A radioactive sample has half-life of 5 years. The percentage of fraction decayed in 10 years will be
A radioactive sample has half-life of 5 years. The percentage of fraction decayed in 10 years will be
$25 \%$
$50 \%$
$75 \%$
$100 \%$
Solution
Given:
Total time, $\mathrm{T}=10$ years
Half life, $\mathrm{T}_{1 / 2}=5$ years
$\therefore \quad$ No. of half lives, $\mathrm{n}=\frac{10}{5}=2$
From $\frac{\mathrm{N}}{\mathrm{N}_0}=\left(\frac{1}{2}\right)^{\mathrm{n}}$
$\therefore \quad \frac{\mathrm{N}}{\mathrm{N}_0}=\left(\frac{1}{2}\right)^2=\frac{1}{4}$
$\therefore \quad$ After 10 years, $\frac{1}{4}^{\text {th }}$ of the original substance will remain.
$\Rightarrow\left(1-\frac{1}{4}\right)=\frac{3}{4} \times 100=75 \%$ of the fraction would get decayed.