Question

The half life of a radioactive material is $24$ hours. The time taken for the radioactive material to decay to $\left(\frac{1}{8}\right)^{th}$ of its initial amount is

• A. $72$ hours
• B. $24$ hours
• C. $96$ hours
• D. $48$ hours

Answer 1

Answer: (A)

$\frac{N}{N_{0}}=\left(\frac{1}{2}\right)^{n}$
where, $n =$ number of half lives
$\therefore \frac{1}{8}=\left(\frac{1}{2}\right)^{n}$
$\Rightarrow n=3$
$\because n=\frac{t}{T_{1 /2}}$
$\because t=n T_{1 /2}=3\times24$ hours
$=72$ hours