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

Answer:

7.1 x 10^9 years

Explanation:

This is the answer according to Mastering Chemistry.

Answer 2

Answer:

$Age=2.52*10^9 years$

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:

$n_{Pb}=\frac{0.337g}{206g/mol}=0.00164 mol$

$n_{U}=\frac{1 g}{238g/mol}=0.0042 mol$

The percentage of U degradation:

$P=\frac{n_{Pb}}{n_{Pb}+n_{U}}$

$P=\frac{0.00164}{0.00164+0.0042}=0.28$

Assuming that the life time is linear:

$Age=\frac{4.5*10^9 years}{0.5 life time}*0.28 life time$

$Age=2.52*10^9 years$