half-life equation

Question

The half-life of cesium-137 is 30 years. Suppose that we start with 90 grams of cesium-137 in a storage pool.

How many half-lives will it take for there to be 10 grams of cesium-137 in the storage pool? (Round your answer to two decimal places.)
_______half-lives

How many years is that? (Round your answer to one decimal place.)
_______yr

Answer 1

90 grams to 10 grams with half life = 30 years

year grams

0 90

30 45

60 22.5

90 11.25

120 5.625

10 grams occurs at a little over 90 years, = a little over 3 half lives

A = 90e^rt

1/2 = e^30r, r= annual decay rate

ln.5 = 30r

r = (ln.5)/30

10 = 90e^(t/30)(ln.5)

ln(1/9) = (ln.5)(t/30)

t/30 = (ln(1/9)/ln.5

t = 30ln(1/9)/ln.5 =about 95.098 years to decay to 10 grams

95.098/30 = number of half lives = about 3.170