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NEET 2013
Exam
NEET
Year
2013
Subject
Physics
Chapter
Nuclear Physics

NEET 2013 · Physics · Nuclear Physics

The half-life of a radioactive isotope X is 20 yr . It decays to...

The half-life of a radioactive isotope XX is 20yr20 \mathrm{yr}. It decays to another element YY which is stable. The two elements XX and YY were found to be in the ratio 1:71: 7 in a sample of a given rock. The age of the rock is estimated to be

Options

  1. A40yr40 \mathrm{yr}
  2. B60yr60 y \mathrm{r}
  3. C80yr80 \mathrm{yr}
  4. D100yr100 \mathrm{yr}

Correct answer

B. 60yr60 y \mathrm{r}

Step-by-step solution

 ( As \text{ ( As }NN0=(12)nNN0=(12)3=18\begin{aligned} \frac{N}{N_0}=& \left(\frac{1}{2}\right)^n \\ & \frac{N}{N_0}=\left(\frac{1}{2}\right)^3=\frac{1}{8} \end{aligned}Number of half lives $=3\begin{aligned} \Rightarrow& T & =20 \mathrm{yr}\\ \therefore & T & =\frac{t}{n} \end{aligned}$$oror\quad t=T \times n=20 \times 3 \mathrm{yr}=60 \mathrm{yr}$
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