Question
Given that the half-life of Polonium-210 is 138 days, a nuclear physicist measures out a 128-gram sample. About how many grams of Polonium-210 would be left after 414 days?(1 point)
Responses
16
16
32
32
64
64
8
Responses
16
16
32
32
64
64
8
Answers
GPT-4o mini
To determine how much Polonium-210 remains after 414 days, we can use the half-life formula. The number of half-lives can be calculated by dividing the total time elapsed by the half-life period.
1. **Calculate the number of half-lives:**
- Half-life of Polonium-210 = 138 days
- Total time = 414 days
\[
\text{Number of half-lives} = \frac{414 \text{ days}}{138 \text{ days}} \approx 3
\]
2. **Calculate the remaining amount after these half-lives:**
Since 3 half-lives have passed, the amount of Polonium-210 will be reduced by half three times.
- Starting amount = 128 grams
After 1 half-life (138 days):
\[
128 \text{ grams} \div 2 = 64 \text{ grams}
\]
After 2 half-lives (276 days):
\[
64 \text{ grams} \div 2 = 32 \text{ grams}
\]
After 3 half-lives (414 days):
\[
32 \text{ grams} \div 2 = 16 \text{ grams}
\]
Thus, the amount of Polonium-210 left after 414 days is **16 grams**. Therefore, the correct answer is **16**.
1. **Calculate the number of half-lives:**
- Half-life of Polonium-210 = 138 days
- Total time = 414 days
\[
\text{Number of half-lives} = \frac{414 \text{ days}}{138 \text{ days}} \approx 3
\]
2. **Calculate the remaining amount after these half-lives:**
Since 3 half-lives have passed, the amount of Polonium-210 will be reduced by half three times.
- Starting amount = 128 grams
After 1 half-life (138 days):
\[
128 \text{ grams} \div 2 = 64 \text{ grams}
\]
After 2 half-lives (276 days):
\[
64 \text{ grams} \div 2 = 32 \text{ grams}
\]
After 3 half-lives (414 days):
\[
32 \text{ grams} \div 2 = 16 \text{ grams}
\]
Thus, the amount of Polonium-210 left after 414 days is **16 grams**. Therefore, the correct answer is **16**.