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)

Question

Responses

16
16

32
32

64
64

8

Answer 1

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.