A sample of I-131 decays from 12 microcuries to 3.0 microcuries in 16 days.What is the half-life of I-131?

Question

Quizplus · Accepted Answer

To find the half-life of I-131, we can use the following formula:
N = N0 x (1/2)^(t/T)
where N is the final amount, N0 is the initial amount, t is the time elapsed, and T is the half-life.
We can plug in the values given in the problem:
N = 3.0 microcuries
N0 = 12 microcuries
t = 16 days
(1/2)^(t/T) = (1/2)^(16/T)
We can simplify this equation by taking the logarithm of both sides:
log[(1/2)^(16/T)] = log(3.0/12)
-(16/T) x log(2) = log(3/12)
-16/T = log(3/12) / log(2)
T = -16 / [log(3/12) / log(2)]
T = 8.0 days
Therefore, the half-life of I-131 is 8.0 days.

A Sample of I-131 Decays from 12 Microcuries to 3