Download A2 Unit G485: Fields, particles and frontiers of physics

Sample student answers
A2 Unit G485: Fields, particles and frontiers of physics
Module 6: Nuclear physics
Question 1
Total marks: 10
A certain carbon (C) nuclide and a certain oxygen (O) nuclide each decay to form the same nitrogen
(N) nuclide. These two decay reactions are represented by the arrows in the figure.
(a)
Write down the symbols for the nuclei of each of these nuclides.
Marks available: 2
Student answer:
(a)
Examiner comments:
(a) Good, straightforward answer
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(b)
Write down the equations for each of the decay reactions: (i) carbon decay; and (ii) oxygen
decay.
Marks available: 2
Student answer:
(b) (i)
(ii)
Examiner comments:
(b) Always be careful to add the neutrinos or antineutrinos, and if writing an equation with mass
and proton numbers included, always show mass and charge of electron or positron.
(c)
Use your answer to (b) to deduce, in their simplest form, the quark equations which occur
in these decay reactions.
Show all the steps in your deduction. Do not neglect leptons in your equations.
Marks available: 4
Student answer:
(c) (i) Carbon decay is a beta minus decay, where a neutron decays into a proton, an electron
and an antineutrino:
n → p + e− +
In terms of quarks a neutron is udd and a proton is uud.
Therefore carbon decay is:
d → u + e− +
(ii) Oxygen decay:
u → d + e+ +
Examiner comments:
(c) Good answer, but always remember that when the question asks you to deduce the simplest
quark equation, you would lose marks if you only wrote the final equation.
So (ii) should start like this:
Oxygen decay is a positron decay, where a proton decays into a neutron, a positron and a
neutrino:
p → n + e+ +
Therefore:
u → d + e+ +
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(d)
The axes shown here can be used to plot a graph of the variation of nuclear mass with
proton number. The nuclear mass scale does not start from zero.
Mark points on a copy of this graph showing possible positions for the carbon, oxygen
and nitrogen nuclei involved in the above reactions. Label your points C, O and N
respectively.
Explain how you arrived at your answer.
Assume that the mass of the electron is negligible.
Marks available: 2
Student answer:
(d)
When decay occurs, the final rest mass is always less than the original rest mass.
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Module 6: Nuclear physics
Question 2
Total marks: 11
This question is about the formation and decay of plutonium-239,
isotope of plutonium.
, which is a fairly stable
Natural uranium is a mixture of the nuclides
and
. When this natural uranium is exposed to
neutrons, one of the heavier nuclei can absorb a neutron. The resulting nucleus then undergoes
two decay reactions, resulting in the formation of a
nucleus.
(a)
Write nuclear equations to represent these three reactions. The nuclide formed in the
second reaction is an isotope of neptunium (Np).
Marks available: 4
Student answer:
(a) Reaction 1:
Reaction 2:
+
Reaction 3:
+
Examiner comments:
(a) Good, you have again remembered the antineutrino.
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(b)
A physicist prepares a sample of the neptunium isotope, which decays to plutonium-239.
She measures the activity of the sample over a period of 5.0 days. She then plots this graph
of the variation with time of the activity of the sample.
(i)
Find the half-life in seconds of the neptunium isotope.
(ii)
Show that the decay constant of the neptunium isotope is 3.4 × 10−6 s−1.
(iii)
Deduce the number of nuclei of the neptunium isotope that are present after 2.00
days.
Marks available:
(i) 2 (ii) 1 (iii) 3
Student answer:
(b) (i) From the graph, T1/2 = 2.36 days
= 2.36 × 24 × 3600 = 2.04 × 105 s
(ii) λ = ln 2/T1/2 = 0.693/(2.04 × 105) = 3.4 × 10−6 s−1
(iii) A = λN
A = 2.8 × 1012 s−1
Therefore N = 2.8 × 1012/(3.4 × 10−6) = 8.24 × 1017
Examiner comments:
(b) Make sure that in the exam you draw the line on the graph to show how you found the halflife.
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(c)
The physicist then measures the activity of a sample of plutonium-239 over the
same period. Sketch a graph of activity against time (in days) that she might obtain.
Marks available: 1
Student answer:
(c)
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