Edexcel A-Level Physics: Nuclear and Particle Physics

The graph of binding energy per nucleon against nucleon number is one of the most important in nuclear physics. It rises steeply from the lightest nuclei, reaches a broad maximum of about 8.8 MeV per nucleon near iron-56, and then falls slowly for the heaviest nuclei.

Explain, with reference to the shape of this curve, why energy is released both when two light nuclei undergo fusion and when a heavy nucleus undergoes fission. In your answer you should make clear what binding energy per nucleon represents, and why both processes can be described as moving towards the iron-56 peak.

(6 marks)

One reaction proposed for a fusion power station is the fusion of a deuterium nucleus ($^{2}_{1}\text{H}$12​H) with a tritium nucleus ($^{3}_{1}\text{H}$13​H) to form a helium-4 nucleus and a neutron:

$^{2}_{1}\text{H} + {}^{3}_{1}\text{H} \rightarrow {}^{4}_{2}\text{He} + {}^{1}_{0}\text{n}$12​H+13​H→24​He+01​n

Use the nuclear masses below. Take $1\ \text{u} = 931.5\ \text{MeV}/c^2$1 u=931.5 MeV/c2 and $1\ \text{MeV} = 1.60 \times 10^{-13}\ \text{J}$1 MeV=1.60×10−13 J.

Particle	Mass / u
proton, $^{1}_{1}\text{p}$11​p	1.00728
neutron, $^{1}_{0}\text{n}$01​n	1.00867
deuterium nucleus, $^{2}_{1}\text{H}$12​H	2.01355
tritium nucleus, $^{3}_{1}\text{H}$13​H	3.01550
helium-4 nucleus, $^{4}_{2}\text{He}$24​He	4.00151

(a) Calculate the mass defect of the helium-4 nucleus, and hence its binding energy per nucleon in MeV. (3 marks)

(b) Calculate the energy released, in MeV, in the deuterium-tritium fusion reaction above. (2 marks)

(c) Express the energy released in part (b) in joules. (1 mark)

A student measures the count rate from a freshly prepared radioactive source using a detector. The background count rate has already been subtracted, so the values below are the corrected count rate due to the source alone:

Time / min	0	10	20	30	40
Corrected count rate / s⁻¹	640	451	322	226	159

(a) Use the data to determine the half-life of the source, explaining how you obtained it. (2 marks)

(b) Hence calculate the decay constant $\lambda$λ of the source, in $\text{s}^{-1}$s−1. (2 marks)

(c) Predict the corrected count rate you would expect at a time of 70 min. (1 mark)

Conservation laws determine which nuclear and particle processes are allowed and fix the identity of any unknown product.

(a) Radium-226 ($^{226}_{88}\text{Ra}$88226​Ra) decays by alpha emission. Write the balanced nuclear equation, identifying the proton number and nucleon number of the daughter nuclide. (2 marks)

(b) Carbon-14 ($^{14}_{6}\text{C}$614​C) decays by beta-minus emission. Write the balanced nuclear equation, including the antineutrino. (1 mark)

(c) In a high-energy collision, two protons interact to produce a proton, a neutron and a single unknown particle $X$X: $\text{p} + \text{p} \rightarrow \text{p} + \text{n} + X$p+p→p+n+X By applying the conservation of charge and of baryon number, deduce the charge and baryon number of $X$X, and hence state what kind of particle $X$X is. (2 marks)

A freshly prepared sample of the medical tracer technetium-99m contains $5.0 \times 10^{16}$5.0×1016 undecayed nuclei. Technetium-99m has a half-life of 6.0 hours.

(a) Calculate the decay constant $\lambda$λ of technetium-99m, in $\text{s}^{-1}$s−1, and hence the initial activity of the sample, in Bq. (3 marks)

(b) Calculate the activity of the sample 18 hours after it was prepared. (1 mark)

This question is about the language of nuclear and particle physics.

(a) Define the half-life of a radioactive isotope. (1 mark)

(b) State the quark composition of a proton and of a neutron. (2 marks)