State what the term radioactive decay means.
The sample contains isotope $X$, which has half-life $T$ and decays to a stable product. The only substances present are $X$ and the stable product. At time $t = 0$, the activity is $A_0$ and the sample contains $N_0$ nuclei of $X$.
On Fig. 10.1, sketch how the number $N$ of nuclei of $X$ in the sample changes with $t$. Your line should run from time $t = 0$ to time $t = 3T$.
On Fig. 10.2, sketch how the activity $A$ of the sample varies with $N$ for values of $N$ from $N = 0$ up to $N = N_0$.
State the name of the quantity shown by the gradient of your line in Fig. 10.1.
State the name of the quantity shown by the gradient of your line in Fig. 10.2.
For the sample in (b), calculate the fraction $\frac{N}{N_0}$ at time $t = 1.70T$.