Question

This question has been bugging me for a long time. A rock contains a Pb-206 to U-238 mass ratio of .145 to 1.00. Assuming that it did not contain any Pb-206 at the beginning of its formation, determine its age.
I assume from the other problems in my book that the 1/2 life is 4.5x10^9. This is what is being used for U-238

I am getting
1.145/1.00=1.145
log 1.145/.3010 =.195
4.5 x 10^9 x .195=8.79x10^8 but the book says 1.0x10^9. I have tried many different methods of coming up with 1.0x10^9 and I am unable to get this answer. Can anyone shed light on it? Any help is greatly appreciated

Answer 1

The problem gives a MASS ratio and not an atom ratio; therefore, you must convert mass Pb to mass U. The mass ratio is 0.145; therefore, the atom ratio is 0.145*(238/206) = 0.1675.
You can start with any number; I chose 100.
........U ==> Pb
I......100.....0
C.......-x.....x.
E......100-x...x
(x/100-x) = 0.1675
x = 14.3 and 100-x = 85.6
ln(100/85.6) = 1.54E-10*t
t = 1E9 yrs.
You can clean up the number of significant digits etc.