use of a contrast medium, such as barium, in the imaging of internal body
structures. Your answer should include
•
how an image of an internal body structure is produced from an X-ray beam
•
an explanation of the use of a contrast medium
•
examples of the types of structure that can be imaged by this process.
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[Total 8 marks]
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61.
Fig. 1 shows data for the intensity of a parallel beam of X-rays after penetration through
varying thicknesses of a material.
intensity / MW m–2
thickness / mm
0.91
0.40
0.69
0.80
0.52
1.20
0.40
1.60
0.30
2.00
0.23
2.40
0.17
2.80
Fig. 1
(a)
On Fig. 2 plot a graph of transmitted X-ray intensity against thickness of
absorber.
1.0
0.8
0.6
intensity
/ MW m –2
0.4
0.2
0
0
1.0
2.0
3.0
thickness / mm
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Fig. 2
[3]
(b)
(i)
Find the thickness that reduces the intensity of the incident beam by one
half.
thickness = …………….. mm
[1]
(ii)
Use your answer to (b)(i) to calculate the linear attenuation coefficient μ.
Give the unit for your answer.
 = …………….. unit ………
[4]
[Total 8 marks]
62.
Fig. 1 shows two protons A and B in contact and at equilibrium inside a nucleus.
A
B
Fig. 1
Proton A exerts three forces on proton B. These are an electrostatic force FE, a
gravitational force FG and a strong force FS.
(a)
On Fig. 1, mark and label the three forces acting on proton B. Assume that every
force acts at the centre of the proton.
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[2]
(b)
Write an equation relating FE, FG and FS.
[1]
(c)
The radius of a proton is 1.40 × 10–15 m.
Calculate the values of
(i)
FE
FE = ..................................... N
[2]
(ii)
FG
FG = ..................................... N
[2]
(iii)
FS.
FS = ..................................... N
[1]
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(d)
Comment on the relative magnitudes of FE and FG.
........................................................................................................................
........................................................................................................................
[1]
(e)
Fig. 2 shows two neutrons in contact and at equilibrium inside a nucleus.
Fig. 2
Without further calculation, state the values of FE, FG and FS for these neutrons.
(i)
FE = .................................................................................. N
[1]
(ii)
FG = .................................................................................. N
[1]
(iii)
FS = ................................................................................. N
[1]
[Total 12 marks]
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63.
This question is about the production and use of plutonium-239 ( 239
94 Pu ).
In a uranium fission reactor, uranium-238 ( 238
92 U ) is bombarded with neutrons.
A nucleus of
238
92 U
can absorb a neutron.
The product of this reaction then undergoes two decay reactions to produce
(a)
239
94 Pu .
Write nuclear equations for these three reactions.
Use X to represent any intermediate nuclide.
(i)
absorption of a neutron
[1]
(ii)
first decay reaction
[2]
(iii)
second decay reaction
[1]
(b)
(i)
State the half-life of plutonium-239.
half-life = ...................................... y
[1]
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(ii)
Calculate the decay constant  of plutonium-239.
decay constant = .................................. s–1
[2]
(c)
Plutonium-239 can be used (with uranium-235) in a different kind of reactor. A
particular fuel rod for such a reactor has a mass of 4.4 kg, of which 5.0 % is
plutonium-239.
(i)
Show that the number of atoms of plutonium in this fuel rod is 5.5 × 1023.
[2]
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(ii)
Calculate the activity of the plutonium in this fuel rod.
State the unit of your answer.
activity = ....................... unit........
[3]
[Total 12 marks]
64.
The Sun’s energy is generated by fusion reactions.
Fusion is most likely to occur when reacting nuclei approach each other along the
same straight line. The figure below shows two protons which have the same initial
speed.
1
1H
(a)
1
1H
Describe the energy changes in this system as the protons approach each other
and come to rest.
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[3]
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(b)
In order to fuse, the centres of the protons must reach a separation of
2.1 × 10–15 m or less. Calculate the minimum initial kinetic energy of each proton
for fusion to occur.
The total potential energy EP of two charges Q1 and Q2 at separation r is given
by
EP =
Q1Q 2
.
4 0 r
kinetic energy = ..................................... J
[2]
(c)
Using the equation
EK = 2.07 × 10–23 T
calculate the temperature T of a plasma such that the kinetic energy of the
protons is equal to your answer to (b).
temperature = .................................... K
[1]
(d)
Proton fusion occurs at a temperature of about 1.5 × 107 K. Suggest why this
fusion can occur at a much lower temperature than your answer to (c).
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[2]
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(e)
Two series of fusion reactions in the Sun are particularly important. One is the
hydrogen cycle which consists of the following reactions. The energy outputs
from each reaction are shown.

2( 11 H)
2
1H 
2( 32 He)
1
1H


2
1H
3
2 He
4
2 He

0
1e

8.8  10 –13 J


 2.3  10 –13 J
0
0ν
2( 11 H) 
20.6  10 –13 J
The hydrogen cycle of reactions may be summarised in the equation 4 (11
4( 11 H)
(i)

4
2 He
 2( 01 e)

2( 00 ν)
 E
Calculate the value of E, the total energy output for this reaction.
E = ..................................... J
[2]
(ii)
Suggest why the amount of heat generated inside the Sun by the hydrogen
cycle of reactions is less than would be expected from your answer to (i).
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[1]
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(f)
Another series of reactions which occurs in the Sun is the carbon cycle. This
involves the fusion of protons with carbon and nitrogen nuclei. It happens to a
greater extent inside stars hotter than the Sun. Suggest why these reactions
require higher temperatures than the hydrogen cycle.
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[2]
[Total 13 marks]
65.
This question is about the ways in which a gold isotope might undergo spontaneous
decay.
Data.
name
symbol
192
79
gold-192
Au
191.92147
platinum-192
192
78 Pt
191.91824
mercury-192
192
80 Hg
191.92141
electron
0
1 e
0.00055
A student suggests that
(a)
mass / u
192
79
Au should undergo either + or – decay.
Write nuclear equations for each of these suggested reactions.
+
–
[2]
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(b)
Deduce whether either of these reactions can take place.
[5]
(c)
Calculate the maximum kinetic energy, in joule, of any emitted  particle.
energy = ..................................... J
[4]
[Total 11 marks]
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66.
With particular reference to two kinds of hadron, discuss the stability or otherwise of
hadrons.
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[Total 5 marks]
67.
Tritium-3 ( 31 H ) decays to helium-3 ( 32 He ) with the emission of a – particle.
(i)
Name the force responsible for this decay process.
........................................................................................................................
[1]
(ii)
Write a nuclear equation to represent this process.
[1]
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(iii)
Write a quark equation, in its simplest form, to represent this process.
[2]
[Total 4 marks]
68.
State what is meant by fission and fusion
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[Total 2 marks]
69.
The charge stored in the capacitor X of capacitance 5 µF in the circuit given in the
figure below is 30 µC.
Z
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Y
25F
X
5F
10F
95
(a)
(i)
Complete the table for this circuit.
capacitor
capacitance / µF
charge / µC
X
5
30
Y
25
Z
10
p.d. / V
energy / µJ
[9]
(ii)
Using data from the table find
1
the e.m.f. of the battery
e.m.f. = ................................................. V
[1]
2
the total charge supplied from the battery
charge = ............................................. µC
[1]
3
the total circuit capacitance
capacitance = ..................................... µF
[1]
4
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the total energy stored in all the capacitors.
96
energy = ............................................. µJ
[1]
(b)
(i)
What law or principle of physics was used to determine (a)(ii)1?
...............................................................................................................
[1]
(ii)
What law or principle of physics was used to determine (a)(ii)2?
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[1]
(c)
The battery is removed and replaced by a resistor of resistance 200 kΩ. The
capacitors now discharge through this resistor. Calculate
(i)
the time constant of the circuit
time constant = ..................................... s
[2]
(ii)
the fraction of the total charge remaining on the capacitors after a time
equal to four time constants.
fraction remaining = .................................
[2]
[Total 19 marks]
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70.
The following is adapted from an article about superconducting devices written by
Archie M. Campbell for “Physics World”. Read the following paragraphs and answer
the questions which follow.
The electrical resistance of a material suddenly vanishes when it becomes
superconducting. This remarkable transition takes place at a critical temperature,
which is within a few degrees of absolute zero for most superconducting
materials. Certain materials have critical temperatures which are appreciably
above absolute zero. Yttrium barium copper oxide (YBCO) has a critical
temperature of 92 K and below this temperature it is superconducting. Such
materials are extremely useful for electrical devices. For example, the very
high currents that can be passed through superconducting materials can be
used to generate large magnetic fields, such as those used in magnetic
separation of charged particles or in making powerful electric motors.
A problem is that heat will enter into such a cold device. The rate at which
work needs to be done to remove the heat leaking into the device increases as
the operating temperature is lowered. At 77 K heat leaking in at the rate of 1 W
requires 30 W of power to be supplied to the cooling mechanism to maintain a
constant temperature. At 4.2 K the power supplied needs to increase to 300 W
for each watt leaking in.
(a)
State the resistance of a superconducting material below the critical temperature.
 ................................................................
[1]
(b)
Calculate the power required by the cooling mechanism at 4.2 K if heat is leaking
into a superconducting device at a rate of 20W.
power = ............................................... W
[1]
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(c)
Suggest why a superconducting device using YBCO will be run at a temperature
of, say, 77 K when its critical temperature is 92 K.
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[2]
(d)
A large electromagnet is made out of superconducting wire of square
cross-section having area 1.0 mm2. It is a circular coil containing 3200 turns of
average radius 0.30 m.
A cut-away diagram is shown in Fig. 1. The wire, when superconducting, has
current density through it of 2.0 × 108 amperes per square metre (A m–2) of
cross-section.
r
Fig. 1
(i)
Show that the current in the wire is 200 A.
[2]
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(ii)
The magnetic flux density B caused by such a coil can be estimated using
the equation
B=
 o IN
2r
where I is the current, N the number of turns, r the average radius of the
coil and µo is a constant equal to 1.26 × 10–6 T m A–1.
Calculate the resulting magnetic flux density.
magnetic flux density = ........................ T
[2]
(e)
Isotopes of an element can be separated by first ionising them and then firing
them into a magnetic field. For example, if singly ionised atoms of U-235 and
U-238 are fired into a magnetic field they are deflected into circular paths of
different radii.
(i)
State the equation for the force F acting on a charge Q moving with velocity
v at right angles to a magnetic field of flux density B.
.................................................................
[1]
(ii)
Calculate the radius of the circular path of a singly-charged U-235+ ion
when it is fired with a velocity of 8.3 × 105 m s–1 at right angles into the
magnetic field caused by the superconducting coil in (d)(ii). Assume that
the charge on this ion is +1.60 × 10–19 C.
radius of path = ................................... m
[4]
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(iii)
A beam containing singly ionised U-235+ and U-238+ ions, all travelling at
the same speed, enters a region of uniform magnetic field. Sketch the
paths of these ions in the region of the magnetic field in Fig. 2. Label the
diagram clearly. No calculation is required.
region of magnetic field
down into the paper
path of U-235+ and
U-238+ ions
Fig. 2
[3]
[Total 16 marks]
71.
This question is about pressing a red hot bar of steel into a sheet in a rolling mill.
(a)
A bar of steel of mass 500 kg is moved on a conveyor belt at 0.60 m s–1.
Calculate the momentum of the bar giving a suitable unit for your answer.
momentum = .................... unit ...................
[2]
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(b)
From the conveyor belt, the bar is passed between two rollers, shown in the
figure below. The bar enters the rollers at 0.60 m s–1. The rollers flatten the bar
into a sheet with the result that the sheet leaves the rollers at 1.8 m s–1.
steel bar
conveyor belt
v = 0.60 ms–1
(i)
roller
conveyor belt
v = 1.8 ms–1
Explain why there is a resultant horizontal force on the bar at the point
immediately between the rollers.
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[2]
(ii)
Draw an arrow on the figure at this point to show the direction of the force.
[1]
(iii)
The original length of the bar is 3.0 m. Calculate the time it takes for the bar
to pass between the rollers.
time = ..................... s
[1]
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(iv)
Calculate the magnitude of the resultant force on the bar during the
pressing process.
force = ..................... N
[3]
(c)
To monitor the thickness of the sheet leaving the rollers, a radioactive source is
placed below the sheet and a detector is placed above the sheet facing the
source. State, with a reason, which radioactive emission would be suitable for
this task. Assume that the thickness of the sheet is about 20 mm.
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[2]
[Total 11 marks]
72.
This question is about the discharge of combinations of capacitors.
In Figs. 1 and 2, the capacitors are charged through a 10 kΩ resistor from a 10 V d.c.
supply when the switch S is connected to X. They discharge when the switch is moved
to Y. The ammeters A1, A2, A3 and A4 monitor the currents in the circuits. Initially, the
switch is connected to X and the capacitors are fully charged.
X
10V
S
X
10k
200F
Y
10V
S
10k
A3
Y
A1
A2
Fig. 1
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200F
50F
50F
A4
Fig. 2
103
(a)
State
(i)
the voltage across each capacitor in Fig. 1 ..................................... V
[1]
(ii)
the voltage across each capacitor in Fig. 2 ..................................... V
[1]
(b)
(i)
Calculate the total charge stored in the circuit of Fig. 2.
charge = ............................. C
[2]
(ii)
Explain why the total charge stored in the circuit of Fig. 1 is the same as in
the circuit of Fig. 2.
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[2]
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(c)
Fig. 3 shows how the reading I on ammeter A2 in the circuit of Fig. 1 varies with
time t as the capacitors discharge, after the switch is moved from X to Y at t = 0.
2.0
I / mA
1.0
0
0
0.5
1.0
1.5
t/s
2.0
Fig. 3
(i)
Describe how and explain why the reading on ammeter A1 varies, if at all,
over the same time interval.
...............................................................................................................
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...............................................................................................................
[2]
(ii)
Sketch curves on Fig. 3 to show how you expect the readings on ammeters
A3 and A4 to vary with time from t = 0, when the switch is moved from X to
Y in Fig. 2. Label your curves A3 and A4 respectively.
[3]
[Total 11 marks]
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73.
A nitrogen atom is initially stationary at point P in Fig. 1, midway between two large
horizontal parallel plates in an evacuated chamber. The nitrogen atom becomes
charged.
There is an electric field between the plates. Ignore any effects of gravity.
P
600 V
Fig. 1
(a)
The direction of the electric force on the nitrogen ion is vertically downwards.
State with a reason the sign of the charge on the ion.
........................................................................................................................
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[1]
(b)
The voltage between the plates is 600 V. At the instant that the ion, charge
1.6 × 10–19 C and mass 2.3 × 10–26 kg, reaches the lower plate, show that
(i)
the kinetic energy of the ion is 4.8 × 10–17 J
[2]
(ii)
the speed of the ion is 6.5 × 104 m s–1.
[2]
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(c)
The electric field strength between the plates is 4.0 × 104 N C–1. Calculate the
separation of the plates.
separation = ................................. m
[2]
(d)
The ion passes through a hole in the lower plate at a speed of 6.5 × 104 m s–1. It
enters a region of uniform magnetic field of flux density 0.17 T perpendicularly
into the plane of Fig. 2.
magnetic field
into the plane of
the paper
Fig. 2
(i)
Sketch on Fig. 2 the semicircular path taken by the ion.
[1]
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(ii)
Calculate how far from the hole the ion will collide with the plate. Use data
from (b).
distance = ......................... m
[5]
[Total 13 marks]
74.
The radioactive radium nuclide 226
88 Ra decays by alpha-particle emission to an isotope
of radon Rn with a half-life of 1600 years.
(a)
State the number of
(i)
neutrons in a radium nucleus ................................................................
[1]
(ii)
protons in the radon nucleus resulting from the decay .........................
[1]
(b)
The historic unit of radioactivity is called the curie and is defined as the number of
disintegrations per second from 1.0 g of 226
88 Ra . Show that
(i)
the decay constant of the radium nuclide is 1.4 × 10–11 s–1
1 year = 3.16 × 107 s
[1]
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(ii)
1 curie equals 3.7 × 1010 Bq.
[3]
(c)
Use the data below to show that the energy release in the decay of a single
–13
nucleus of 226
J.
88 Ra by alpha-particle emission is 7.9 × 10
nuclear mass of Ra-226 = 226.0254 u
nuclear mass of Rn-222 = 222.0175 u
nuclear mass of He
= 4.0026 u
[3]
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(d)
Estimate the time it would take a freshly made sample of radium of mass 1.0 g to
increase its temperature by 1.0 °C. Assume that 80% of the energy of the
alpha-particles is absorbed within the sample so that this is the energy which is
heating the sample. Use data from (b) and (c).
specific heat capacity of radium = 110 J kg–1 K–1
time = ......................... s
[4]
[Total 13 marks]
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75.
In this question, two marks are available for the quality of written communication.
This question is about electromagnetic induction.
State Faraday’s law of electromagnetic induction. Explain the terms magnetic flux and
magnetic flux linkage which you may have used in your statement of the law.
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[5]
Quality of Written Communication [2]
[Total 7 marks]
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76.
In this question, two marks are available for the quality of written communication.
This question is about electromagnetic induction.
Fig. 1 shows a simple a.c. generator used for demonstrations in the laboratory. It
consists of a magnet being rotated inside a cavity in a soft iron core. The output from
the coil, wound on the iron core, is connected to an oscilloscope.
N
to oscilloscope
S
soft iron core
Fig. 1
Sketch on Fig. 2 a typical output voltage which would be seen on the oscilloscope
screen. State and explain, using Faraday’s law and/or the terms magnetic flux and
magnetic flux linkage, how doubling each of the following factors will alter this output
voltage:
•
the speed of rotation of the magnet
•
the number of turns on the coil
Fig. 2
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Finally, explain how the output voltage would be different if the soft iron core were
removed, leaving the magnet and coil in the same positions.
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[7]
Quality of Written Communication [2]
[Total 9 marks]
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77.
When a star ceases to be Main Sequence, it may evolve in several different ways.
Explain the circumstances which will lead to the formation of a neutron star.
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[Total 4 marks]
78.
(i)
A star of mass 7 × 1030 kg becomes a neutron star of radius 10 km. Calculate the
average density of the neutron star, assuming that 50% of the original star’s
mass has been lost.
density = ……………….. kg m–3
[3]
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(ii)
State how the density of a neutron star compares to that of materials commonly
found on Earth.
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[2]
[Total 5 marks]
79.
Some stages in the early evolution of the Universe are represented in the figure below.
big
bang
opaque
Universe
1 millisecond
transparent
Universe
approx 105 years
time
(i)
What limits our understanding of events in the first millisecond?
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[1]
(ii)
State and explain how the temperature of the Universe has changed after the first
millisecond.
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[2]
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(iii)
Explain how the Universe became transparent.
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[3]
[Total 6 marks]
80.
Describe and explain two pieces of evidence which suggest that the Universe did in
fact begin with a big bang.
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[Total 5 marks]
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81.
What is meant by the cosmological principle?
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[Total 2 marks]
82.
The ultimate fate of the Universe is not yet clear. The figure below shows a graph
where the size of the Universe is represented from the big bang B to the present day P.
The graph has been extended into the future by the dotted line (– – – – –).
size
measure of
Universe
P
B
0
(i)
time
Calculate a value for the age of the Universe in years. Assume the Hubble
constant to be 75 km s–1 Mpc–1.
age = …..……………… years
[3]
(ii)
Describe and explain what final fate for the Universe is represented in the figure
above.
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[2]
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(iii)
The mass of the Universe may be significantly greater than that assumed in the
first paragraph of this question.
Taking this to be case, sketch a second graph on the figure above using the
same scales to show the future evolution of the Universe.
[2]
(iv)
Comment upon the implications of your graph for the future of the Universe.
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[1]
[Total 8 marks]
83.
For a spacecraft launched into the outer regions of the solar system, it is not practical
to have its battery recharged by solar panels. Such spacecraft use a Radioisotope
Thermoelectric Generator (RTG). This generator has no moving parts and contains two
different metals joined to form a closed electric circuit. When the two junctions between
these metals are kept at different temperatures, an electric current is produced. One
junction is cooled by space while the other is heated by the decay from a radioactive
isotope. RTGs are very reliable sources of power.
Nowadays, RTGs use plutonium-238 which is an alpha emitter with a half-life of 88
years.
Each alpha particle is emitted with a kinetic energy of 5.0MeV.
(a)
State one reason why solar panels are not practical in deep space.
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[1]
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(b)
Suppose such a spacecraft transmits for 120 minutes each day from a 12 V
circuit which draws a current of 5.0 A while transmitting back to Earth. During the
rest of the day, the transmitting circuit is shut down. The battery charging,
however, carries on continuously.
(i)
Show that the energy required per day for transmission is about 0.4 MJ.
[2]
(ii)
The overall efficiency in the RTG battery charging system is 25%. Show
that the steady power output required from the RTG is about 20 W.
[2]
(iii)
Calculate the minimum activity of the source (i.e. the number of 5 MeV
alpha particles emitted per second) required to generate this power.
activity = ................ Bq
[2]
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(c)
(i)
Show that the decay constant λ of Pu-238 is 2.5 × 10–10 s–1.
[2]
(ii)
Calculate the number N of nuclei of Pu-238 required to generate the activity
calculated in (b)(iii).
N = ......................
[2]
(iii)
Calculate the mass of Pu-238 corresponding to this number of nuclei.
mass = ................. kg
[2]
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(d)
Plutonium is one of the most dangerous chemical poisons known, as well as
being a radioactive hazard. It has been estimated that 1 kg of this substance,
suitably distributed, would be enough to kill everyone on Earth. Comment on the
risks involved in using plutonium as a fuel for spacecraft.
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[2]
[Total 15 marks]
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84.
The figure below shows a cross-section of a radiographic detector which uses fllm and
intensifying screens. Describe how an image of an internal body structure may be
produced using X-ray film. Within your answer you should include details of the use
and advantages of an intensifying screen.
X-ray photons
plastic coating
intensifying screen
film
intensifying screen
metal backing
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85.
Explain how ultrasound is produced using a piezoelectric crystal such as quartz.
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[Total 2 marks]
86.
Quartz is a compound of silicon and oxygen. Each silicon atom is attached to four
oxygen atoms. See Fig. 1 below. Each oxygen atom carries a negative charge. The
silicon atom carries a positive charge.
–
oxygen ion
silicon ion
–
–
–
–
–
–
+
+
–
–
E-field
–
–
–
+
Fig. 1
(i)
+
+
+
+
+
+
Fig. 2
On Fig. 2, draw possible positions for the negatively-charged oxygen ions when
an electric field is applied in the direction shown. The central silicon ion and one
oxygen ion have been drawn in for you.
[1]
(ii)
Use your answer to (i) to explain why a single crystal of quartz is piezoelectric.
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[1]
[Total 2 marks]
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87.
(a)
Acoustic impedance Z is the product of the density  of a medium and the speed
of ultrasound v.
The fraction f of ultrasound reflected at a boundary between two media of
acoustic impedances Z1 and Z2 is given by the equation
f=
(Z 2  Z1 ) 2
(Z 2  Z1 ) 2
medium
density / kg m–3
ultrasound velocity v / m s–1
air
1.299
330
skin
1075
1590
coupling medium
1090
1540
bone
1750
4080
Fig. 1
(i)
Use the data in Fig. 1 to find the fraction f of ultrasound reflected at an
air-skin boundary.
f = ...........................
[2]
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(ii)
Hence explain the need for a coupling medium in ultrasound imaging.
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[2]
(b)
Fig. 2 is a CRO display showing the reflected ultrasound signal from the front
edge F and the rear edge R of a bone. The time-base setting is 1.0 × 10–5 s
cm–1.
F
R
1 cm
1 cm
1.0 × 10–5 s
Fig. 2
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Using appropriate data from Fig. 1 and Fig. 2, calculate the thickness of the bone.
thickness = ........................................... cm
[4]
[Total 8 marks]
88.
The figure below shows a solenoid carrying an electric current.
On the figure above, sketch the pattern and show the direction of the magnetic field
inside the solenoid.
[Total 3 marks]
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89.
This question is about nuclear fission.
When a uranium-235 ( 235
92 U ) nucleus absorbs a neutron, it becomes uranium-236
( 236
92 U ) which may undergo fission.
(a)
In order to increase the probability of neutron-induced fission, neutrons from a
fission reaction are slowed down before they collide with another 235
92 U nucleus.
This is achieved by causing the neutrons to collide elastically with other nuclei.
Explain why these other nuclei should have a mass which is similar to the
neutron mass.
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[2]
(b)
The fission of
236
92 U
can produce many different pairs of nuclei.
The table below shows 3 possible pairs of product nuclei and their relative yields.
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nucleus 1
nucleus 2
relative yield
zirconium-100 ( 100
40 Zr )
tellurium-135 ( 135
52 Te )
6.4%
selenium-83 ( 83
34 Se )
cerium-152 ( 152
58 Ce )
0.40%
rhodium-110 ( 110
45 Rh )
silver-121 ( 121
47 Ag )
0.020%
127
Write an equation to show the fission reaction which produces
110
45 Rh
and
121
47 Ag .
[2]
[Total 4 marks]
90.
Describe briefly the quark model of hadrons.
•
Illustrate your answer by referring to the composition of one hadron.
•
Include in your answer the names of all the known quarks.
•
Give as much information as you can about one particular quark.
(Allow one lined page).
[Total 5 marks]
91.
This question is about obtaining energy from fusion reactions.
(a)
Energy may be generated by fusing deuterium nuclei in the reaction
2
1H

2
1H
 32 He 
1
0n
The values of binding energy per nucleon for
table below.
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 energy
2
1H
and
reaction 1
3
2 He
are given in the
nuclide
binding energy per nucleon / MeV
2
1H
1.11
3
2 He
2.57
128
(i)
Calculate the energy in joule released in reaction 1.
energy = ................................................... J
[3]
(ii)
Energy may also be generated by the fusion of deuterium and tritium in the
reaction
2
1H

3
1H
 42 He 
1
0n
 energy
reaction 2
The amount of energy generated in reaction 2 is 2.82 × 10–12 J. State why
this shows that reaction 2 is more suitable than reaction 1 for generating
energy.
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[1]
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(b)
The energy generated in reaction 2 is shared between the helium-4 nucleus and
the neutron.
Calculate what percentage of the energy released is gained by the neutron.
Assume that the initial momentum of the products is zero.
percentage = .................................................. %
[5]
[Total 9 marks]
92.
(i)
An important development in particle physics was the building of an accelerating
machine capable of creating a proton-antiproton pair.
Calculate the minimum energy in GeV needed for creating this pair of particles.
energy = .............................................. GeV
[3]
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(ii)
Suggest, without mathematical calculation, why it is not possible to accelerate a
particle to this energy using a cyclotron.
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[3]
[Total 6 marks]
93.
Neptunium-239 ( 239
93 Np ) is formed in a fission reactor. This nuclide decays to form
plutonium-239 ( 239
94 Pu ), thus:
239
93 Np
The half-lives are:
239
93 Np
 239
94 Pu 
: 2.36 days;
239
94 Pu :
A sample consisting of 3.00 × 1020 atoms of
0
1 e

0
0v
24 100 years.
239
93 Np
is isolated and the number of
239
93 Np
nuclei is monitored. This number of nuclei is plotted against time to give the
graph labelled Np in the figure below.
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The number of nuclei of
239
94 Pu
is also monitored to give the graph labelled Pu.
3.00 × 10 20
Pu
number of
nuclei
Np
0
(a)
0
time
Explain in words the shapes of these graphs.
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(b)
Calculate the time taken in days for the number of
239
94 Pu
nuclei to reach
20
2.70 × 10 .
time = ............................................. days
[4]
[Total 7 marks]
94.
This question is about changing the motion of electrons using electric fields. The
diagram below shows a horizontal beam of electrons moving in a vacuum. The
electrons pass through a hole in the centre of a metal plate A. At B is a metal grid
through which the electrons can pass. At C is a further metal sheet. The three vertical
conductors are maintained at voltages of +600 V at A, 0V at B and +1200 V at C. The
distance from plate A to grid B is 40 mm.
+600 V
0V
+1200V
electron
beam
A
B
C
40mm
(a)
On the diagram above draw electric field lines to represent the fields in the
regions between the three plates.
[3]
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(b)
Show that the magnitude of the electric field strength between plate A and grid B
is 1.5 × 104 V m–1.
[2]
(c)
Calculate the horizontal force on an electron after passing through the hole in A.
force = ..................... N
[2]
(d)
Show that the minimum speed that an electron in the beam must have at the hole
in A to reach the grid at B is about 1.5 × 107 m s–1.
[2]
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(e)
Calculate the speed of these electrons when they collide with sheet C.
speed = ..................... m s–1
[1]
(f)
Describe and explain the effect on the current detected at C when the voltage of
the grid B is increased negatively.
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[2]
[Total 12 marks]
95.
The diagram below shows the graph of charge Q stored against potential difference V
across a capacitor.
Q / C 25
20
15
10
5
0
0
1
2
3
4
V/V
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(i)
Use the graph to find the capacitance of the capacitor.
capacitance = .................... µF
[2]
(ii)
Calculate the energy in the capacitor when it is charged to 3.0 V.
energy = .................... µJ
[2]
(iii)
The capacitor is discharged through a resistor. The charge falls to 0.37 of its
initial value in a time of 0.040 s. This is the time constant of the circuit. Calculate
the resistance of the resistor.
resistance = .................... 
[2]
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(iv)
Explain why the discharge time of the capacitor is independent of the initial
charge on the capacitor.
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[2]
[Total 8 marks]
96.
You are provided with a number of identical capacitors, each of capacitance 3.0 F.
Three are connected in a series and parallel combination as shown in the diagram
below.
3.0 F
3.0 F
A
B
3.0 F
(i)
Show that the total capacitance between the terminals A and B is 2.0 F.
[3]
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(ii)
Draw a diagram in the space below to show how you can produce a total
capacitance of 2.0 F using six 3.0 F capacitors.
[2]
[Total 5 marks]
97.
The activity of the potassium source is proportional to the count rate minus the
background count rate, that is
activity = constant × (count rate – background count rate).
(i)
Explain the meaning of the terms
activity. ...........................................................................................................
........................................................................................................................
[1]
background count rate ...................................................................................
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[1]
(ii)
Suggest, with a reason, one of the factors which affect the value of the constant
in the equation above.
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[2]
[Total 4 marks]
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98.
The activity of the potassium source is proportional to the count rate minus the
background count rate, that is
activity = constant × (count rate – background count rate).
(i)
The radioactive decay law in terms of the count rate C corrected for background
can be written in the form
C = Coe–t
where  is the decay constant.
Show how the law can be written in the linear form
ln C = –t + lnCo
[2]
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(ii)
Fig. 2 shows the graph of ln C against time t for the beta-decay of potassium.
4.6
ln C
4.4
4.2
4.0
0
2
4
6
8
10
t/h
Fig. 2
Use data from the graph to estimate the half-life of the potassium nuclide.
half-life = ………………….h
[3]
[Total 5 marks]
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99.
State three ways in which decay by emission of an -particle differs from decay by
emission of a -particle.
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100. A single-turn square coil of side 0.050m is placed in a magnetic field of flux density B of
magnitude 0.026 T.
(a)
The coil is placed in three different orientations to the field as shown in Fig. 1(a),
(b) and (c).
B
B
(a)
B
(b)
(c)
Fig. 1
In Fig. 1(a), the plane of the coil is perpendicular to the field. In (b), it is at 45° to
the field and in (c), it is parallel to the field. Calculate the value, giving a suitable
unit, of the magnetic flux linking the coil for the position shown in
(i)
Fig. 1(a)
magnetic flux = …………..unit………
[3]
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(ii)
Fig. 1(b)
magnetic flux = …………..unit………
[1]
(iii)
Fig. 1(c).
magnetic flux = …………..unit………
[1]
(b)
The coil is rotated in the magnetic field to generate an e.m.f. across its ends. The
graph of the variation of e.m.f. with time is shown in Fig. 2.
150
100
50
voltage/mV
0
4
8
12
16
20
time / ms
–50
–100
–150
Fig. 2
(i)
On Fig. 2 mark, with an X, a point on the graph at a time when the flux
linking the coil is a maximum.
[1]
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(ii)
Give your reasoning for your choice of position X.
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[2]
(iii)
The rate of rotation of the coil is doubled. On Fig. 2 draw a graph showing
at least two cycles of the e.m.f. now generated across the ends of the coil.
[3]
[Total 11 marks]
101. In this question, two marks are available for the quality of written communication.
Describe what conclusions can be drawn about the structure of the atom from
Rutherford’s experiment in which -particles are scattered by gold nuclei. Explain how
and why the experiment differs when high-speed electrons are fired at nuclei.
(Allow one lined page)
[7]
Quality of Written Communication [2]
[Total 9 marks]
102. (a)
The cosmic microwave background radiation is evidence for the way in which the
Universe began. State a feature of the intensity of this microwave background
radiation.
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[1]
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(b)
The first stars are thought to have formed many years after the Universe came
into being. What are the similarities and differences between the composition of
the Sun and that of the very first stars?
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[3]
[Total 4 marks]
103. In 1929 Edwin Hubble showed that the Universe was expanding by studying the light
from stars and galaxies. Explain how.
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104. (a)
Suggest why many stars within our galaxy do not conform with Hubble’s law.
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[2]
(b)
Estimate the age of the Universe, giving your answer in seconds. Show your
working and take the Hubble constant to be 75 km s–1 Mpc–1.
age = .............................. s
[3]
[Total 5 marks]
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105. Describe how the fate of the Universe depends upon its mean density and explain why
this ultimate fate is not yet known.
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[Total 5 marks]
106. The primary coil of a transformer is connected to the 230 V mains supply. The 12 V
output of the secondary coil is applied to a bulb which draws a current of 3.0 A. At the
frequency of the mains the transformer operates with an efficiency of 96 %. Calculate
(i)
the power supplied to the bulb
power = ................... W
[2]
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(ii)
the current in the primary coil.
current = ................... A
[3]
[Total 5 marks]
107. This question is about the strong and electrostatic forces inside a nucleus.
The figure below shows how the strong force (strong interaction) and the electrostatic
force between two protons vary with distance between the centres of the protons.
strong
force
force
electrostatic
force
0
(a)
0
distance
between centres
Label on the figure the regions of the force axis which represent attraction and
repulsion respectively.
[1]
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(b)
(i)
On the figure above, mark a point which represents the distance between
the centres of two adjacent neutrons in a nucleus. Label this point N.
Explain why you chose point N.
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[2]
(ii)
On the figure, mark a point P which represents the distance between two
adjacent protons in a nucleus.
Explain why you chose point P.
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[2]
(c)
On the figure, sketch a line to show how the resultant force between two
protons varies with the distance between their centres. Pay particular attention
to the points at which this line crosses any other line.
[3]
(d)
(i)
Write an expression for the electrostatic force between two point charges Q
which are situated at a distance x apart.
[1]
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(ii)
The electrostatic force between two protons in contact in a nucleus is 25 N.
Calculate the distance between the centres of the two protons.
distance = ...................................... m
[2]
[Total 11 marks]
108. This question is about two isotopes of plutonium.
(a)
State briefly (without nuclear equations) how plutonium-239 can be produced.
........................................................................................................................
........................................................................................................................
........................................................................................................................
........................................................................................................................
........................................................................................................................
[2]
(b)
(i)
State what particle is emitted when plutonium-239 decays.
...............................................................................................................
[1]
(ii)
Write a nuclear equation for the decay of plutonium-239 ( 239
94 Pu ).
...............................................................................................................
...............................................................................................................
[2]
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149
(c)
A sample contains 5.00 × 1020 atoms of plutonium-239 and 40.0 × 1020 atoms of
plutonium-240.
(i)
State the half-life of plutonium-239.
...............................................................................................................
[1]
(ii)
Show that after 9000 years there will be 3.85 × 1020 atoms of
plutonium-239 left in the mixture.
[2]
(d)
After 9000 years, there will be 15.4 × 1020 atoms of plutonium-240 left in the
mixture.
(i)
State the ratio
number of atoms of plutonium - 240
after 9000 years.
number of atoms of plutonium - 239
ratio = ............................................. to two significant figures only
[1]
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150
(ii)
Use this ratio, together with the numbers of atoms in the original mixture, to
deduce the total time (from the start) before the number of atoms of
plutonium-239 and plutonium-240 are equal.
time = ............................................ years
[3]
[Total 12 marks]
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151
109. When a helium nucleus ( 42 He ) is produced by hydrogen fusion, 28.4 MeV of energy is
released.
Calculate how much energy is released when 1.00 kg of
Give your answer in joule.
4
2 He
nuclei is produced.
energy = .............................................. J
[3]
[Total 3 marks]
110. In the Sun there is a series of reactions called the hydrogen cycle.
(a)
In one of these reactions, a hydrogen nucleus ( 11 H ) fuses with a deuterium
nucleus ( 21 H ). Write an equation for this fusion reaction.
........................................................................................................................
........................................................................................................................
[1]
(b)
Fusion of a hydrogen nucleus and a deuterium nucleus is most likely when they
approach each other along the same line. The figure below illustrates this.
1
1H
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2
1H
152
In one such interaction, the two nuclei both decelerate and come to rest.
(i)
Describe the energy changes which occur during this deceleration.
...............................................................................................................
...............................................................................................................
...............................................................................................................
...............................................................................................................
[2]
(ii)
The electric potential energy EP of two particles carrying charges Q1 and Q2
at a separation r is given by
EP =
Q1Q 2
4π 0 r
where 0 is the permittivity of free space.
The hydrogen and deuterium nuclei come to rest at a separation of
3.07 × 10–13 m.
Show that their combined initial kinetic energy is 7.5 × 10–16 J.
[2]
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153
(iii)
The deuterium nucleus has an initial speed v.
Show that the initial speed of the hydrogen nucleus is 2v.
[2]
(iv)
Using the answers to (ii) and (iii), calculate the initial kinetic energies of the
hydrogen nucleus and the deuterium nucleus.
kinetic energy of hydrogen nucleus = ....................................... J
kinetic energy of deuterium nucleus = ....................................... J
[4]
[Total 11 marks]
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154
111. (a)
The table of Fig. 1 shows four particles and three classes of particle.
hadron
baryon
lepton
neutron
proton
electron
neutrino
Fig. 1
Indicate using ticks, the class or classes to which each particle belongs.
[2]
(b)
The neutron can decay, producing particles which include a proton and an
electron.
(i)
State the approximate half-life of this process.
...............................................................................................................
[1]
(ii)
Name the force which is responsible for it.
...............................................................................................................
[1]
(iii)
Write a quark equation for this reaction.
...............................................................................................................
...............................................................................................................
[2]
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155
(iv)
Write number equations which show that charge and baryon number are
conserved in this quark reaction.
charge ..................................................................................................
...............................................................................................................
baryon number .....................................................................................
...............................................................................................................
[2]
(c)
Fig. 2 illustrates the paths of the neutron, proton and electron only in a decay
process of the kind described in (b).
proton
neutron
electron
Fig. 2
Fig. 3 represents the momenta of the neutron, pn, the proton, pp and the electron,
pe on a vector diagram.
pe
pp
pn
Fig. 3
(i)
Draw and label a line on Fig. 3 which represents the resultant pr of vectors
pp and pe.
[1]
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156
(ii)
According to the law of momentum, the total momentum of an isolated
system remains constant.
Explain in as much detail as you can, why the momentum pr is not the
same as pn.
...............................................................................................................
...............................................................................................................
...............................................................................................................
...............................................................................................................
...............................................................................................................
...............................................................................................................
[3]
[Total 12 marks]
112. In nuclear fission, energy is released.
(a)
Explain what is meant by nuclear fission.
........................................................................................................................
........................................................................................................................
[1]
(b)
In a possible fission reaction
nucleus before splitting into
235
92 U
141
56 Ba
captures a neutron to become a compound
and
92
36 Kr
releasing three neutrons.
Write down the nuclear reaction equation for this event.
........................................................................................................................
[2]
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157
(c)
The total mass of the compound nucleus 236
92 U before fission is 236.053 u. The
total mass of the fission products is 235.867 u. Use these data to calculate the
energy released in the fission process.
energy = …………………..J
[3]
(d)
Most of the energy released arises from the electrostatic repulsion of the two
nuclei as they move apart. Use the information in (b) to show that the force F
between the two nuclei at the instant after fission occurs is about 3000N.
Assume the nuclei act as point charges a distance r apart of 1.3 × 10–14 m.
[4]
[Total 10 marks]
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158
113. (a)
Define magnetic flux density.
........................................................................................................................
........................................................................................................................
........................................................................................................................
[2]
(b)
The figure below shows an evacuated circular tube in which charged particles
can be accelerated. A uniform magnetic field of flux density B acts in a direction
perpendicular to the plane of the tube.
Protons move with a speed v along a circular path within the tube.
evacuated
tube
P
(i)
path of
proton
On the figure above draw an arrow at P to indicate the direction of the force
on the protons for them to move in a circle within the tube.
[1]
(ii)
State the direction of the magnetic field. Explain how you arrived at your
answer.
...............................................................................................................
...............................................................................................................
...............................................................................................................
[2]
(iii)
Write down an algebraic expression for the force F on a proton in terms of
the magnetic field at point P.
...............................................................................................................
[1]
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159
(iv)
Calculate the value of the flux density B needed to contain protons of speed
1.5 × 107 m s–1 within a tube of radius 60 m. Give a suitable unit for your
answer.
B = …………………unit………………
[5]
(v)
State and explain what action must be taken to contain protons, injected at
twice the speed (2v), within the tube.
...............................................................................................................
...............................................................................................................
...............................................................................................................
...............................................................................................................
[2]
[Total 13 marks]
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160
114. In this question, two marks are available for the quality of written communication.
State and compare the nature and properties of the three types of ionising radiations
emitted by naturally occurring radioactive substances.
.................................................................................................................................
.................................................................................................................................
.................................................................................................................................
.................................................................................................................................
.................................................................................................................................
.................................................................................................................................
.................................................................................................................................
.................................................................................................................................
.................................................................................................................................
.................................................................................................................................
.................................................................................................................................
.................................................................................................................................
.................................................................................................................................
.................................................................................................................................
.................................................................................................................................
.................................................................................................................................
.................................................................................................................................
.................................................................................................................................
[6]
Quality of Written Communication [2]
[Total 8 marks]
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161
115. In this question, two marks are available for the quality of written communication.
Describe experiments which would enable you to determine the nature and energy of
the emissions from a sample of rock containing several radioactive nuclides. A space
has been left for you to draw suitable diagram(s), if you wish to illustrate your answer.
.................................................................................................................................
.................................................................................................................................
.................................................................................................................................
.................................................................................................................................
.................................................................................................................................
.................................................................................................................................
.................................................................................................................................
.................................................................................................................................
.................................................................................................................................
.................................................................................................................................
.................................................................................................................................
.................................................................................................................................
.................................................................................................................................
[6]
Quality of Written Communication [2]
[Total 8 marks]
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162
116. State Kepler’s laws of planetary motion.
.................................................................................................................................
.................................................................................................................................
.................................................................................................................................
.................................................................................................................................
.................................................................................................................................
.................................................................................................................................
[Total 3 marks]
117. Astronomers are searching for planets which orbit distant stars. The planets are not
visible from the Earth. Their existence is revealed by the star’s motion which causes a
shift in the wavelength of the light it emits.
A large planet P is shown orbiting a star S in the Fig. 1. Both the star and the planet
rotate about their common centre of mass C.
P
C
S
light to Earth
Fig. 1
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163
When measured from a stationary source in the laboratory, a spectral line has a
wavelength  of 656.3 nm.
The light from star S is examined over a period of 74 hours. The change in wavelength
∆ for the same spectral line is recorded. The velocity has been calculated and the
data shown in Fig. 2.
∆λ /10–15 m
velocity / m s–1
1
6.7
3.1
6
38.1
17.5
12
66.0
30.3
19
76.0
34.9
23
69.1
31.7
29
43.8
20.1
35
6.8
3.1
41
–32.2
–14.8
48
–66.0
–30.3
55
–76.0
–34.9
61
–62.5
–28.7
67
–32.2
–14.8
time / h
74
6.1
Fig. 2
(i)
Use the Doppler equation relating ∆ with velocity v to calculate the change in
wavelength for the final velocity of 6.1 m s–1.
change in wavelength = ………….........m
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164
[3]
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165
(ii)
Plot a graph of the star’s velocity against time using the grid in Fig. 3. The first
seven points are already completed. The data required from Fig. 2 are repeated
beneath the grid.
velocity / m s –1
40
30
20
10
0
10
20
30
40
50
60
70
time
80 / h
–10
–20
–30
–40
Fig. 3
[2]
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time / h
velocity / m s
41
–14.8
48
–30.3
55
–34.9
61
–28.7
67
–14.8
74
6.1
–1
166
(iii)
Draw a curve through all the points on the graph.
[1]
(iv)
On Fig. 1, mark a point on the star’s orbit that would correspond to a velocity of
zero on the graph. Label this point X.
[1]
(v)
Use your graph to estimate the time T for the planet to make one complete
revolution around the star.
time .........................h
[1]
(vi)
The mass M of the star is estimated to be 4 × 1030 kg. Calculate the radius of the
planet’s orbit using the relationship below.
r=
3
GMT 2
4π 2
radius = .....................m
[2]
[Total 10 marks]
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167
118. Large distances in the Universe may be measured in parsecs. Explain what is meant
by a parsec.
.................................................................................................................................
.................................................................................................................................
.................................................................................................................................
[Total 2 marks]
119. Explain how a main sequence star can develop into a supernova. Discuss what may
remain after the explosion.
.................................................................................................................................
.................................................................................................................................
.................................................................................................................................
.................................................................................................................................
.................................................................................................................................
.................................................................................................................................
.................................................................................................................................
.................................................................................................................................
.................................................................................................................................
[Total 6 marks]
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120. It is estimated that the Sun radiates energy at the rate of 3.8 × 1026 W and that a
supernova explosion may produce 1044 J of energy.
(i)
Calculate the rate at which mass is converted into energy within the Sun.
mass rate = ........................................ kg s–1
[2]
(ii)
Calculate the time, in years, that it would take the Sun to produce the same
amount of energy as that released in a supernova explosion. Assume 1 year to
be 3.2 × 107 s.
time = .................................... y
[2]
[Total 4 marks]
121. What is the Cosmological Principle?
.................................................................................................................................
.................................................................................................................................
.................................................................................................................................
[Total 2 marks]
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169
122. Describe the important properties of the cosmic microwave background radiation and
how the standard model of the Universe explains these properties. Explain their
significance as evidence for the past evolution of the Universe.
.................................................................................................................................
.................................................................................................................................
.................................................................................................................................
.................................................................................................................................
.................................................................................................................................
.................................................................................................................................
.................................................................................................................................
.................................................................................................................................
.................................................................................................................................
.................................................................................................................................
.................................................................................................................................
.................................................................................................................................
[Total 5 marks]
123. Why is our understanding of the very earliest moments of the Universe unreliable?
.................................................................................................................................
.................................................................................................................................
.................................................................................................................................
.................................................................................................................................
.................................................................................................................................
[Total 2 marks]
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170
124. The future of the Universe may be open, closed or flat. Explain the meaning of the
terms in italics, using a graph to illustrate your answer.
'size measure'
of Universe
age of Universe
.................................................................................................................................
.................................................................................................................................
.................................................................................................................................
.................................................................................................................................
.................................................................................................................................
.................................................................................................................................
.................................................................................................................................
[Total 4 marks]
125. The mean density of the Universe, 0, is thought to be approximately 1 × 10–26 kg m–3.
Calculate a value for the Hubble constant H0.
H0 = ...........................s–1
[Total 2 marks]
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171
126. The figure below shows a simplified X-ray tube.
Explain briefly, with reference to the parts labelled C and A,
•
how X-rays are generated
•
the energy conversions that occur.
.................................................................................................................................
.................................................................................................................................
.................................................................................................................................
.................................................................................................................................
.................................................................................................................................
.................................................................................................................................
.................................................................................................................................
.................................................................................................................................
.................................................................................................................................
.................................................................................................................................
.................................................................................................................................
.................................................................................................................................
[Total 7 marks]
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127. In order to take an X-ray photograph, the X-ray beam is passed through an aluminium
filter to remove low energy X-ray photons before reaching the patient.
(a)
Suggest why it is necessary to remove these low-energy X-rays.
........................................................................................................................
........................................................................................................................
[1]
(b)
The average linear attenuation coefficient for X-rays that penetrate the aluminium
is 250 m–1. The intensity of an X-ray beam after travelling through 2.5 cm of
aluminium is 347 W m–2.
Show that the intensity incident on the aluminium is about 2 × 105 W m–2.
[3]
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173
(c)
The X-ray beam at the filter has a circular cross-section of diameter 0.20 cm.
Calculate the power of the X-ray beam emerging from the aluminium filter.
Assume that the beam penetrates the aluminium filter as a parallel beam.
power = ............................ W
[2]
(d)
The total power of X-rays generated by an X-ray tube is 18W.
The efficiency of conversion of kinetic energy of the electrons into X-ray photon
energy is 0.15%.
(i)
Calculate the power of the electron beam.
power = ..................... W
[2]
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174
(ii)
Calculate the velocity of the electrons if the rate of arrival of electrons is
7.5 × 1017 s–1. Relativistic effects may be ignored.
velocity = ..................... m s–1
[2]
(iii)
Calculate the p.d. across the X-ray tube required to give the electrons the
velocity calculated in (ii).
p.d.= ........................ V
[3]
[Total 13 marks]
128. The ratio of reflected intensity to incident intensity for ultrasound reflected at a
boundary is related to the acoustic impedance Z1 of the medium on one side of the
boundary and the acoustic impedance Z2 of the medium on the other side of the
boundary by the following equation.
reflected intensity (Z 2  Z1 ) 2

incident intensity (Z 2  Z1 ) 2
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175
(a)
State the two factors that determine the value of the acoustic impedance.
........................................................................................................................
........................................................................................................................
[2]
(b)
An ultrasound investigation was used to identify a small volume of substance in a
patient. It is suspected that this substance is either blood or muscle.
During the ultrasound investigation, an ultrasound pulse of frequency
3.5 × 106 Hz passed through soft tissue and then into the small volume of
unidentified substance. A pulse of ultrasound reflected from the front surface of
the volume was detected 26.5 μs later. The ratio of the reflected intensity to
incident intensity for the ultrasound pulse reflected at this boundary was found to
be 4.42 × 10–4. The table below shows data for the acoustic impedances of
various materials found in a human body.
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medium
acoustic impedance Z /kg m–2 s–1
air
4.29 × 102
blood
1.59 × 106
water
1.50 × 106
brain tissue
1.58 × 106
soft tissue
1.63 × 106
bone
7.78 × 106
muscle
1.70 × 106
176
(i)
Use appropriate data from the table to identify the unknown medium. You
must show your reasoning.
medium = ............................
[4]
(ii)
Calculate the depth at which the ultrasound pulse was reflected if the speed
of ultrasound in soft tissue is 1.54 km s–1.
depth = ...................... cm
[2]
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177
(iii)
Calculate the wavelength of the ultrasound in the soft tissue.
wavelength = ............................... m
[2]
[Total 10 marks]
129. A transformer is assumed to be 100% efficient in its operation. The primary coil is
connected to a 230 V a.c. source. The secondary coil is connected to a 50 Ω resistor.
The potential difference across the resistor is 12 V a.c.
Calculate
(i)
the current through the 50 Ω resistor
current = ................... A
[2]
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178
(ii)
the current in the primary circuit.
current = ................... A
[2]
[Total 4 marks]
130. (a)
(i)
State what is meant by nuclear binding energy.
...............................................................................................................
...............................................................................................................
...............................................................................................................
[1]
(ii)
The diagram below shows the binding energy per nucleon for five nuclides,
plotted against nucleon number.
10.0
56
26 Fe
9.0
95
Y
39
binding energy per
nucleon / MeV
135
I
53
8.0
235
U
92
12
6C
7.0
6.0
0
50
100
150
200
250
nucleon number
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179
56
26 Fe
has the highest binding energy per nucleon. 126 C and 235
92 U have
less binding energy per nucleon.
Explain how these values relate to the possibility of fission or fusion of the
12
235
nuclides 56
26 Fe , 6 C and
92 U .
...............................................................................................................
...............................................................................................................
...............................................................................................................
...............................................................................................................
...............................................................................................................
...............................................................................................................
...............................................................................................................
...............................................................................................................
...............................................................................................................
...............................................................................................................
...............................................................................................................
[4]
(b)
(i)
A 235
92 U nucleus inside a nuclear reactor can absorb a thermal neutron.
State what is meant by a thermal neutron.
...............................................................................................................
...............................................................................................................
...............................................................................................................
[1]
(ii)
Write a nuclear equation for this reaction.
[1]
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180
(iii)
The resulting nucleus undergoes fission. Iodine-135 ( 135
53 I ) and yttrium-95
( 95
39 Y ) are produced.
Write a nuclear equation for this reaction.
[1]
(iv)
Use data from the diagram above to deduce how much energy in MeV is
released when one nucleus of 235
92 U undergoes these reactions.
energy = ................................................... MeV
[4]
[Total 12 marks]
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181
131. In the JET fusion experiment, a plasma consisting of a mixture of deuterium ( 21H ) and
tritium ( 31 H ) is confined within a magnetic field of high flux density.
The plasma is heated using two methods.
method 1
A very large current is passed through the plasma.
Fig. 1 shows the variation with time of this current.
The average electromotive force driving this current is 1.2 V.
4
current /
106 A
3
2
1
0
0
5
10
15
20
25
30
time / s
Fig. 1
method 2
Wilson's School
Fast-moving deuterium atoms are injected into the plasma. The nuclei of
the injected deuterium atoms collide with nuclei in the plasma and so
transfer energy to it.
182
When the plasma temperature is high enough, deuterium and tritium nuclei fuse,
producing a helium nucleus and a neutron. This reaction may be represented as
follows.
2
1H

3
1H

4
2 He

1
0n
+
energy
The energy released is shared between the helium nucleus and the neutron, which
move off in opposite directions.
4
2 He
1
0n
Fig. 2
(a)
For method 1, calculate the total energy input provided by the current source.
energy = ....................................... J
[4]
(b)
Explain why in method 2 a beam of neutral deuterium atoms is injected, rather
than a beam of deuterium nuclei.
........................................................................................................................
........................................................................................................................
........................................................................................................................
........................................................................................................................
........................................................................................................................
[2]
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183
(c)
Show that the helium nucleus gains 20% of the total energy released in the
fusion reaction, and the neutron gains 80% of the energy released.
You may assume that the initial momentum of the helium-neutron system is zero.
[4]
[Total 10 marks]
132. This question is about the properties of baryons.
Choose two examples of baryons
For each example discuss
•
their composition
•
their stability.
(Allow one lined page).
[Total 6 marks]
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184
133. This question is about the properties of leptons.
Choose two examples of leptons
For each example discuss
•
their composition
•
the forces which affect them
•
where they may be found.
(Allow one lined lage).
[Total 6 marks]
134. A radioactive material is known to contain a mixture of two nuclides X and Y of different
half-lives. Readings of activity, taken as the material decays, are given in the table,
together with the activity of nuclide X over the first 12 hours.
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time / hour
activity of
material / Bq
activity of
nuclide X /Bq
activity of
nuclide Y /Bq
0
4600
4200
400
6
3713
3334
12
3002
2646
18
2436
24
1984
30
1619
36
1333
1323
296
185
(a)
State the meaning of the terms
(i)
radioactive
...............................................................................................................
...............................................................................................................
[1]
(ii)
nuclide
...............................................................................................................
...............................................................................................................
[1]
(iii)
half-life.
...............................................................................................................
...............................................................................................................
[1]
(b)
(i)
The half-life of nuclide X is 18 hours. Complete the activity of nuclide X
column.
[3]
(ii)
Using your answer to (i) complete the activity of nuclide Y column.
[2]
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186
(c)
Calculate, or use a graph to determine, the half-life of nuclide Y.
0
20
40
60
80
time/hour
half-life of Y = ......................... hours
[3]
(d)
Indicate briefly how it would be possible experimentally to obtain the initial
activity (4200 Bq in this case) of nuclide X by itself.
........................................................................................................................
........................................................................................................................
........................................................................................................................
[2]
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187
(e)
Explain why it is not possible to give a half-life for a mixture of two nuclides.
........................................................................................................................
........................................................................................................................
........................................................................................................................
........................................................................................................................
........................................................................................................................
........................................................................................................................
........................................................................................................................
[3]
[Total 16 marks]
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