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NEET 2011
Exam
NEET
Year
2011
Subject
Physics
Chapter
Nuclear Physics

NEET 2011 · Physics · Nuclear Physics

The half-life of a radioactive isotope X is 50 yr . It decays to...

The half-life of a radioactive isotope XX is 50yr50 \mathrm{yr}. It decays to another element YY which is stable. The two elements XX and YY were found to be in the ratio of 1:151: 15 in a sample of a given rock. The age of the rock was estimated to be

Options

  1. A200yr200 \mathrm{yr}
  2. B250yr250 \mathrm{yr}
  3. C100yr100 \mathrm{yr}
  4. D150yr150 \mathrm{yr}

Correct answer

A. 200yr200 \mathrm{yr}

Step-by-step solution

We know that NN0=(12)t/t1/2116=(12)t/50t=4×50t=200yr\begin{aligned}\frac{N}{N_0}& =\left(\frac{1}{2}\right)^{t / t_1 / 2}\\ \frac{1}{16}& =\left(\frac{1}{2}\right)^{t / 50}\\ t & =4 \times50 \\ t & =200 \mathrm{yr} \end{aligned}
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