Nuclear physics question

[roam]

Homework Statement

A rock contains three ²⁰⁷Pb nuclei for every ²³⁵U nucleus. Determine the age of the rock assuming all of the ²⁰⁷Pb was formed through the decay of uranium. (The half life of ²³⁵U is 0.71x10⁹).

Homework Equations

N=N₀e^-λt

The Attempt at a Solution

So the decay constant is ln 2/T_1/2=9.76x10^-10. So

N₀ = 1 e^{(9.76x10-10)t}

But the problem is I don't know how to find N₀, the remaining nuclei. How could I find it using the information given? They just say there are 3 Pb's for every uranium nucleus... How do we find the amount decayed so we can subtract it from the total to get the remaining N₀?

 

[SteamKing]

Look at the problem this way: When the rock was formed, there was no Pb-207 present because the U-235 had not begun to decay. In the present, assume that each Pb-207 nucleus resulted from the decay of a U-235 nucleus present at the time of formation. The initial concentration of lead was 0% of the number of U-235 nuclei. By the present time, 3 out of every 4 U-235 nuclei have decayed to Pb-207.

Instead of trying to find how many nuclei existed, find out how long it took for the present ratio of lead to uranium nuclei to be created.

 

[roam]

Look at the problem this way: When the rock was formed, there was no Pb-207 present because the U-235 had not begun to decay. In the present, assume that each Pb-207 nucleus resulted from the decay of a U-235 nucleus present at the time of formation. The initial concentration of lead was 0% of the number of U-235 nuclei. By the present time, 3 out of every 4 U-235 nuclei have decayed to Pb-207.

Instead of trying to find how many nuclei existed, find out how long it took for the present ratio of lead to uranium nuclei to be created.

Thank you 3/4 have decayed so 1/4 left, so that gave me the correct answer. Thanks!