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NEET 2008
Exam
NEET
Year
2008
Subject
Physics
Chapter
Nuclear Physics

NEET 2008 · Physics · Nuclear Physics

Two radioactive materials X_1 and X_2 have decay constants 5 λ and...

Two radioactive materials X1X_1 and X2X_2 have decay constants 5λ5 \lambda and λ\lambda respectively. If initially they have the same number of nuclei, then the ratio of the number of nuclei of X1\mathrm{X}_1 to that of X2X_2 will be 1e\frac{1}{e} after a time

Options

  1. Aeλ\frac{e}{\lambda}
  2. Bλ\lambda
  3. C12λ\frac{1}{2} \lambda
  4. D14λ\frac{1}{4 \lambda}

Correct answer

D. 14λ\frac{1}{4 \lambda}

Step-by-step solution

Nx1Nx2=e−5λte−λt=1e⇒t=14λ\begin{aligned}& \frac{N_{x_1}}{N_{x_2}}=\frac{e^{-5 \lambda t}}{e^{-\lambda t}}=\frac{1}{e}\\ & \Rightarrow \quad t=\frac{1}{4 \lambda} \end{aligned}
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