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Samarium-neodymium (Sm-Nd) dating is a process for determining the ages of rocks based on the radioactive decay of two samarium isotopes (Sm-147 and Sm-146) to two neodymium isotopes (Nd-143 and Nd-142 respectively).
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The main challenge of Sm-Nd dating is accurately determining the ratios between the different isotopes of neodymium, specifically Nd-144: Nd-143 and Nd-144: Nd-142.
Nd-144 is a naturally-occurring isotope of neodymium and so its relative abundance compared with the two isotopes produced by the radioactive decay of samarium can reveal the extent of that decay.
The energies involved are so large, and the nucleus is so small that physical conditions in the Earth (i.e. The rate of decay or rate of change of the number N of particles is proportional to the number present at any time, i.e.
The half-life is the amount of time it takes for one half of the initial amount of the parent, radioactive isotope, to decay to the daughter isotope.
When combined with data on the precise concentration of samarium and neodymium in the rocks, this can reveal their age.