Radioactive Dating of Rocks

Looking at the Moon's surface we have used relative terms ("older" and "younger") to describe the various regions of the Moon. How can we assign absolute ages to the lunar surfaces? And what would this tell us about the conditions in the early solar system?

Radioactive Dating

Use the fact that many elements have radioactive isotopes, that is, unstable forms of the element which radioactively decay (change) into other forms. For example Rubidium into Strontium:

The rate at which the atoms decay is given in units of inverse seconds:

So we can define the rate of change of the abundances of an isotope as

Or, shuffling terms,

So let's integrate this. at t=0, there was some initial abundance N_0 of the isotope in the rock. At the present time t, the abundance is N. So integrate like this:

We get

Or, finally

Lets define the half-life of a radioactive isotope to be the time it takes for half of it to go away:

Different decays have different half-lives:

Decay	Half Life
(129)Iodine to (129)Xenon	16 million years
(235)Uranium to (207)Lead	700 million years
(40)Krypton to (40)Argon	1.28 billion years
(238)Uranium to (206)Lead	4.47 billion years
(232)Thorium to (208)Lead	14.0 billion years
(87)Rubidium to (87)Strontium	47.5 billion years

How do we use this to age date rocks (from Earth or Moon)?

Pick up a rock.
Measure the amount of (87)Rubidium in it.
Calculate an age!

Is it really that easy? Nope... why not???