Question

A radioactive isotope, having a half life of $3$ days was received after $9$ days. It was found that there was only $4\text{gms}$ of the isotope left in the container. The initial weight of the isotope, when it was packed, must be,

• A. $8\text{gms}$
• B. $32\text{gms}$
• C. $48\text{gms}$
• D. $64\text{gms}$

Answer 1

The correct option is B $32\text{gms}$

$T=3$ days, $t=9$ days, $m=4\text{gms}$ $m_0=?$
We know that,
$t=nT$
$9=n\times 3$
$\therefore n=3$
i.e. the time elapsed is equal to three times the half life.

Now, $m=\frac{m_0}{2^n}$

$4=\frac{m_0}{2^3}$
$\therefore m_0=4\times 8=32\text{gms}$

Hence, $\left(B\right)$ is the correct answer.