Chemistry
posted by Jay on .
A rock containing 238U and 206Pb was examined to determine its appropriate age. The molar ratio of 206Pb to 238U was 0.1462. Assuming no lead was originally present and that all lead formed remained in the rock. What is the age of the rock in years? The half life of 238U is 4.500*10^9yr

Let's start with 100 atoms of U238. Suppose x atoms of U238 decompose to Pb. Then there must be 100x atoms U238 not yet decomposed. We know the ratio is 0.1462; therefore,
(x/100x) = 0.1462 and solve for x which is the amount of Pb formed and 100x is the amount of U left.
So No = 100 and N = 100x, whatever that value is. Substitute into
ln(No/N) = kt
You know No and N. You want to find t. k = 0.693/t_{1/2} and you have the half life. Solve for k and substitute into the equation above. 
Thank you so much DrBob222. You are the best