Q99 / 180 · AIIMS 2019 (25 May) · Physics

The half-life of ${ }^{215} \mathrm{At}$ is $100 \mu \mathrm{s}$. The time taken for the radioactivity of a sample of ${ }^{215}$ At to decay to $1 / 16^{\text {th }}$ of its initial value is

  • Correct answer
    A
    $400 \mu \mathrm{s}$
  • B
    $6.3 \mu \mathrm{s}$
  • C
    $40 \mu \mathrm{s}$
  • D
    $300 \mu \mathrm{s}$

Solution

After $n$ half lives $N=N_0\left(\frac{1}{2}\right)^n$ $\therefore{ }^{215}$ At decays to $\frac{1}{16}^{\text {th }}$ in 4 half-lives i.e., after $400 \mu \mathrm{s}$.

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

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