Question

1) 239Pu has a half-life of 24000 years.

If we have 10 g of 239Pu, how many grams will be left after 75000 years?
Answer in units of g.

2) The half-life of 137Ce is 30 years.
How many grams of 137Ce must be produced now to have a sample containing 37 g of 137Ce 160 years from now?
Answer in units of g.

Answer 1

1)

`1.2 \; \text{g}`

There are
`75000/24000 = 25/8 = 3.125` half lives in a period of 75,000 years. The sample of plutonium-239 would thus expect a loss in mass that would results in a mass ratio of
`(1/2)^(25/8)` which is the same as
`2^(-25/8) \approx 0.12` relative to the initial mass.
`0.12 * 10 \; \text{g} = 1.2 \; \text{g}` of plutonium-239 would thus remain in the initial
`10 \; \text{g}` sample after 75,000 years.

2)

`1.5 * 10^(3) \; \text{g}`

There are
`160/30 = 16/3 \approx 5.3` half lives in 160 years.

`\text{mass remaining in 160 years} / \text{initial mass} = (1/2)^(160/30) \approx 2.5 * 10^(-2)`

Thus

`\text{initial mass} = 37 \; \text{g} / (2.5 * 10^(-2))= {\text{initial mass} } \approx 1.5 * 10^(3) \; \text{g}`