Approximately how many half-life periods must elapse if the activity of a radioactive isotope sample is to be reduced to 0.004 of the original value?

Question

Quizplus · Accepted Answer

The fraction of remaining activity after n half-lives is given by (1/2)^n. We are given that the remaining activity is 0.004 times the original activity, which means that the fraction remaining is 0.004. 
Therefore, we need to solve the equation (1/2)^n = 0.004 for n:
(1/2)^n = 0.004
Taking the logarithm of both sides:
n*log(1/2) = log(0.004)
n = log (0.004) / log (1/2)
n ≈ 6.9
Since we cannot have partial half-lives, we need to round up to 7 half-lives, which is the closest integer value. Therefore, the answer is (C) 7.

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