Half-Lives and Radioactivity

Question

50.0mg of potassium-45 was isolated in pure form. After one hour, only 3.125mg of the radioactive material was left. What is the half-life of potassium-45?

Answer 1

You can use the following rather simple formula to solve this, and other similar problems.

Fraction remaining = 0.5ⁿ where n = number of half lives that have elapsed.

Here, we will solve for n

fraction remaining = 3.125 mg/50.0 mg = 0.0625

0.0625 = 0.5ⁿ

log 0.0625 = log 0.5 n

-1.20 = -0.301 n

n = 4 half lives have elapsed

Since this took 1 hour, each half live = 1/4 hour = 15 minutes