(a(i))[2]
Define the term radioactive half-life.
(a(ii))[1]
Show that the decay constant for phosphorus-33 equals $3.23 \times 10^{-7}\,\text{s}^{-1}$.
(b(i))[2]
A pure phosphorus-33 sample has an initial activity of $3.7 \times 10^{6}\,\text{Bq}$. Calculate how many phosphorus-33 nuclei are present initially in the sample.
(b(ii))[2]
Calculate how many phosphorus-33 nuclei are left in the sample after $30$ days.
(c)[2]
After $30$ days, the sample in (b) contains both phosphorus-33 and sulfur-33 nuclei. Use your answers in (b) to work out the ratio $$\frac{\text{number of phosphorus-33 nuclei after 30 days}}{\text{number of sulfur-33 nuclei after 30 days}}.$$