Q155 / 160 · TS EAMCET 2015 · Physics

A radioactive nucleus can decay by two different processes. The half lives of the first and second decay processes are $5 \times 10^3$ and $10^5$ years respectively. Then, the effective half-life of the nucleus is

  • A
    $105 \times 10^5 \mathrm{yr}$
  • Correct answer
    B
    $4762 \mathrm{yr}$
  • C
    $10^4 \mathrm{yr}$
  • D
    $47.6 \mathrm{yr}$

Solution

The effective half-life of the nucleus $\begin{aligned} \lambda & =\lambda_1+\lambda_2 \\ \frac{0.69}{T} & =\frac{0.69}{T_1}+\frac{0.69}{T_2} \\ T & =\frac{T_1 T_2}{T_1+T_2} \\ & =\frac{5 \times 10^3 \times 10^5}{5 \times 10^3[1+20]}=\frac{5 \times 10^5}{105} \\ & =4762 \mathrm{yr} \end{aligned}$

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

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