An isotope of a radioactive element has half-life equal to 9 thousand years. Imagine a sample that is so old that most of its radioactive atoms have decayed, leaving just 10 percent of the initial quantity of the isotope remaining. How old is the sample? (Give your answer correct to at least one decimal place.)

Question

Mathematics

Arely Lowery

15 March, 22:44

An isotope of a radioactive element has half-life equal to 9 thousand years. Imagine a sample that is so old that most of its radioactive atoms have decayed, leaving just 10 percent of the initial quantity of the isotope remaining. How old is the sample? (Give your answer correct to at least one decimal place.)

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Easton Castro · Answer 1

For this problem, we use the formula for radioactive decay which is expressed as follows:

An = Aoe^-kt

where An is the amount left after time t, Ao is the initial amount and k is a constant.

We calculate as follows:

An = Aoe^-kt

0.5 = e^-k (9000)

k = 7.7 x 10^-5

An = Aoe^-kt

.10 = e^ - 7.7 x 10^-5 (t)

t = 29903.7 years