` 1 mg` of `Th` emits 22 `alpha`-particles per unit solid angle per minute. Calculate `t_(1//2)` or `Th (Th = 232)`.

Explanation

To calculate the half-life (\( t_{1/2} \)) of Thorium-232 (\( ^{232}Th \)), we will follow these steps:

### Step 1: Calculate the number of Thorium atoms in 1 mg
1. Convert 1 mg to grams:
\[ 1 \text{ mg} = 10^{-3} \text{ g} \]
2. Use Avogadro's number (\( N_A = 6.02 \times 10^{23} \text{ atoms/mol} \)) to calculate the number of moles of Thorium:
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