1. ## Half-Life

The oldest moon rocks that have been found are about 4.4 billion years. One of the bases for this claim is based on the fact that 92$\displaystyle U^{238}$ ultimately decays via a chain of individual decay steps into 82$\displaystyle Pb^{206}$ with a half-life of about 4.8 billion years and each one of the oldest moon rocks all contain a total amount of 92$\displaystyle U^{238}$ and 82$\displaystyle Pb^{206}$ in the relative amount of about _____%.

(a) 25 & 75, (b) 50 & 50, (c) 53 & 47, (d) 75 & 25, (e) 87.5 & 12.5

I'm not sure how to solve this...

2. Originally Posted by viet
The oldest moon rocks that have been found are about 4.4 billion years. One of the bases for this claim is based on the fact that 92$\displaystyle U^{238}$ ultimately decays via a chain of individual decay steps into 82$\displaystyle Pb^{206}$ with a half-life of about 4.8 billion years and each one of the oldest moon rocks all contain a total amount of 92$\displaystyle U^{238}$ and 82$\displaystyle Pb^{206}$ in the relative amount of about _____%.

(a) 25 & 75, (b) 50 & 50, (c) 53 & 47, (d) 75 & 25, (e) 87.5 & 12.5

I'm not sure how to solve this...
The half life is 4.8 billion years which is slightly more than the age of the moon given. Therefore by inspection C is correct as they will be close but not equal

If you want to show it mathematically for Pb-206:

$\displaystyle 0.5 \times \frac{4.4}{4.8} \times 100\%$