Paper 4 Nuclear Physics Answers

Q1 Half-life from Counting Data

1. Corrected rates: $641$, $450$, $322$, $224$, $161$, $112\mathrm{counts}\mathrm{mi}{\mathrm{n}}^{-1}$. One mark for correct subtraction and one for all values. [2]
2. Axes correctly oriented and labelled [1]; sensible scales [1]; six points accurately plotted [2]; smooth best-fit decay curve [1].

3. The time for the corrected rate to fall from approximately $640$ to $320\mathrm{counts}\mathrm{mi}{\mathrm{n}}^{-1}$ is about $8.0\min$. A second pair of values may be used; accept graph-consistent values. [2]
4. $\lambda =\ln 2/T_{1/2}=0.693/(8.0\times 60)=1.44\times 10^{-3}{\mathrm{s}}^{-1}$. Accept follow-through from part 3. [2]
5. Radioactive counting has an absolute statistical uncertainty of order $\sqrt{N}$ [1], so the fractional uncertainty $\sqrt{N}/N=1/\sqrt{N}$ increases as the number of source counts decreases [1]. Background subtraction further matters more when the source rate is small.
6. Count for a longer interval at each time, or repeat readings and combine/average counts under unchanged conditions. [1]

Q2 Nuclear Equation Checks

1. Conservation of nucleon number and conservation of proton/charge number. [2]
2. Nuclear charge number counts protons in nuclei and emitted nuclear particles; chemical charge concerns electron gain/loss around atoms/ions. [2]
3. Random decay/counting fluctuations. [1]