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NEET 2007
Exam
NEET
Year
2007
Subject
Physics
Chapter
Nuclear Physics

NEET 2007 · Physics · Nuclear Physics

Two radioactive substances A and B have decay constants 5 λ and λ...

Two radioactive substances A\mathrm{A} and B\mathrm{B} have decay constants 5λ5 \lambda and λ\lambda respectively. At t=0t=0 they have the same number of nuclei. The ratio of number of nuclei of A to those of B\mathrm{B} will be (1/e)2(1 / e)^2 after a time interval.

Options

  1. A4λ4 \lambda
  2. B2λ2 \lambda
  3. C12λ\frac{1}{2} \lambda
  4. D14λ\frac{1}{4} \lambda

Correct answer

C. 12λ\frac{1}{2} \lambda

Step-by-step solution

According to the question NANB=1e4λt⇒1e4λt=1e2⇒t=12λ\begin{aligned} \frac{N_A}{N_B} & =\frac{1}{e^{4 \lambda t}} \\ \Rightarrow \quad \frac{1}{e^{4 \lambda t}} & =\frac{1}{e^2} \\ \Rightarrow \quad t & =\frac{1}{2 \lambda} \end{aligned}
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