Question

A radioactive element due to an accident in research laboratory gets embedded in its floor and walls. The initial rate of decay is $64$ times the safe limit. The half-life of the element is $32$ days. Calculate the time after which the laboratory will be safe for use.

Answer 1

$N_0=64N$
$\frac{0.693}{t_{1/2}}=\frac{2.303}{t}{\log }_{10}\frac{N_0}{N}$
$\frac{0.693}{32}=\frac{2.303}{t}{\log }_{10}\left[\frac{64N}{N}\right]$
$t=192$ days