Approximately how many half-life periods must elapse if the activity of a radioactive isotope sample is to be reduced to 0.003 of the original value?
A)5
B)4
C)9
D)16
E)8

Question

Approximately how many half-life periods must elapse if the activity of a radioactive isotope sample is to be reduced to 0.003 of the original value?
A)5
B)4
C)9
D)16
E)​8

Quizplus · Accepted Answer

To solve this problem, we need to use the half-life formula:

A = A0 * (1/2)^(t/h)

where A is the final activity, A0 is the initial activity, t is the time elapsed, and h is the half-life of the isotope.

We can rearrange this formula:

t/h = log( A / A0 ) / log(1/2)

We know that the final activity (A) is 0.003 times the initial activity (A0):

A = 0.003 * A0

So, we can substitute:

t/h = log( 0.003 ) / log(1/2)

t/h = 9.9658

We need to round this up to the nearest integer, which is 10. Therefore, approximately 10 half-life periods must elapse if the activity of a radioactive isotope sample is to be reduced to 0.003 of the original value.

The closest answer choice is C: 9.

Approximately How Many Half-Life Periods Must Elapse If the Activity