Question

A sample of Francium-212 will decay to one sixteenth of its original amount after 80 minutes. What is the half-life of Francium-212.

Answer 1

20 minutes.

The sample would lose one half the quantity of francium in each half-life.

$1/16 = 1/2^{4} = 1/2 \times1/2 \times1/2 \times1/2$

Thus a mass decrease by a factor of 16 would correspond to a period of four half-lives. It took 80 minutes for the sample to lose all these francium, therefore

$t_{1/2} = 80/4 = 20$ minutes.