Atoms And Nuclei Question 381
Question: Average life of a radioactive sample is 4ms. Initially the total number of nuclei is $ N_{0} $ . A charged capacitor of capacity $ 20\mu F $ is connected across a resistor R. The value of R such that ratio of number of nuclei remaining to charge on capacitor remains constant with time is
Options:
A) 100 $ \Omega $
B) 200 $ \Omega $
C) 300 $ \Omega $
D) 400 $ \Omega $
Show Answer
Answer:
Correct Answer: B
Solution:
- $ N=N_{0}{{e}^{-\lambda t}}q=q_{0}{{e}^{-t/RC}} $ and $ \frac{N}{q}= $ constant when $ {{e}^{-\lambda t}}={{e}^{t/RC}}\Rightarrow \lambda =\frac{1}{RC},R=200\Omega $ .
