(a) Plot a graph showing the variation of undecayed nuclei $N$ versus time $t$. From the graph, find out how one can determine the half-life and average life of the radioactive nuclei.

(b) The air in some caves includes a significant amount of radon gas, which can lead to lung cancer if breathed over a prolonged time. In British caves, the air in the cave with the greatest amount of the gas has an activity per volume of

$1.55×10_{5}Bq/m_{3}$ . Suppose that you spend two full days exploring (and sleeping in) that cave. Approximately how many

$_{222}Rn$ atoms would you take in and out of your lungs during your two-day stay? The radionuclide

$_{222}Rn$ in radon gas has a half-life of 3.82 days. You need to estimate your lung capacity and average breathing rate.