A radioisotope has half life of 10 years. What percentage of the original amount of it would you expect to remain after 20 years?

Options

A. 0
B. 12.5
C. 25
D. 8

Explanation

To solve the problem of how much of a radioisotope remains after 20 years given its half-life of 10 years, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Half-Life**:
The half-life of the radioisotope is given as 10 years. This means that every 10 years, half of the remaining amount of the substance will have decayed.

2. **Determine the Total Time**:
The total time we are considering is 20 years.

3. **Calculate the Number of Half-Lives**:
To find out how many half-lives fit into the total time, we divide the total time by the half-life:
\[ n = \frac{\text{Total Time}}{\text{Half-Life}} = \frac{20 \text{ years}}{10 \text{ years}} = 2 \]
This means that 2 half-lives have passed in 20 years.

4. **Calculate the Remaining Amount**:
The formula to calculate the remaining amount after n half-lives is:
\[ \text{Remaining Amount} = \frac{\text{Original Amount}}{2^n} \]
If we assume the original amount is 100% (for simplicity), we can substitute n:
\[ \text{Remaining Amount} = \frac{100\%}{2^2} = \frac{100\%}{4} = 25\% \]

5. **Conclusion**:
After 20 years, 25% of the original amount of the radioisotope would remain.

### Final Answer:
**25% of the original amount of the radioisotope would remain after 20 years.**

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