Question

The half-life of cesium-137 is 30 years. Suppose we have a 170 mg sample.(a) Find the mass that remains after t years.(b) How much of the sample remains after 60 years? (Round your answer to two decimal places.)(c) After how long will only 1 mg remain? (Round your answer to one decimal place.)

Answer 1

212.9 years

Explanation:

Given that the half-life of cesium-137 is 30 years. Suppose we have a 170 mg sample

P0 = 175

P(30) = 87.5

So we can write equation as

`P(t) = 170((1)/(2) )^{(t)/(30) }`

b) After 60 years t = 30

In 30 years it becomes half and hence in 60 years it would become 1/4

i.e.
`P(60) = 137(1/2^4) = 34.25` mg

c) If P(t) =1, let us find t

`137(1/2)^{(t)/(30) } =1\\\\n = 7.098 years\\n = 7.1*30 = 212.9 years`

212.9