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.
(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
for a) i meant lower not higher
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.
To answer these questions, we need to understand radioactive decay and how it affects the relative concentrations of the isotopes U-238 and U-235 in natural uranium.
(a) The U-238 percentage in the future will be higher. This is because U-238 has a longer half-life compared to U-235. Over time, U-235 undergoes radioactive decay more rapidly, causing its concentration to decrease relative to U-238. As U-235 decays, it transforms into other elements through a series of decay processes, eventually leading to stable isotopes of lead. On the other hand, U-238 decays at a much slower rate, so its concentration remains relatively stable over long periods.
(b) To determine the relative concentration of U-235 in natural uranium billions of years ago, we need to consider the amount of time that has passed and the half-life of U-235.
Given that the half-life of U-235 is 7.038*10^8 years, if we go back 2.5*10^9 years (2.5 billion years), we need to determine the number of half-lives that have passed during that period. Divide the given time by the half-life:
2.5*10^9 years / (7.038*10^8 years) ≈ 3.56
So, approximately 3.56 half-lives have occurred during this time. Each half-life constitutes a division by two in the concentration of U-235.
Starting with the initial concentration of 0.72% U-235, we divide by 2 for each half-life:
0.72% / (2^3.56) ≈ 0.144%
Therefore, if dinosaurs could measure the relative concentration of U-235 in natural uranium approximately 2.5 billion years ago, they would find a value of about 0.144% for the atom percentage of U-235.
When approaching questions like this, it's helpful to understand the concept of radioactive decay, the half-life of isotopes, and how they impact the relative concentrations over time.