Download Unit 7 Review

Unit 7 Review
Quiz #2 Solutions
1. A nucleus of the nuclide 19K (potassium-40) decays to a stable
nucleus of the nuclide 18Ar (argon-40).
State the names of the two particles emitted in this decay.
Since we lost a proton in the process, it is a positron emission
b+, it emits a positron (e+) and a neutrino
2. One of the wavelengths in the absorption spectrum of helium
occurs at 588 nm.
Show that the energy of a photon of wavelength 588 nm is
3.38 × 10 –19 J.
E
hc


6.62 10 3 10 

34
588 10 9
1.99 10  25

588 10 9
 3.38 10 19 J
8
3. The nucleus 30
P undergoes radioactive decay to the nucleus
15
The particles emitted in the decay are
A.
a positron and an antineutrino.
B.
an electron and an antineutrino.
C.
a positron and a neutrino.
D.
an electron and a neutrino
30
Si.
14
4. This question is about nuclear reactions.
(a)(i) Distinguish between fission and radioactive decay.
Fission:
nucleus splits;
into two parts of similar mass;
radioactive decay:
nucleus emits;
a particle of small mass and / or a photon;
A nucleus of uranium-235 ( 235
U) may absorb a neutron and
92
then undergo fission to produce nuclei of strontium-90 ( 90
Sr)
38
and xenon-142 ( 14254 Xe ) and some neutrons.
The strontium-90 and the xenon-142 nuclei both undergo
radioactive decay with the emission of β– particles.
(ii) Write down the nuclear equation for this fission reaction.
(iii)
State the effect, if any, on the mass number (nucleon
number) and on the atomic number (proton number) of a
nucleus when the nucleus undergoes β– decay.
Mass number: mass number unchanged
Atomic number: atomic number increases by +1
The uranium-235 nucleus is stationary at the time that the
fission reaction occurs. In this fission reaction, 198 MeV of
energy is released. Of this total energy, 102 MeV and 65 MeV
are the kinetic energies of the strontium-90 and xenon-142
nuclei respectively.
(b)(i) Suggest what has happened to the remaining 31 MeV of
energy.
kinetic energy of neutrons; and energy of gamma ray photons;
5. This question is about the Bohr model of the hydrogen atom.
(a) The diagram below shows the three lowest energy levels of a
hydrogen atom as predicted by the Bohr model.
Energy
n=3
–1.51 eV
n=2
–3.40 eV
n=1
–13.6 eV
State two physical processes by which an electron in the ground
state energy level can move to a higher energy level state.
collisions with (external) particles; heating the gas to a high
temperature; absorption of photons;
(b)
A parallel beam of white light is directed through
monatomic hydrogen gas as shown in the diagram below. The
transmitted light is analyzed.
hc
White light consists of photons
E

that range in wavelength from

6.62 10 34 3 108 
approximately 400 nm for violet

658 10 9
to 700 nm for red light.
1.99 10  25
Determine that the energy of photons 
658 10 9
of light of wavelength 658 nm is
 3.02 10 19 J
about 1.89 eV.
19

white light
beam
hydrogen
gas
transmitted light
beam
3.02 10 J
 1.89eV
19
1.6 10 J / eV
7. This question is about radioactive decay.
A nucleus of the isotope xenon, Xe-131, is produced when a
nucleus of the radioactive isotope iodine I-13 decays.
(a)
Explain the term isotopes.
the nuclei of different isotopes of an element have the same
number of protons; but different numbers of neutrons;
(b)
Fill in the boxes below in order to complete the nuclear
reaction equation for this decay.

53
The activity A of a freshly prepared sample of the iodine isotope
is 6.4 × 105 Bq and its half-life is 8.0 days.
8. This question is about radioactive decay and the age of rocks.
A nucleus of the radioactive isotope potassium-40 decays into a
stable nucleus of argon-40.
(a)
Complete the equation below for the decay of a
potassium-40 nucleus.
A certain sample of rocks contains 1.2 × 10–6 g of potassium-40
and 7.0 × 10–6 g of trapped argon-40 gas.
(b)
Assuming that all the argon originated from the decay of
potassium-40 and that none has escaped from the rocks,
calculate what mass of potassium was present when the rocks
were first formed.
6
6
6
1.2 10  7 10  8.2 10 g
The half-life of potassium-40 is 1.3 × 109 years.
(c)
Determine
(i) the decay constant of potassium-40;
ii)
the age of the rocks.
6. Which of the following graphs best shows how photon energy
E varies with the wavelength λ of the light?
A.
0
C.
B.
E
0
0
D.
E
0
E
E
0
0
E
E
0
hc
0

1.99 10  25 Jm

9. Nuclear binding energy and nuclear decay
(a)
State what is meant by a nucleon.
(a nucleon is either) a proton or a neutron
(b)
Define what is meant by the binding energy of a nucleus.
energy released when a nucleus is formed from its
constituent nucleons / (minimum) energy needed to
break a nucleus up into its
constituent nucleons
Use the graph to explain why energy can be released in both the
fission and the fusion processes
energy release being possible as products have higher (average)
binding energy per nucleon;
A sample of carbon-11 has an initial mass of 4.0 x 10–15 kg.
Carbon-11 has a half-life of approximately 20 minutes. Calculate
the mass of carbon-11 remaining after one hour has elapsed.
realization that time elapsed is 3 half-lives; so one eighth
remains 5 x 10-16 kg;
1hr.  3  20 min .
3
1 1
  
2 8
1
 4.0 10 15  5 10 16
8


(e)
Uranium-238, undergoes a-decay to form an isotope of
thorium. Write down the nuclear equation for this decay.
10. When the isotope aluminium-27 is bombarded with alpha
particles, the following nuclear reaction can take place
Which one of the following correctly gives the atomic (proton)
number and mass (nucleon) number of the nucleus X?
11. The initial activity of a sample of a radioactive isotope of
half-life 10 hours is A. What is the age of the sample when its
activity is 32A ?
x
A.
30 hours
1  1 
   
 2   32 
B.
40 hours
 1 
C.
50 hours
log 
 32   5
x
D.
320 hours
1
log 
2
5 10  50hrs
12. The binding energy per nucleon of the nucleus is 73 Li
approximately 5 MeV. The total energy required to completely
separate the nucleons of this nucleus is approximately
A.
15 MeV.
B.
20 MeV.
C.
35 MeV.
7 nucleons
7 x 5 = 35 MeV
D.
50 MeV.
This question is about nuclear binding energy.
The table below gives the mass defect per nucleon of deuterium 21 H 
and helium-4 42 He.
Explain the term mass defect
the difference in mass between mass of nucleus;
and mass of (totally) separate nucleons;
Calculate the energy, in joule, that is released when two
deuterium nuclei fuse to form a helium-4 nucleus.
mass of helium-4 = 4 x 0.00760 = 0.0304 u
and mass of two deuteriums = 4 x 0.00120 = 0.0048u;
mass defect = 0.0256u;
energy = 0.0256 x 1.66 x 10-27 x (3 x 108)2; = 3.8 x 10-12 J;