A rock contains 200. µmol 238U (t1/2 = 4.5 109 yr) and 116 µmol 206Pb. Assuming that all the 206Pb comes from decay of the 238U, estimate the rock's age.

Question

Please explain step by step.

Answer 1

I would do this.
Take the ratio of moles U/moles Pb which is 200/116 = 1.72
Suppose we start with 100 atoms U, then X of them will decay to form Pb and 100-X will remain.
U/Pb = (100-X/X) = 1.72 and solve for X. I get something like 63 but that's an estimate and you need to recalculate it.
Then k = 0.693/t_1/2 and substitute below.
ln(No/N) = kt
Use 100 for No
Use 63 (the more accurate number you get from above).
k from above
Solve for t in years.

Answer 2

I don't understand the part when it says 100-X/X. How do you solve for X?

Answer 3

Cross multiply.
100-X = 1.72X and go from there.

Answer 4

where are you getting that k value from? if you look at the half life of U i calculated it to be 1.5e-10