Question

A freshly prepared radio medicine has half life $2$ hours. Its activity is $64$ times the permissible safe value. The minimum time after which it would be possible to treat the patients with the medicine is:

• A. $3$ hrs
• B. $9$ hrs
• C. $24$ hrs
• D. $12$ hrs

Answer 1

The correct option is D $12$ hrs

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

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

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

$n=6$ half lives

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

Hence, the correct option is $\text{D}$