Please help me solve this

Question

Barium-139 has a half-life of 86 minutes. If we start with a 10 gm sample of Ba-139, how much time will elapse before the remaining amount of Ba-139 is 1 gm?

Answer 1

One sort of simple equation that seems to work for all of these types of problems is the following:

FR = 0.5ⁿ

FR = fraction remaining = 1 gm/10 g = 0.1

n = number of half lives that have elapsed = ?

So if we find the number of half lives needed to have 0.1 remaining, and then multiply that by 86 minutes per half life, we'll have the answer to our question.

0.1 = 0.5ⁿ

log 0.1 = n log 0.5

-1 = -0.301 n

n = 3.32 half lives needed

3.32 half lives x 86 minutes/half life = 286 minutes