Atoms And Nuclei Question 358
Question: A radioactive material of half-life ln2 was produced in a nuclear reactor. Consider two different instants A and B. The number of undecayed nuclei at instant B was twice of that of instant A. If the activities at instants A and B are $ A_{1} $ and $ A_{2} $ respectively then the difference in the age of the sample at these instants equals.
Options:
A) $ | \ell n( \frac{2A_{1}}{A_{2}} ) | $
B) $ \ell n2| \ell n( \frac{A_{1}}{A_{2}} ) | $
C) $ | \ell n( \frac{A_{1}}{2A_{2}} ) | $
D) $ \ell n2| \ell n( \frac{A_{1}}{A_{2}} ) | $
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Answer:
Correct Answer: C
Solution:
- $ A_{1}=(\lambda N_{0}){{e}^{-\lambda t_{1}}} $ …..(i) $ A_{2}=(\lambda 2N_{0}){{e}^{-\lambda t_{2}}} $ ….(ii) $ t_{1}-t_{2}=\frac{1}{\lambda }\ell n( \frac{A_{2}}{2A_{1}} )=\ell n( \frac{A_{2}}{2A_{1}} ) $
