A radioactive sample has a half life of 12 years. The fraction of sample that will decay in 24 years is:

$\frac{3}{4}$

The correct answer is Option (2) → $\frac{3}{4}$

The decayed fraction of a sample is -

Decayed fraction = 1 - Remaining fraction

$=1-\left(\frac{1}{2}\right)^{\frac{t}{T_{1/2}}}$

where,

t = time elapsed = 24 years

$T_{1/2}$ = half-life = 12 years

∴ Remaining fraction = $\left(\frac{1}{2}\right)^{\frac{24}{12}}=\frac{1}{4}$

∴ Decayed fraction = $1-\frac{1}{4}=\frac{3}{4}$