The limit of a particular detection system is 0.002 dps for 1g sample. Find the maximum `t_((1)/(2))` that this system could detect in a 1-g sample of a nuclide of mass number 200.

Explanation

To find the maximum half-life (\( t_{1/2} \)) that the detection system could detect in a 1-g sample of a nuclide with mass number 200, we can follow these steps:

### Step 1: Understand the relationship between disintegration rate, half-life, and the number of atoms.

The disintegration constant (\( \lambda \)) is related to the half-life (\( t_{1/2} \)) by the equation:
\[ \lambda = \frac{0.693}{t_{1/2}} \]
...