The half-life of polonium-218 is 3.0 minutes. If you start with 30.0 g, how long will it be before only 3.0 g remains?

Answer 1

An easy way to do problem like this involving decay and half life is to use the simple formula

FR = 0.5ⁿ

FR = fraction remaining = 3.0 g / 30.0 = 0.1

n = number of half lives that have elapsed = ?

Solving for n, we have

0.1 = 0.5ⁿ

log 0.1 = log 0.5 * n

-1 = -0.301 n

n = 3.32 half lives must elapse to get 0.1 fraction remaining

Converting this to minutes, we have

3.32 half lives x 3.0 minutes/half life = 9.97 minutes = 9.8 minutes