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NEET 2003
Exam
NEET
Year
2003
Subject
Physics
Chapter
Nuclear Physics

NEET 2003 · Physics · Nuclear Physics

A sample of radioactive element has a mass of 10 ~g at an instant...

A sample of radioactive element has a mass of 10 g10 \mathrm{~g} at an instant t=0t=0. The approximate mass of this element in the sample after two mean lives is:

Options

  1. A1.35 g1.35 \mathrm{~g}
  2. B2.50 g2.50 \mathrm{~g}
  3. C3.70 g3.70 \mathrm{~g}
  4. D6.30 g6.30 \mathrm{~g}

Correct answer

A. 1.35 g1.35 \mathrm{~g}

Step-by-step solution

N=N0e−λt⇒m=m0e−λt=m0e−λ(2/λ)=10e2=1.35gm\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})$
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