A particular radioactive sample has a half life of 12 years. The fraction of it that remains undecayed after 48 years, will be:

$\frac{1}{16}^{\text {th}}$ of its initial amount

The correct answer is Option (3) → $\frac{1}{16}^{\text {th}}$ of its initial amount

$N=\frac{N_0}{2^n}$

N is the number of remaining nuclei

$N_0$ is the number of initial nuclei

n is the number of half life

half life $\left(\frac{T_1}{2}\right)=12$

$n=\frac{48}{12}=4$

$\frac{N}{N_0}=\frac{1}{2^4}=\frac{1}{16}$