Question

A radioactive isotope of ${}^{32}\text{P}(t_{1/2}=14.3day)$ used in biotracer studies of phosphorus metabolism accumulates in waste material having activity 1 millicurie. If it is unsafe to dispose off this waste material until the activity falls to 0.01 microcurie, number of days we must store the waste in lead container before it is safe to dispose it is :

Answer 1

$k=\frac{0.693}{t_{1/2}}=\frac{2.303}{t}log\frac{a}{a-x}$

Substitute values in the above expression.

$\frac{0.693}{14.3}=\frac{2.303}{t}log\frac{1000}{0.01}$

$t=47.522\times 5=238days$

Hence, we must store the waste in lead container for 238 days before it is safe to dispose it.