Question

A freshly prepared radioactive sample of half life $2$ hours 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 this source is:

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

Answer 1

The correct option is B $12$ hrs

We know using half-life method,

$N=N_0{\left(\frac{1}{2}\right)}^n,\frac{N}{N_0}={\left(\frac{1}{2}\right)}^n$

$\frac{1}{64}={\left(\frac{1}{2}\right)}^n\Rightarrow n=6$

$\therefore$ $t=2\times 6=12hrs$