Q124 / 150 · MHT CET 2023 (14 May Shift 2) · Physics

Half life of radio-active element is 1600 years. The fraction of sample remains undecayed after 6400 years will be

  • Correct answer
    A
    $\frac{1}{16}$
  • B
    $\frac{1}{4}$
  • C
    $\frac{1}{8}$
  • D
    $\frac{1}{24}$

Solution

$\frac{\mathrm{N}}{\mathrm{N}_0}=\left(\frac{1}{2}\right)^{\frac{\mathrm{t}}{\mathrm{T}}}$ Here, $\mathrm{t}=6400$ years and $\mathrm{T}=1600$ years $\therefore \quad \frac{\mathrm{N}}{\mathrm{N}_0}=\left(\frac{1}{2}\right)^{\frac{6400}{1600}}=\left(\frac{1}{2}\right)^4=\frac{1}{16}$

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

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