# Nuclear physics question

• roam
In summary, the problem is to determine the age of a rock based on the ratio of Pb-207 to U-235 nuclei. By assuming that each Pb-207 nucleus resulted from the decay of a U-235 nucleus present at the time of formation, and that the initial concentration of lead was 0%, the present ratio of 3 Pb-207 to 4 U-235 nuclei can be used to calculate the time it took for the remaining 1/4 of U-235 nuclei to decay, giving the age of the rock.

## 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).

N=N0e-λt

## The Attempt at a Solution

So the decay constant is ln 2/T1/2=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? 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.

SteamKing said:
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! 