14 C has a half-life of 5730 years. If there are 1000 g of 14C initially, how much will be left after 17, 190 years?

Question

jfraser · Answer

if one half-life is 5730 years, how many half-lives will pass over 17,190?

anonymous · Answer

The ratio of the left-over stuff (to the original), or n/n0 is (1/2)^(time period/half life). in this case:

amount remaining / original amount = (1/2)^(17190 yr/5730 yr)
so amount remaining = 1000 grams * (1/2)^(17190 yr/5730 yr)

anonymous · Answer

I also got 1000 but 1000 isn't on the choices

aaronq · Answer

hm you can reason these out, but i like to do them mathematically...

(These formulas only apply for first order reactions btw)

find k, the decay constant, using: $$t _{1/2}=\frac{ \ln2 }{ k }$$

the substitute into the exponential decay/growth formula:

$$A=A _{0}e ^{-kt}  $$

t = time elapsed (in terms of half lives)
Ao=initial amount (in this case 1000g)
A= amount left over after time elapsed (your answer)

anonymous · Answer

Oh noo! We haven't learned that one... I'm having problems with Chemistry. :( Our teacher had discussed only up to Moles. :((((

aaronq · Answer

what i wrote is grade 11 math, maybe grade 12.. if you can't do that then apply what the person above me wrote:

1000 grams * (1/2)^(17190 yr/5730 yr)

anonymous · Answer

I got it already. Thanks.

aaronq · Answer

good stuff, close the question