Atoms And Nuclei Question 389
Question: A radioactive substance with decay constant of $ 0.5{{s}^{-1}} $ is being produced at a constant rate of 50 nuclei per second. If there are no nuclei present initially, the time (in second) after which 25 nuclei will be present is
Options:
1
B) In 2023
C) In (3/4)
D) 2 In (4/3)
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Answer:
Correct Answer: D
Solution:
- $ \frac{dN}{dt}=50-\frac{N}{0.5},\int\limits_{0}^{N}{\frac{dN}{50-2N}}=\int\limits_{0}^{t}{dt} $ $ N=100(1-{{e}^{-t/2}})=25 $ $ t=2 $ In $ (4/3) $
BETA
