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AP EAMCET · PHYSICS · Nuclear Physics

An element X of a half-life of \(1.4 \times 10^9\) years decays to form another stable element Y. A sample is taken from a rock that contains both X and Y in the ratio \(1: 7\). If at the time of formation of the rock, \(Y\) was not present in the sample, then the age of the rock in years is

  1. A \(4.2 \times 10^9\)
  2. B \(1.4 \times 10^9\)
  3. C \(0.35 \times 10^9\)
  4. D \(2.8 \times 10^9\)
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Answer & Solution

Correct Answer

(A) \(4.2 \times 10^9\)

Step-by-step Solution

Detailed explanation

\( \frac{N}{N_0} = \frac{N_X}{N_X + N_Y} = \frac{1}{1+7} = \frac{1}{8} \) \( \frac{1}{8} = \left(\frac{1}{2}\right)^n \Rightarrow n = 3 \) \( \text{Age} = n \times T_{1/2} = 3 \times (1.4 \times 10^9 \text{ years}) = 4.2 \times 10^9 \text{ years} \)
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