One material used in nuclear bombs is ²³⁹Pu,with a half-life of 24,000 years.How long must we wait for a buried stockpile of this substance to decay to 1/1000 of its original activity?

Question

Quizplus · Accepted Answer

The decay of radioactive materials follows an exponential decay model. The formula for the amount of radioactive material remaining after a certain time t is given by:

N = N0 * (1/2)^(t/T)

where N is the amount remaining, N0 is the initial amount, T is the half-life, and t is the time that has elapsed.

We are given that the half-life of the material is T = 24,000 years. We want to find t such that N/N0 = 1/1000.

1/1000 = N/N0 = (1/2)^(t/24000)

Taking the logarithm of both sides, we get:

log(1/1000) = (t/24000) * log(1/2)

-3 = (t/24000) * (-0.301)

t = 24000 * (-3/-0.301)

t = 240,000 years

Therefore, the answer is B: 240,000 years.

One Material Used in Nuclear Bombs Is 239Pu,with a Half-Life

One Material Used in Nuclear Bombs Is ²³⁹Pu,with a Half-Life