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CUET · PHYSICS · PYQ PAPER 2023

A piece of ancient wood shows an activity of 3.9 disintegrations per second per gram of C\(^{14}\). The age of wood, if half life of C\(^{14}\) is 5568 years, and activity of fresh C\(^{14}\) is 15.6 disintegrations per second per gram, is (take \(\log_e 2 = 0.693\)).

  1. A 9,324 years
  2. B 13,142 years
  3. C 19,121 years
  4. D 11,136 years
Verified Solution

Answer & Solution

Correct Answer

(D) 11,136 years

Step-by-step Solution

Detailed explanation

\(t = \frac{T_{1/2}}{\ln 2} \ln\left(\frac{A_0}{A}\right)\) \(t = \frac{5568}{0.693} \ln\left(\frac{15.6}{3.9}\right)\) \(t = \frac{5568}{0.693} \ln(4)\) \(t = \frac{5568}{0.693} (2 \ln 2)\) \(t = \frac{5568}{0.693} (2 \times 0.693)\) \(t = 5568 \times 2\) \(t = 11136\) years