(a(i))[2]
Define radioactive half-life.
(a(ii))[1]
Show that the decay constant for phosphorus-33 is $3.23 \times 10^{-7}\,\text{s}^{-1}$.
(b(i))[2]
A pure sample of phosphorus-33 starts with an activity of $3.7 \times 10^{6}\,\text{Bq}$. Calculate the initial number of phosphorus-33 nuclei in the sample.
(b(ii))[2]
Calculate how many phosphorus-33 nuclei remain in the sample after $30\,\text{days}$.
(c)[2]
Once $30\,\text{days}$ have passed, the sample in (b) contains phosphorus-33 and sulfur-33 nuclei. Use your answers in (b) to calculate the ratio $$\frac{\text{number of phosphorus-33 nuclei after 30 days}}{\text{number of sulfur-33 nuclei after 30 days}}.$$