Physics 9702 · AS & A Level · Radioactive decay

Radioactive decay — practice question

A sample containing a radioactive isotope has $N$ nuclei of the isotope at time $T$. By time $(T + \Delta T)$, it contains $(N - \Delta N)$ nuclei of the isotope. The interval $\Delta T$ is short.
(a(i))[1]

Using the symbols $N$, $\Delta N$, $T$ and $\Delta T$, write an expression for the sample’s average activity over the interval $\Delta T$.

(a(ii))[1]

Using the symbols $N$, $\Delta N$, $T$ and $\Delta T$, write an expression for the probability that a nucleus decays in the time $\Delta T$.

(a(iii))[1]

Using the symbols $N$, $\Delta N$, $T$ and $\Delta T$, write an expression for the decay constant $\lambda$ of the isotope.

(b(i))[1]

The isotope polonium-208 ($^{208}_{84}\text{Po}$) is radioactive and decays to produce lead-204 ($^{204}_{82}\text{Pb}$). The nuclear equation for this process is $^{208}_{84}\text{Po} \rightarrow ^{204}_{82}\text{Pb} + ^{4}_{2}\text{He}$. Determine, for the decay of one nucleus of polonium-208: 1. the change, in $\text{u}$, of the mass.

(b(i)2)[3]

Determine, for the decay of one nucleus of polonium-208: 2. the total energy, in $\text{pJ}$, released.

(b(ii))[2]

The polonium-208 nucleus starts off at rest. The initial kinetic energy of the $^{4}_{2}\text{He}$ nucleus (α-particle) is measured to be smaller than the energy calculated in part (i) 2. Suggest two possible reasons for this difference.

Worked solution & mark scheme

This 9-mark question has a full step-by-step worked solution and mark scheme. One marking point: $\Delta N / \Delta T$

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