Question

Carbon-11 has a half-life of about 20 minutes. If we start with 200grams, how much will be left after 3 hours?

Answer 1

To calculate how much Carbon-11 will remain after 3 hours when starting with 200 grams, we will use the half-life formula.

1. **Determine the number of half-lives that occur in 3 hours:**
- The half-life of Carbon-11 is 20 minutes.
- Convert 3 hours into minutes: \(3 \text{ hours} = 3 \times 60 = 180 \text{ minutes}\).
- Calculate the number of half-lives in 180 minutes:
\[
\text{Number of half-lives} = \frac{180 \text{ minutes}}{20 \text{ minutes/half-life}} = 9 \text{ half-lives}
\]

2. **Calculate the remaining amount of Carbon-11 after 9 half-lives:**
- The formula for the remaining amount after n half-lives is:
\[
\text{Remaining} = \text{Initial Amount} \times \left(\frac{1}{2}\right)^n
\]
- Substitute the values:
\[
\text{Remaining} = 200 \text{ grams} \times \left(\frac{1}{2}\right)^9
\]
- Calculate \(\left(\frac{1}{2}\right)^9\):
\[
\left(\frac{1}{2}\right)^9 = \frac{1}{512} \approx 0.001953125
\]

3. **Now compute the remaining amount:**
\[
\text{Remaining} = 200 \text{ grams} \times 0.001953125 \approx 0.390625 \text{ grams}
\]

Therefore, after 3 hours, approximately **0.39 grams** of Carbon-11 will remain.