A sample of radioactive isotope with a half life of 20 days weighs `1 g`. After 40 days the weight of the remaining elements is
a. `0.5 g` b. `0.0 g` c. `0.25 g` d. `1//6 g`

Options

A. a. `0.5 g`
B. b. `0.0 g`
C. c. `0.25 g`
D. d. `1//6 g`

Explanation

To solve the problem, we need to determine the remaining weight of a radioactive isotope after a certain period, given its half-life.

### Step-by-Step Solution:

1. **Identify the Half-Life**: The half-life of the radioactive isotope is given as 20 days. This means that every 20 days, the amount of the isotope will reduce to half of its previous weight.

2. **Initial Weight**: The initial weight of the radioactive isotope is 1 gram.

3. **Calculate the Weight After 20 Days**:
- After the first half-life (20 days), the weight will be:
\[ \text{Weight after 20 days} = \frac{1 \text{ g}}{2} = 0.5 \text{ g} \]

4. **Calculate the Weight After Another 20 Days (Total 40 Days)**:
- After the second half-life (another 20 days, totaling 40 days), the weight will again reduce to half of the weight after the first half-life:
\[ \text{Weight after 40 days} = \frac{0.5 \text{ g}}{2} = 0.25 \text{ g} \]

5. **Final Result**: After 40 days, the remaining weight of the radioactive isotope is 0.25 grams.

### Conclusion:
The weight of the remaining radioactive isotope after 40 days is **0.25 g**, which corresponds to option **c**.

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