Q140 / 200 · NEET 2003 · Physics

A sample of radioactive element has a mass of $10 \mathrm{~g}$ at an instant $t=0$. The approximate mass of this element in the sample after two mean lives is:

  • Correct answer
    A
    $1.35 \mathrm{~g}$
  • B
    $2.50 \mathrm{~g}$
  • C
    $3.70 \mathrm{~g}$
  • D
    $6.30 \mathrm{~g}$

Solution

\(\begin{aligned} & \mathrm{N}=\mathrm{N}_0 \mathrm{e}^{-\lambda \mathrm{t}} \Rightarrow \mathrm{m}=\mathrm{m}_0 \mathrm{e}^{-\lambda \mathrm{t}}=\mathrm{m}_0 \mathrm{e}^{-\lambda(2 / \lambda)} \\ & =\frac{10}{\mathrm{e}^2}=1.35 \mathrm{gm}\end{aligned}\)

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

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