A 2,000g of c-14 is left to decay radioactively. the half-life of carbon-14 is approximately 5,700 years. what fraction of the sample will remain after 17,100 years?

Question

Physics

Jacob Lane

22 May, 01:37

A 2,000g of c-14 is left to decay radioactively. the half-life of carbon-14 is approximately 5,700 years. what fraction of the sample will remain after 17,100 years?

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Gregory Strickland · 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 (5700)

k = 1.22x10^-4

An = Aoe^-kt

An = 2000 e^-1.22x10^-4 (17100)

An = 248 g left