Question

You are dating Moon rocks based on their proportions of uranium-238 (half-life of about 4.5 billion years) and its ultimate decay product, lead.
1. Find the age for a rock for which you determine that 55% of the original uranium-238 remains, while the other 45% has decayed into lead.

2. Find the age for a rock for which you determine that 68% of the original uranium-238 remains, while the other 32% has decayed into lead.

Answer 1

1. Use the formula:

$-kt = ln[\frac{FinalAmount}{InitialAmount}]$

$k = ln2 / half-life$

So, $t = - \frac{4.5}{ln2} \times ln[\frac{0.55}{1}]$

t =  3.8 billion yr

2.  Same formula:

$t = - \frac{4.5}{ln2} \times ln[\frac{0.63}{1}]$

t = 2.93 billion yr.