Q41 / 200 · AP EAMCET 2002 · Chemistry

$10 \mathrm{~g}$ of a radioactive element is disintegrated to $1 \mathrm{~g}$ in 2.303 minutes. What is the half-life (in minutes) of that radioactive element?

  • A
    $1 / 0.693$
  • B
    $6.93$
  • C
    $1$
  • Correct answer
    D
    $0.693$

Solution

Radioactive disintegration is first order reaction $$ \begin{aligned} k & =\frac{2303}{t} \log \frac{a}{a-x} \\ & =\frac{2.303}{2.303} \log \frac{10}{1} \\ k & =1 \\ t_{1 / 2} & =\frac{0.693}{k}=\frac{0.693}{1} \\ & =0.693 \mathrm{~min} \end{aligned} $$

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

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