The half-life of a radioactive material undergoing $\beta$-decay is 12.5 years. What fraction the material remains undecayed after 25 years?

$\frac{1}{4}$

The correct answer is Option (1) → $\frac{1}{4}$

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

Here N is number of remaining nuclei

$N_0$ is the number initial nuclei

n is the number of half life

$n=\frac{25}{T_{1 / 2}}=\frac{25}{12.5}$

$=2$

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