Radiometric dating

There are certain large elements that are radioactive. That means that they decay to form different elements and in the process release particles. The rate of change from one material to the other can be calculated and observed. This is known as the elements half life. It is a measure of the length of time for an element to change half of the mass of the parent element into its daughter elements. The half life of each radioactive element is different, and by studying the quantities of radioactive rocks in the crust the age of the rocks can be calculated. This is known as radiometric dating.

As can be seen, after 713 Million years, half the U²³⁵ has decayed into Pb²⁰⁷. This means by calculating how much Pb²⁰⁷ and U²³⁵ there is in a rock, the amount of original U²³⁵ can be worked out.

The same can be done for each of the above, and for others and they have all agree very closely.

For more details, see radiometric dating - a Christian perspective

Also, thanks to Gallo, the following two links are very good:

Tim Thompson's Radiometric Dating Resource List

the Brookhaven National Laboratory (Table of Nuclides).

Taken from 'Lucy - the beginnings of humankind' by Johansen. The example is one used to help date Lucy. Samples of feldspar crystals were taken from a volcanic tuff above Lucy. The best samples taken still showed tiny levels of weathering, so it was known that a tiny amount of Argon would have leaked from the sample. This meant that the age of the Tuff must be slightly older than the date given by the dating.

1. Measure potassium - this sample contains 1/10 gram of Potassium
2. Calculate annual decay rate. K⁴⁰ decays at 3.5 atoms per second per gram, so it decays at a rate of 110,376,000 atoms per year
   So, 1/10 gram decays at 11,037,600 atoms per year.
3. Boil off sample and residue of air in vacuum.
4. Measure atoms in a mass spectrometer
   Ar⁴⁰ Is very common in the air, Ar³⁶ is not. In order to differentiate between the radiogenic Ar⁴⁰ from the sample and the Ar⁴⁰ from the air it is necessary to find out the level of Ar³⁶ that is only found in air:
   
   36,765,875,000,000 Atoms of Ar⁴⁰ from air and sample
   27,070,000,000 Atoms of Ar³⁶ from air
5. Eliminate the argon from the air.
   It is known that the ratio of Ar⁴⁰ to Ar³⁶ in the atmosphere is 295.5:1, so
   27,070,000,000 X 295.5 = 79,918,500,000 - Contaminant Ar⁴⁰
   36,765,875,000,000 - 79,918,500,000 = 28,774,025,000,000 - Argon from sample
6. Calculate age
   28,774,025,000,000 = 2,606,909.5
   11,037,600
   
   So, age of sample = 2.6 Million years old

Fission Track dating

Slightly less reliable than radiometric dating, but still very useful, especially if a lot of contamination is expected and as a confirmation of other dating methods. fission track dating is a way of taking a crystal of Zircon and counting the number of traces of nuclear decay of Uranium in it. Every time an atom of Uranium decays, it releases energy in a tiny explosion, and this leaves a tell tale track in the Zircon. A direct count of these gives a good indicator of age.

 Isochron dating

Rubidium⁸⁷ à Strontium⁸⁷ 1/2 life = 4.8 BY

Based on decay of Rb ⁸⁷ Into Sr ⁸⁷

Rb ⁸⁷ Sr ⁸⁷
Non radiogenic Sr (Sr ⁸⁴, Sr ⁸⁶, Sr ⁸⁸)
As time goes by ratio of Rb ⁸⁷ à Sr ⁸⁷ increases
And ratio of Sr 87 à Sr ⁸⁴, Sr ⁸⁶ & Sr ⁸⁸ increases
Other minerals in same rock will have same ratio of Sr ⁸⁴à Sr ⁸⁶ à Sr ⁸⁸ but different ratio of Sr ⁸⁷ à Sr ⁸⁴
But this ratio will change in proportion to Rb ⁸⁷ Sr ⁸⁷.
These ratio's plotted together will give a straight line, and any contamination will be off this line.

Carbon 14 dating applicable for 50,000 years