Question

Average life of a radioactive sample is 4 ms. Initially the total number of nuclei is $N_{\left(0\right)}$ 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 respect to time is

• A. $100\Omega$
• B. $200\Omega$
• C. $300\Omega$
• D. $400\Omega$

Answer 1

The correct option is B $200\Omega$

$N=N_0{e}^{-\lambda t};q=q_0{e}^{-\frac{t}{RC}};\frac{N}{q}$=constanct when $e^{-\lambda t}=e^{-\frac{t}{RC}}$
$\lambda =\frac{1}{RC};R=200\Omega$