If halfe-life of a substance is 5 yrs, then the total amount of substance left after 15 years, when initial amount is 64 grams is

Options

A. 16 grams
B. 2 grams
C. 32 grams
D. 8 grams

Explanation

To solve the problem of determining the amount of a substance left after 15 years given its half-life and initial amount, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Half-Life**: The half-life of the substance is given as 5 years.

2. **Determine the Total Time**: We need to find the amount left after 15 years.

3. **Calculate the Number of Half-Lives**:
\[ \text{Number of half-lives} = \frac{\text{Total time}}{\text{Half-life}} = \frac{15 \text{ years}}{5 \text{ years}} = 3 \]
This means that 3 half-lives have passed in 15 years.

4. **Calculate the Remaining Amount**:
- The initial amount of the substance is 64 grams.
- After each half-life, the amount of substance is halved:
- After 1st half-life (5 years):
\[ 64 \text{ grams} \div 2 = 32 \text{ grams} \]
- After 2nd half-life (10 years):
\[ 32 \text{ grams} \div 2 = 16 \text{ grams} \]
- After 3rd half-life (15 years):
\[ 16 \text{ grams} \div 2 = 8 \text{ grams} \]

5. **Final Amount**: After 15 years, the total amount of substance left is 8 grams.

### Conclusion:
The total amount of the substance left after 15 years is **8 grams**.