An isotope of an element is radioactive. Explain what radioactive decay means.
A sample of a radioactive isotope contains $N$ nuclei at time $t$. Over a short time $\Delta t$, $\Delta N$ nuclei decay. State expressions, in terms of the symbols $t$, $\Delta t$, $N$ and $\Delta N$, for the number of undecayed nuclei at time $(t + \Delta t)$.
State an expression, in terms of the symbols $t$, $\Delta t$, $N$ and $\Delta N$, for the sample’s mean activity over the time interval $\Delta t$.
State an expression, in terms of the symbols $t$, $\Delta t$, $N$ and $\Delta N$, for the probability that a nucleus decays during the time interval $\Delta t$.
State an expression, in terms of the symbols $t$, $\Delta t$, $N$ and $\Delta N$, that gives the decay constant.
The change with time $t$ of the activity $A$ of a sample of a radioactive isotope is shown in Fig. 9.1. The radioactive isotope decays to form a stable isotope $S$. At time $t = 0$, there are no nuclei of $S$ in the sample. On the axes of Fig. 9.2, sketch a graph to show how the number $n$ of nuclei of $S$ in the sample varies with time $t$.