A radiation lab orders 64 μCi of P-32.After 42.9 days the activity of the sample is 8.0 μCi.What is the half-life of P-32?

Question

Quizplus · Accepted Answer

We can use the radioactive decay formula to solve for the half-life:

A = A0(1/2)^(t/T)

Where A is the final activity (8.0 μCi), A0 is the initial activity (64 μCi), t is the time elapsed (42.9 days), and T is the half-life we are trying to find.

Substituting in the values, we get:

8.0 = 64(1/2)^(42.9/T)

Simplifying and solving for T, we get:

1/8 = (1/2)^(42.9/T)
log(1/8) = log((1/2)^(42.9/T))
-3 = (42.9/T)log(1/2)
T = 42.9/(-3log(1/2))
T ≈ 14.3 days

Therefore, the half-life of P-32 is approximately 14.3 days, which is choice B.

A Radiation Lab Orders 64 μCi of P-32