If we ignore the small fraction of U-234, natural uranium has a concentration of 99.28 atom% of U-238 and 0.72% U-235. Their half-lives are, respectively, 4.68*109 and 7.038*108 years.

Question

(a) In the future, will the U-238 percentage be higher or lower?
(b) In Oklo, Gabon, Africa, a fission reactor was operating naturally (on its own) billions of years ago. So, for example, say 2.5*109 years ago, if dinosaurs could measure the relative concentration of U-235 in the natural uranium of the time, what value would they find for the atom percentage of U-235?

s) it would be higher because it undergoes decay right?
b) I don't know how to even start this question

Answer 1

for a) i meant lower not higher

Answer 2

a. Won't the 238 percent be higher in the future? If the half life of 235 is not quite 10 times faster (10^8 for 235 and 10^9 for 238) so 235 is decaying faster which means percent 238 is increasing.

b. I did this. If we start with 100 atoms today, then 99.28 of them are 238 and 0.72 of them are 235 (I know we can't split atoms (we really can split U235 can't we) and have 0.72 of an atom but in math we can). So what would the 99.28 and 0.72 be 2.5E9 years ago?
k for U235 = 0.693/7.038E8 = 9.85E-10
k for U238 = 0.693/4.68E9 = 1.48E-10

ln(No/N) = kt
For 238 we have
ln(No/99.28) = 1.48E-10*2.5E9
I get No = 143.7 but you should confirm that.
For 235 we have
ln(No/0.72) = 9.85E-10*2.5E9
I get No = 8.45.

So 2.5E9 years ago we would have had 143.7 atoms of 238 and 8.45 atoms of 235. The total is about 152 or so and
%238 = (143.7/152)*100 = ?
and %235 = (8.45/152)*100 = ?
Check my work. I've estimated here and there. But I believe this shows, too, that the answer for a is higher. 2.4E9 years ago the 238 was a lower percentage than it is today. It's increasing because the 235 is decaying faster than it is.