The half-life of polonium-218 is 3.0 minutes. If you start with 50.0 g, how long will it be before only 2.6 g remains?

Answer 1

An easy way to solve this problem is by using the simplified equation F = 0.5ⁿ

F = fraction remaining

n = number of half lives that have elapsed

F (fraction remaining) = 2.6 g / 50.0 g = 0.052

Now we can solve for n (the number of half lives that have elapsed)

0.052 = 0.5ⁿ

log 0.052 = log 0.5 n

-1.28 = -0.301 n

n = 4.25

So 4.25 half lives have elapsed, and each half life is 3.0 minutes.

Total time = 4.25 half lives x 3.0 minutes/half life = 12.8 minutes = 13 minutes (2 sig. figs.)