Q109 / 150 · MHT CET 2023 (13 May Shift 1) · Physics

A radioactive sample has half-life of 5 years. The percentage of fraction decayed in 10 years will be

  • A
    $25 \%$
  • B
    $50 \%$
  • Correct answer
    C
    $75 \%$
  • D
    $100 \%$

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.

Hence, the correct answer is option: 'C'.

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