Question

Aluminum-30 has a half-life of 3.6 s.

(a) What percent of an initial sample will remain after 10 s?

Answer 1

But the answer is 15%. How?

Answer 2

To find the percent of an initial sample that will remain after 10 seconds, we first need to determine how many half-lives have passed in that time.

10 seconds / 3.6 seconds per half-life = 2.78 half-lives

This means that after 10 seconds, approximately 2.78 half-lives of Aluminum-30 will have passed.

Now we can use the formula for calculating the remaining percentage of a substance after a certain number of half-lives:

Remaining percentage = (1/2)^(number of half-lives)

Remaining percentage = (1/2)^2.78 ≈ 0.253

Therefore, after 10 seconds, approximately 25.3% of an initial sample of Aluminum-30 will remain.

Answer 3

I apologize for the mistake in my calculation. Let's correct the calculation now:

10 seconds / 3.6 seconds per half-life = 2.78 half-lives

This means that after 10 seconds, approximately 2.78 half-lives of Aluminum-30 will have passed.

Now we can use the formula for calculating the remaining percentage of a substance after a certain number of half-lives:

Remaining percentage = (1/2)^(number of half-lives)

Remaining percentage = (1/2)^2.78 ≈ 0.15

Therefore, after 10 seconds, approximately 15% of an initial sample of Aluminum-30 will remain. Thank you for pointing out the error, and I appreciate your understanding.