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AL-LQ-Modern phy / p.1
1.
(88-IIB-12)
Figure (a)
Figure (b)
A student performs an experiment with an ionisation chamber, using the arrangement shown in
Figure (a). The current flowing through the chamber is found by measuring the p.d. across the 10 
9
resistance using a voltmeter with an internal resistance of the order of 10  .
14
(a)
After introducing an Americium-241 radioactive source (which emits alpha-particles) into the chamber,
the student gradually increases the p.d. between the source and the chamber wall. A plot of the
voltmeter readings against the E.H.T. supply voltages is shown in Figure (b). It is found that the
voltmeter reading increases as the E.H.T. voltage is increased, but remains at 6 V when the E.H.T.
voltage reaches 800 V.
(i)
Why is the ionisation current not increased further by increasing the applied anode voltage?
(2 marks)
(ii)
At what anode voltage should the ionisation chamber be normally operated? Explain briefly.
(2 marks)
(b)
(i)
Assuming the charge on a single ion to be the same as that on an electron, calculate the
number of ion-pairs detected per second. (Charge of an electron = 1.6  10
(ii)
The activity of the Americium source used in the experiment is
19
C)
(2 marks)
5
2 10 Bq (1 Bq = 1
disintegration per second). Find the number of ion-pairs produced per alpha particle. You may
assume that for each disintegration of an Americium nuclide, an alpha particle is produced.
(1 mark)
(iii) Estimate the energy of the emitted alpha particles. You may assume that, on average, an alpha
particle loses 30 eV of its energy for each ion-pair produced.
(c)
(i)
(1 mark)
The student said, ‘one major source of error in this experiment to determine the alpha
particle energy (as in (b) above) is that the energy imparted to the emitted alpha particles by the
potential field set up inside the chamber has not been considered.’ Is he correct? Explain briefly.
(1 mark)
(d)
(ii)
Mention ONE other source of error besides the one given above.
(i)
If the volume of the chamber is significantly reduced, would the saturated current be
increased or decreases? Explain briefly.
(ii)
(1 mark)
(2 marks)
Another student wants to use the same set-up to measure the energy of gamma-ray photons
emitted by a cobalt-60 radioactive source. Do you think that he can get a reliable result?
Explain your answer.
(2 marks)
AL-LQ-Modern phy / p.2
2.
(89-IIB-12)
In a mass spectrometer, positive ions are produced in a chamber D and then accelerated through a potential
difference V. Some of these ions pass through a small hole X into a uniform magnetic field B, traverse a
circular path of radius r and then pass through another hole Y into a detector.
(a)
Describe a method by which positive ions may be produced in the chamber D.
(b)
Show that the charge to mass ratio of an ion passing through the hole Y into the detector is proportional
to the accelerating potential V.
(c)
(2 marks)
(3 marks)
When potassium ions are examined by this mass spectrometer, the detector registers a peak current
when the accelerating p.d. is 613 V with another much smaller peak at 583 V. A student comments that
this is due to the presence of isotopes. Explain why the above phenomenon may be explained by the
presence of isotopes.
(d)
(2 marks)
If the relative atomic mass of potassium is 39.1, estimate
(i)
the relative atomic masses of these two isotopes.
(2 marks)
(ii)
their relative proportion.
(2 marks)
AL-LQ-Modern phy / p.3
3.
(90-IIB-12)
The figure shows the variation of the average binding energy per nucleon with nucleon number.
(a)
Explain why the nuclear binding energy is negative.
(b)
Consider the following 2 nuclear reactions :
(2 marks)
90
1
U  01n144
56 Ba  36 Kr  2 0 n
Fission reaction
235
92
Fusion reaction
2
1
H  12H  23He  01n
(i)
Explain, with reference to the figure why these two reactions are possible.
(ii)
Which reaction process is currently being used in power generating stations and why is the other,
at present, not practical?
(2 marks)
(3 marks)
In answering the following questions, you should refer to the fission reaction described in (b) above.
(c)
What is the significance of the two neutrons produced in the fission reaction?
(2 marks)
(d)
Make a rough estimate of the energy (in MeV) released in the fission of a uranium-235 nucleus.
(2 marks)
(Binding energy of
(e)
235
92
U = -7.50 MeV/nucleon
Binding energy of
144
56
Binding energy of
90
36
Ba = -8.30 MeV/nucleon
Kr = -8.65 MeV/nucleon)
Mention TWO differences between the fission of a nucleus and the spontaneous decay of a radioactive
nuclide.
(3 marks)
AL-LQ-Modern phy / p.4
4.
(91-IIB-11)
(Given :
Planck constant h  6.63  10
34
charge of electron e  1.60  10
Js
19
C
1
speed of light in vacuum c  3.00  10 ms )
8
Figure (a)
Figure (b)
Figure (a) shows the schematic diagram of the apparatus used by Franck and Hertz. The electrons emitted at
the cathode C are accelerated to the grid G by a potential difference of
V1 . The electrons A has a voltage V2
of 1 V negative with respect to the grid G. Inside the glass tube there is mercury vapour at a pressure of about
100Nm-2. A graph of anode current
(a)
I a against V1 is shown in Figure (b).
Account for the shape of the graph when
(i)
less than P,
(ii)
between P and Q,
V1 is
(iii) between Q and R.
(5 marks)
(b)
From the graph in Figure (b), estimate the lowest excitation energy for mercury.
(1 mark)
(c)
What is the wavelength of the radiation emitted by the mercury atoms as they return to their ground
state? Could such a radiation be detected? Explain your reasoning.
(d)
Energy in eV
(4 marks)
0.0
-1.6
-3.7
Diagram NOT to scale
-5.5
-10.4
(i)
The energy level diagram shows that mercury has another excitation potential at 6.7 V. Why is this
not shown by the graph in Figure (b)?
(ii)
Ground state
(2 marks)
What would you expect to happen to a photon of energy 9 eV when it collides with a mercury
atom? Explain your answer briefly.
(2 marks)
AL-LQ-Modern phy / p.5
5.
(91-IIB-12)
4
A tiny charged oil drop falls at a terminal speed of 1.50  10 ms
1
in air between two horizontal and
parallel plates placed 2.00 cm apart.
(a)
Given that the density of oil is
900 kgm3 , the viscosity of air is 1.81105 N s m2 and g is
9.80 ms 2 , calculate the radius of the oil drop.
(b)
The oil drop can be held stationary when a p.d. of 2.50 kV is applied between the plates. Find the
magnitude of the charge on the oil drop.
(c)
(2 marks)
(4 marks)
After the space between the plates has been irradiated by X-rays, the charge on the oil drop is increased.
With the p.d. across the plates unchanged, the oil drop moves up with a terminal velocity of
1.02  10 4 ms 1
(i)
Explain briefly how the X-rays can alter the charge on the oil drop.
(ii)
Calculate the magnitude of the charge on the oil drop after it has been irradiated by the
X-rays.
(d)
(4 marks)
The experiment is repeated twice and the charges on the oil drops are found to be 6.41 10
9.59  10
19
(2 marks)
19
C and
C respectively. Use this data and the results obtained in parts (b) and (c) to deduce a
probable value of the charge of the electron. Explain your reasoning.
(1 mark)
AL-LQ-Modern phy / p.6
6.
(92-IIB-12)
(a)
In an experiment with an illuminated photocell using caesium as the cathode, a small current is
detected by the microammeter even when the anode is made slightly negative with respect to the
cathode, using the above circuit. Briefly account for this.
(b)
(2 marks)
The current falls to zero only when the reverse p.d. across the tube reaches a value
Vs , which varies
with the frequency f of the radiation used to illuminate the cathode. The figure shows the
relationship between
(i)
Vs and f .
What is the relationship between
Vs and f as predicted by Einstein’s photoelectric theory?
(2 marks)
(ii)
What is the value of the threshold frequency for caesium?
(iii) If the electronic charge is 1.6  10
19
C , estimate a value for the Planck constant.
(iv) Calculate the work function for caesium in electron-volts.
(v)
(1 mark)
Sketch on the above figure the corresponding variation between
whose cathode has a larger work function than caesium.
(2 marks)
(3 marks)
Vs and f for a photocell
(2 marks)
AL-LQ-Modern phy / p.7
7.
(93-IIB-12)
(a)
The figure shows the decay series for
(i)
235
92
U.
Name the particles emitted when Uranium (U) decays to Thorium (Th) and Thorium (Th) decays
to Protactinium (Pa).
U
Th
(ii)
(1 mark)
 Th : ________________________
 Pa : ________________________
Given that the half-life of
U is 7.1108 years, what will be the percentage of
235
92
10 8 years?
235
92
U left after
(3 marks)
(b) The following equation represents a possible nuclear reaction in a fission reactor :
235
92
U+
Given : the mass of one nuclide of
1
0
n  3691 Kr +
235
92
= 235.0439 u,
n
= 1.0087 u,
Kr
= 90.9234 u,
142
56
unified atomic mass unit
(i)
(c)
Ba
= 141.9164 u,
1u
=
1.66 10 27 kg .
According to the above equation, what is the mass defect between the reactants and products
when one
(ii)
Ba + 301 n
U
1
0
91
36
142
56
If
235
92
U nucleus undergoes fission?
4.00 10 5 kg of
(2 marks)
235
92
U splits per second, calculate the rate of energy production. (3 marks)
Explain how energy can be extracted from the core of a fission reactor for producing electricity.
(3 marks)
AL-LQ-Modern phy / p.8
8.
(94-I-5)
The figure shows the essential structure of an X-ray tube. The electrons emitted from the filament are
accelerated by a high voltage V. X-rays are produced when the target in the anode is bombarded by the fast
electrons. The spectrum of the X-rays emitted is shown below.
Given : Planck constant = 6.6  10
34
Electronic charge = 1.6  10
Velocity of light = 3  10 ms
8
(a)
Js
19
C
1
(i)
Find the maximum energy of the X-ray photons emitted.
(2 marks)
(ii)
Calculate the accelerating voltage V.
(1 mark)
(iii) On the above figure, sketch a graph to show how the intensity of the X-rays emitted varies with
wavelength if the current in the filament is reduced.
(b)
Assuming the efficiency of the X-ray tube is 0.5%, calculate the number of electrons bombarding the
target per second if heat is generated in the target at a rate of 600 W.
(c)
(2 marks)
(2 marks)
Compare the production mechanism of X-rays in the continuous spectrum and the line spectrum.
(4 marks)
(d)
Explain why some early television sets emitted X-rays. Suggest a method to reduce this hazard.
(2 marks)
AL-LQ-Modern phy / p.9
9.
(95-I-10)
A geologist wants to find the age of a sample of rock containing
40
K which decays to give the stable isotope
40
Ar . The activity of the sample is found to be 1.6 Bq while the original activity of a similar rock having the
40
same mass is 4.8 Bq. The half-life of
K is 1.3  10 9 years.
(a) (i) Find the decay constant of
40
K.
(ii) Give the physical meaning of the decay constant of a radioactive isotope.
(2 marks)
(b) Find the age of the rock sample.
(2 marks)
(c) Give two factors that determine the activity of a radioactive source.
(2 marks)
K to 40 Ar is spontaneous. How is the magnitude of the binding energy of 40 K
40
compared to that of
(2 marks)
Ar ?
(d) The decay of
40
(e) Mention a difficulty involved in measuring such a small decay rate of 1.6 Bq.
(1 mark)
AL-LQ-Modern phy / p.10
10. (96-I-9)
In a photoelectric experiment, a thin metal plate of dimension
8.0 10  8.0 10 m
3
3
2
is illuminated
with a parallel beam of ultraviolet light of wavelength 230 nm. The work function of the metal is 2.21 eV.
Given : Planck constant = 6.63  10
34
Js
Charge of an electron = 1.60  10
19
C
(a)
What is meant by the work function of a metal?
(b)
Explain why photoelectrons are emitted with different speeds though the energy of each incident
(c)
(d)
(1 mark)
photon is fixed.
(1 mark)
(i)
Calculate the maximum kinetic energy of the photoelectrons emitted.
(2 marks)
(ii)
Find the stopping potential.
(1 mark)
The intensity of the ultraviolet light used is 3 Wm
2
and it falls normally on one side of the metal plate.
Find, in the absence of the stopping potential, the number of photoelectrons emitted per second.
Assume that every incident photon can successfully release a photoelectron.
(e)
(3 marks)
State the change in (i) the stopping potential and (ii) the number of photoelectrons emitted per second, if
another source of ultraviolet light with the same intensity, but having a shorter wavelength, is used.
Explain briefly.
(4 marks)
AL-LQ-Modern phy / p.11
11.
(96-I-10)
A thyratron tube filled with xenon gas at low pressure is used for measuring the excitation potential of xenon.
The figure below shows the circuit used.
In the experiment, electrons emitted from the hot cathode, C, are accelerated by the variable potential
difference between cathode C and the perforated grid, G. Collisions occur between the electrons and the
xenon atoms. The potential of anode A is made slightly negative with respect to grid G by using a cell E.
Electrons with enough energy to reach A constitute a current, which is detected by the light beam
galvanometer. The voltage of the d.c. supply is varied and a graph of the galvanometer reading, I, plotted
against the voltmeter reading, V, is shown below :
(a)
Explain why a heater is required to heat up cathode C.
(2 marks)
(b)
(i)
State the condition for a collision between an electron and a xenon atom to be inelastic. (1 mark)
(ii)
Deduce from the above figure the first excitation potential of xenon.
(1 mark)
(c)
Explain why the potential of anode A is made slightly negative with respect to grid G.
(2 marks)
(d)
Describe the energy change of an electron when, after emitting from the hot cathode C, it accelerates
towards the grid G and undergoes an inelastic collision with a xenon atom, and finally reaches anode A.
(3 marks)
AL-LQ-Modern phy / p.12
12. (97-I-8)
The figure shows a device for accelerating protons to a high speed in a vacuum. It consists of two semicircular
chambers within which a uniform magnetic field, B, is present (not shown in the diagram). A potential
difference, V, is set up across the narrow gap between the chambers such that its polarities reverse every time
the proton goes from one chamber to the other.
When a proton of negligible speed is injected into the centre of the device, it is accelerated by the potential
different towards one chamber and describes a semi-circle inside that chamber due to the magnetic field
present. The proton is then accelerated across the gap through a potential difference of V and describes
another semi-circle of greater radius in the other chamber since its speed has increased. This process is
repeated and the path of proton is shown in the above figure.
(a)
(i)
Indicate in the above figure the direction of the magnetic field in the chambers.
(1 mark)
(ii)
For a proton of mass m and charge q moving with speed v in a circle of radius r in one of the
chambers, express v in terms of r. Explain why the proton does not gain kinetic energy in the
chambers.
(3 marks)
(iii) Show that the time spent by the proton in describing any semi-circle is independent of v and r.
(2 marks)
(b)
It is known that the strength of the magnetic field, B, is 1.5 T and the alternating potential difference, V,
is 10 kV.
(Given : electronic charge = 1.6 x10
19
C ; mass of a proton = 1.66 x10 27 kg)
(i)
Find the gain in kinetic energy, in eV, of the proton in each complete revolution.
(1 mark)
(ii)
Calculate the time taken for a proton to gain a kinetic energy of 1 MeV.
(3 marks)
AL-LQ-Modern phy / p.13
13. (97-I-10)
In an experiment to investigate the absorption of

and
 rays by materials, a source emitting  and 
rays is placed at a distance of about 5 cm from a G-M tube as shown below.
The count rates, N, are measured for different thicknesses, d, of absorber plates. The results are shown in the
figure below, with curve A corresponding to the measurements using aluminium absorber plates while curve
B corresponds to those using lead absorber plates.
(a)
(i)
Curve A shows a considerable decrease in count rates up to a thickness of 7 mm; a further
increase in d only results in a slight decrease in count rates. Explain why this is so.
(ii)
(2 marks)
From the above graphs, estimate the minimum thickness of lead needed to absorb most of the

rays. (1 mark)
(iii) The source also emits
 - particles. Explain why their effects can be neglected in this experiment.
(1 mark)
(b)
The count rates, N ' , corrected for background, corresponding to different thicknesses, d, of lead
absorber plates are tabulated as follows :
d / mm
N ' / s-1
ln N '
1
28.0
2
24.8
3
22.0
4
20.0
5
18.2
6
16.8
7
15.7
(i)
What is meant by the count rates being ‘corrected for background’?
(ii)
Complete the table and plot a graph of ln N ' against d.
(iii) Write down a relation between N ' and d. (2 marks)
(4 marks)
(1 mark)
AL-LQ-Modern phy / p.14
14. (98-I-5)
A reaction which takes place in the core of a nuclear reactor is described by the following equation:
235
92
U +
1
0
Mass of one nuclide of
235
92
Mass of one nuclide of
142
56
Mass of one nuclide of
91
36
n 
142
56
(ii)
Kr + 3 01 n + 174.4MeV
Ba = 141.9164 u
Kr = 90.9234 u
(electronic charge = 1.6 x10
(i)
91
36
U = 235.0439 u
1 u (atomic mass unit) = 1.660 x10
(a)
Ba +
19
27
kg, which corresponds to 934 MeV
C)
Calculate the mass, in atomic mass unit, of a neutron.
The fuel rods in the reactor contain 1.0 x10 kg of U-235 isotope. Calculate the total energy
released from the complete fission of all the U-235 nuclei in the fuel rods.
(iii)
(3 marks)
4
(3 marks)
If the mean power output of the reactor is 500 MW and the efficiency of conversion of nuclear
energy to electrical energy is 40%, estimate the time for which the fuel rods can be used.
(2 marks)
(iv) Explain why the fuel rods are usually replaced well before the time estimated in (a) (iii) has
elapsed.
(b)
In an emergency, explain how the reactor can be shut down immediately.
(2 marks)
(2 marks)
AL-LQ-Modern phy / p.15
15.
(99-I-5)
People are often killed in a fire as a result of suffocation. To minimize the loss of lives, smoke detectors can be
installed in buildings and a loud sound and a flashing light are triggered when smoke is detected. The figure
shows a common ionization smoke detector which has a small radioactive source inside. During normal
operation, the radioactive source keeps emitting ionizing particles and a certain ionization current is
maintained inside the chamber of the detector.
(a)
The manufacturer claims that the radioactive source in the smoke detector presents no hazard to health
in normal use. Comment on this claim and briefly explain which type of radioactive source should be
used in the smoke detector.
(b)
(3 marks)
When the radioactive source in the detector is placed close to a GM-tube, the count rate measured is
2000 s. The average number of ion-pairs produced by each radiation particle is 5  10
carries a charge of 1.6  10
(i)
19
and each ion
C.
Estimate the maximum ionization current in the smoke detector. Why is the ionization current in
the smoke detector significantly less than this maximum value?
(ii)
4
(3 marks)
The smoke detector should be disposed of when its maximum ionization current drops below
5  10 12 A. The manufacturer claims that the life of the detector is 10 years. Estimate the half-life
of the radioactive source used in the detector.
(3 marks)
AL-LQ-Modern phy / p.16
16.
(00-I-5)
Figure (a) shows an ionization chamber that can be used to estimate the activity of a sample of uranium-238. The sample
is placed inside a metal can held at a negative potential. Electrons produced inside the metal can migrate to the sample
while positive ions migrate to the wall of the can. The sample is connected to the ground via a 10 9  resistor. The
potential difference across the 109  resistor is measured by an op-amp circuit.
Figure (a)
(a)
Name the op-amp circuit used in Figure (a).
(1 mark)
(b)
Figure (b) shows the variation of the voltmeter reading with the potential difference across the metal can
and the sample.
Figure (b)
Explain the variation of the voltmeter reading. (3 marks)
(c)
In the sample, uranium-238 decays into thorium-234 by emitting an
 -particle. This nuclear reaction can be
represented as :
238
92
Given :
U
Th  42 He
234
90
Mass of one nuclide of U-238 = 238.0508 u
Mass of one nuclide of Th-234 = 234.0436 u
Mass of one nuclide of He-4 = 4.0026 u
1 u (atomic mass unit) = 1.660  10
27
kg, which corresponds to 934 MeV
(i)
Calculate the energy, in MeV, released in this nuclear reaction.
(2 marks)
(ii)
From the information provided in Figure (b), calculate the number of air particles being ionized per
second inside the metal can. Assume that each ionized air particle carries one electronic charge.
(electronic charge = 1.6  10
(iii)
19
C)
(2 marks)
If the energy required to produce an ion-electron pair is 30 eV, estimate the activity, in disintegrations per
second, of the U-238 sample. State the assumption(s) in your calculation.
(iv)
Is this experimental method suitable for estimating the activity of a sample emitting
TWO reasons to support your answer.
(3 marks)

-particles? Give
(2 marks)
AL-LQ-Modern phy / p.17
17.
(00-I-9)
A diffraction grating is used to study the hydrogen spectrum from a discharge tube. The first-order diffraction angles of
some of the various discrete lines are tabulated below.
First-order diffraction angle
Wavelength  / nm
 /o
23.19
16.96
15.09
14.25
12.64
656.3
486.1
434.0
410.2
364.6
(a)
Plot a suitable graph to find the grating spacing, in lines per mm, of the diffraction grating.
(5 marks)
(b)
(i)
Which line corresponds to blue light?
(1 mark)
(ii)
One of the lines cannot be seen by naked eyes. Name the region in the electromagnetic spectrum to which
this line belongs.
(c)
(1 mark)
What activity within an atom gives rise to these emission lines? What is the physical significance of the spectrum
consisting of discrete lines?
(d)
(2 marks)
In fact, the wavelengths of the emission lines satisfy the formula of the Balmer series:
n2
  (364.6 nm) 2
, where n = 3, 4, 5,…
n 4
(i)
 1 1
  , where v represents the frequencies
2
4
n
Show that the formula can be transformed into hv  K 
of the emission lines, h is the Plank constant and K is a constant.
(ii)
(1 mark)
Find K in units of eV. State the physical significance of the sign and the magnitude of the term
K
n
2
in
the formula of hv.
(Planck constant = 6.626  10
34
Js; electronic charge = 1.6  10
19
C)
(4 marks)
AL-LQ-Modern phy / p.18
18.
(02-IB-7)
In this question you are asked to estimate the lifetime of the sun (i.e. How long can the sun shine?) based on some
theories of physics, standard constants and given information.
(a)
Given: Universal gravitational constant =
6.7  10 11 Nkg 2 m 2
1 year = 3.2  10 s
7
The surface area of a sphere of radius is 4r .
2
(i)
Solar radiation takes about 8 minutes 20 seconds to reach the earth. Estimate the sun-earth separation to 2
significant figures.
(ii)
Calculate the mass of the sun to 1 significant figure.
(iii)
The intensity of the solar radiation when it reaches the earth is 1.35kW per unit area. Estimate the total
power of the solar radiation from the sun. Assume that the sun radiates evenly in all directions.
(b)
The energy released by the sun is the result of thermonuclear fusion in its core, where
protons are fused together into helium nuclei through a complicated process. The overall
reaction can be represented by the following equation
411H 24He  other particles of negligible mass  energy
(i)
Why is the above process of forming helium nuclei from protons very difficult to achieve on earth, but
easily achieved at the sun’s core?
(ii)
Given: mass of proton = 1.00728u
mass of helium nucleus = 4.00150u
1u =
1.66  10 27 kg
Calculate the energy released by the sun for every kilogram of protons fused to form helium
nuclei.
(c) Estimate the lifetime, in years, of the sun assuming that it initially consists mainly of hydrogen and it ‘burns’ at a
constant rate until all its hydrogen is consumed.
AL-LQ-Modern phy / p.19
19.
(03-IIB-8)
(a)
The graph shows the number of ion-pairs produced per mm by a certain type of nuclear radiation versus distance
along its track in air.
(i)
What type of nuclear radiation is represented by the graph? Give one piece of evidence.
(ii)
Use the graph to estimate
(I)
the total number of ion-pairs produced by the radiation.
(II)
the total energy of the radiation in MeV.
(Given: average energy required to produce an ion-pair is 5  10
electronic charge, e  1.6  10
19
(2 marks)
(2 marks)
(3 marks)
18
J
C)
(iii) Explain why there is a peak near the end of the track.
(1 mark)
(b)
X


Y
24 days 72 s
Z
The above series shows the decay of a radioactive isotope X to isotope Y and finally to isotope Z. The half-lives of
X and Y are 24 days and 72 s respectively. The half-life of Z is much longer than 24 days. The disintegration of
both X and Y would each emit a

and a
  radiation. A sample containing 1 mg of pure X only is prepared
initially.
(Given: Avogadro constant = 6.02  10
23
mol -1
Molar mass of X = 234.0 g)
(i)
Find the total number of nuclear radiations that could be emitted from the sample.
(2 marks)
(ii)
Estimate the time required for the activity of the sample to decrease by 10%.
(3 marks)