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 $

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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 $ .


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