The half-life for the process 238 U --> 206 Pb is 4.5*10^9 yr. A mineral sample contains 66.0 mg of 238 U and 16.0 mg of 206Pb. What is the age of the mineral?

Answer 1

mass U-238 originally is mass Pb x (238/206) = 16.0 x (206/238) = about 13.8 but you need to get a more accurate answer.
mass U-238 initially = 66 mg + 13.8 = about 80.
k = 0.693/t_1/2 - 0.693/4.5E9 = 1.5E-10(approx)

Substitute these values into the first order equation below and solve for t (in years).
ln(No/N) = kt
No = about 80
N = 66
k from above.
t = unknown.

All of the numbers above are estimates. You should go through and confirm everything.