Q107 / 180 · AIIMS 2019 (26 May) · Physics

A sample has half life of $10^{33}$ year. If initial number of nuclei of the sample is $26 \times 10^{34}$. Then find out the number of nuclei decayed in 1 year.

  • A
    $1.82$
  • Correct answer
    B
    $182$
  • C
    $18.2$
  • D
    $1820$

Solution

$\begin{aligned} & \text { }-\frac{d N}{d t}=\lambda N \\ & -d N=\frac{\ln 2}{T_{1 / 2}} \times N \times d t=\frac{0.7}{10^{33}} \times 26 \times 10^{34} \times 1=182 .\end{aligned}$

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

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