Q13 / 160 · TS EAMCET 2005 · Chemistry

The half-lives of two radioactive nuclides $A$ and $B$ are 1 and $2 \mathrm{~min}$ respectively. Equal weights of $A$ and $B$ are taken separately and allowed to disintegrate for $4 \mathrm{~min}$. What will be the ratio of weights of $A$ and $B$ disintegrated?

  • A
    1:1
  • Correct answer
    B
    5:4
  • C
    1:2
  • D
    1:3

Solution

For, $A t_{1 / 2}=1 \mathrm{~min}$ $\therefore$ part of $A$ remained after 4 minutes $\text { (i.e., } 4 \text { half- life) will be }=\frac{1}{16}$ $\therefore$ part of $A$ disintegrated in the same period $=\frac{15}{16}$ For $B, t_{1 / 2}=2 \mathrm{~min}$ $\therefore$ Part of $B$ remained after 4 minutes (i.e., 2 half life) $=\frac{1}{4}$ $\therefore$ part of $B$ disintegrated in the same time $=\frac{3}{4}$ Hence, ratio of disintegrated weights of $A$ and $B=\frac{15}{16}: \frac{3}{4}=15: 12=5: 4$

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

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