Half-life of radium is 1,620 years. After how many half-lives 0.75 mg of radium will be disintegrated out of its initial m ass of 1 mg?

Explanation

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

### Step-by-Step Solution:

1. **Understand the Initial Mass and Disintegrated Mass**:
- Initial mass of radium = 1 mg
- Mass disintegrated = 0.75 mg
- Remaining mass after disintegration = Initial mass - Disintegrated mass = 1 mg - 0.75 mg = 0.25 mg

2. **Determine the Mass Remaining After Each Half-Life**:
- After 1 half-life, the remaining mass will be half of the initial mass:
- Remaining after 1 half-life = 1 mg / 2 = 0.5 mg
- After 2 half-lives, the remaining mass will be half of the remaining mass after the first half-life:
- Remaining after 2 half-lives = 0.5 mg / 2 = 0.25 mg

3. **Count the Number of Half-Lives**:
- From the calculations, we see that it takes 2 half-lives for the mass to reduce from 1 mg to 0.25 mg.

4. **Conclusion**:
- Therefore, the number of half-lives after which 0.75 mg of radium will be disintegrated is **2 half-lives**.

### Final Answer:
The answer is **2 half-lives**.

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