Nuclear Physics And Radioactivity Question 348
Question: During mean life of a radioactive element, the fraction that disintegrates is [CPMT 2001]
Options:
A) e
B) $ \frac{1}{e} $
C) $ \frac{e-1}{e} $
D) $ \frac{e}{e-1} $
Show Answer
Answer:
Correct Answer: C
Solution:
By using $ N=N_{0}{{e}^{-\lambda t}} $ and average life time $ t=\frac{1}{\lambda } $ So $ N=N_{0}{{e}^{-\lambda \times 1/\lambda }}=N_{0}{{e}^{-1}}\Rightarrow \frac{N}{N_{0}}={{e}^{-1}}=\frac{1}{e} $ Now disintegrated fraction $ =1-\frac{N}{N_{0}}=1-\frac{1}{e}=\frac{e-1}{e} $
BETA
