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:
A) 1
B) In 2
C) In (4/3)
D) 2 to (4/3)
Show Answer
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) $
