Nuclear Physics And Radioactivity Question 70
Question: Two radioactive materials $ X_{1} $ and $ X_{2} $ have decay constants $ 10\lambda $ and $ \lambda $ respectively. If initially they have the same number of nuclei, then the ratio of the number of nuclei of $ X_{1} $ to that of $ X_{2} $ will be $ 1/e $ after a time [IIT-JEE (Screening) 2000]
Options:
A) $ 1/(10\lambda ) $
B) $ 1/(11\lambda ) $
C) $ 11/(10\lambda ) $
D) $ 1/(9\lambda ) $
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Answer:
Correct Answer: D
Solution:
$ N_{1}=N_{0}{{e}^{-10\lambda t}} $ and $ N_{2}=N_{0}{{e}^{-\lambda t}} $
$ \Rightarrow \frac{N_{1}}{N_{2}}=\frac{1}{e}={{e}^{-1}}={{e}^{(-10\lambda +\lambda )t}}={{e}^{-9\lambda t}}\Rightarrow t=\frac{1}{9\lambda } $ .
BETA
