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
8
8
64
64
16
16
32
Responses
8
8
64
64
16
16
32
Answers
GPT-4o mini
To find out how much Polonium-210 remains after 414 days, we need to use the concept of half-lives. Given that the half-life of Polonium-210 is 138 days, we can determine how many half-lives fit into 414 days.
First, calculate the number of half-lives in 414 days:
\[
\text{Number of half-lives} = \frac{\text{Total time}}{\text{Half-life}} = \frac{414 \text{ days}}{138 \text{ days}} \approx 3
\]
Next, we can use the initial amount of Polonium-210 (128 grams) and determine how much remains after 3 half-lives:
1. After 1 half-life (138 days), the remaining amount is:
\[
128 \, \text{grams} \div 2 = 64 \, \text{grams}
\]
2. After 2 half-lives (276 days), the remaining amount is:
\[
64 \, \text{grams} \div 2 = 32 \, \text{grams}
\]
3. After 3 half-lives (414 days), the remaining amount is:
\[
32 \, \text{grams} \div 2 = 16 \, \text{grams}
\]
Therefore, the amount of Polonium-210 left after 414 days is **16 grams**.
First, calculate the number of half-lives in 414 days:
\[
\text{Number of half-lives} = \frac{\text{Total time}}{\text{Half-life}} = \frac{414 \text{ days}}{138 \text{ days}} \approx 3
\]
Next, we can use the initial amount of Polonium-210 (128 grams) and determine how much remains after 3 half-lives:
1. After 1 half-life (138 days), the remaining amount is:
\[
128 \, \text{grams} \div 2 = 64 \, \text{grams}
\]
2. After 2 half-lives (276 days), the remaining amount is:
\[
64 \, \text{grams} \div 2 = 32 \, \text{grams}
\]
3. After 3 half-lives (414 days), the remaining amount is:
\[
32 \, \text{grams} \div 2 = 16 \, \text{grams}
\]
Therefore, the amount of Polonium-210 left after 414 days is **16 grams**.