An isotope of an element is radioactive. Explain what radioactive decay means.
At time $t$, a sample of a radioactive isotope has $N$ nuclei. Over a brief time $\Delta t$, $\Delta N$ nuclei decay. State expressions, using the symbols $t$, $\Delta t$, $N$ and $\Delta N$, for the number of undecayed nuclei at time $(t + \Delta t)$.
State an expression for the mean activity of the sample over the time interval $\Delta t$.
State an expression for the probability that a nucleus decays during the time interval $\Delta t$.
State an expression for the decay constant.
Fig. 9.1 shows how the activity $A$ of a sample of a radioactive isotope changes with time $t$. The radioactive isotope decays to produce a stable isotope $S$. At time $t = 0$, the sample contains no nuclei of $S$. On the axes in Fig. 9.2, sketch a graph to show how the number $n$ of nuclei of $S$ in the sample varies with time $t$.