Question

In the last question, I measured 1000 atoms of U-235 (parent) and 3000 atoms of Pb-207 (daughter) in a mineral. If the half life of U-235 is 700 million years, then how old is the mineral? If the mineral came from an igneous rock, then how old is the rock?

Answer 1

1400 millon years, it is probable that if the mineral came from igneous rock, ithe rock age would be the same. There were active volcanoes 1400 year ago in proterozoic era.

Step-by-step explanation:

Lifetime of radiactive compound is calculated with

`ln((N_t)/(N_0))=-kt` with
`N_t:` mass at time t,
`N_0:` original mass,
`k:` decay constant.

So we know that when 700 millon years pass, the half of original material decays (
`(N_t)/(N_0))=0.5`. With that information we can know k.

`ln(0.5)=-k*700` so,
`k=-ln(0.5)/700=0.00099`

With k, the actual and original quantity of material we can know how old is the rock:

`t=-ln((N_t)/(N_0))/k` so,
`t=-ln((1000)/(4000))/0.00099=1400 millon years`

([text]N_0=1000+3000[/text] is the actual quantity plus the quantity that decays to Pb-207)