Question

A freshly prepared radioactive source of half-life $2h$ emits radiation of intensity which is $64$ times the permissible safe level. The minimum time after which it would be possible to work safely with the source is

• A. $6h$
• B. $12h$
• C. $24h$
• D. $128h$

Answer 1

The correct option is B $12h$

$t_{1/2}=2$
$\lambda =\frac{ln2}{2}h{r}^{-1}$

First order decay:
$N\left(t\right)=N_o{e}^{-\lambda t}$

For permissible level:
$\frac{1}{64}=e^{-\lambda t}$

$6ln2=\lambda t$

$t=12hr$