Question

A geological sample is found to have a Pb-206/U-238 mass ratio of 0.337/1.00. Assuming there was no Pb-206 present when the sample was formed, how old is it? The half-life of U-238 is 4.5 × 109 years.

Answer 1

7.1 x 10^9 years

Step-by-step explanation:

This is the answer according to Mastering Chemistry.

Answer 2

`Age=2.52*10^9 years`

Step-by-step explanation:

To determine the age, we need to know how much U have become Pb, so first we have to calculate the Pb moles present in a sample:

`n_(Pb)=(0.337g)/(206g/mol)=0.00164 mol`

`n_(U)=(1 g)/(238g/mol)=0.0042 mol`

The percentage of U degradation:

`P=(n_(Pb))/(n_(Pb)+n_(U))`

`P=(0.00164)/(0.00164+0.0042)=0.28`

Assuming that the life time is linear:

`Age=(4.5*10^9 years)/(0.5 life time)*0.28 life time`

`Age=2.52*10^9 years`