10 g-atoms of an `alpha`-active radioisotope are disintegrating in a sealed container. In one hour the helium gas collected at STP is `11.2 cm^(2)`. Calculate the half life of the radioisotope.

Explanation

To solve the problem, we need to calculate the half-life of an alpha-active radioisotope based on the given information. Here’s a step-by-step solution:

### Step 1: Determine the initial number of atoms (N0)
We are given that there are 10 gram-atoms of the radioisotope. We can convert this to the number of atoms using Avogadro's number (Na = 6.022 × 10²³ atoms/mol).

\[ N_0 = 10 \text{ g-atoms} \times N_a = 10 \times 6.022 \times 10^{23} \text{ atoms} = 6.022 \times 10^{24} \text{ atoms} \]
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