Q33 / 150 · MHT CET 2008 · Chemistry

A radioactive isotope having $t_{1 / 2}=3$ days was read after 12 days. If $3 g$ of isotope is contained in container, the initial weight of isotope was

  • A
    $12 \mathrm{~g}$
  • B
    $24 \mathrm{~g}$
  • C
    $36 \mathrm{~g}$
  • Correct answer
    D
    $48 \mathrm{~g}$

Solution

$\begin{aligned} T &=n \times t_{1 / 2} \\ 12 &=n \times 3 \\ n &=4 \\ N &=N_{0} \times\left(\frac{1}{2}\right)^{n} \\ 3 &=N_{0} \times\left(\frac{1}{2}\right)^{4} \\ 3 &=N_{0} \times \frac{1}{16} \\ N_{0} &=16 \times 3=48 \mathrm{~g} \end{aligned}$

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

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