Half-life of radium is 1,620 years. After how many years 0.75 mg of radium will be disintegrated out of its initial mass of 1 mg.

Explanation

To solve the problem, we need to determine how long it takes for 0.75 mg of radium to disintegrate from an initial mass of 1 mg.

### Step-by-Step Solution:

1. **Identify Initial Mass and Disintegrated Mass**:
- Initial mass of radium, \( n_0 = 1 \, \text{mg} \)
- Disintegrated mass = 0.75 mg
- Remaining mass after disintegration = \( n = n_0 - \text{disintegrated mass} = 1 \, \text{mg} - 0.75 \, \text{mg} = 0.25 \, \text{mg} \)
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