The average life of a radioactive sample is 100 millisecond. A charged capacitor having capacitance 200 `muF` is connected across a resistance R. For what value of R, the ratio of charge on capacitor to the activity of the sample remains constant with time or independent of time.

Explanation

To solve the problem, we need to find the value of the resistance \( R \) such that the ratio of the charge on the capacitor to the activity of the radioactive sample remains constant over time.

### Step-by-Step Solution:

1. **Understand the Average Life and Decay Constant**:
The average life \( \tau \) of a radioactive sample is related to the decay constant \( \lambda \) by the formula:
\[
\tau = \frac{1}{\lambda}
...