As the isotopes decay, they give off particles from their nucleus and become a different isotope.
The parent isotope is the original unstable isotope, and daughter isotopes are the stable product of the decay. In the first 5,730 years, the organism will lose half of its C-14 isotopes.
Many rocks and organisms contain radioactive isotopes, such as U-235 and C-14.
These radioactive isotopes are unstable, decaying over time at a predictable rate.
So accurate determinations require very pure samples, very accurate and selective detectors, or both.
Integrating both sides, we get: ln N(t) = -Kt C C is the constant of integration that we can often ignore, but not here.
When t = 0, ln N(0) = C Taking exponentials of both sides, we get N(t) = N(0)exp(-Kt) If t = one half life, then N(t)/N(0) = 1/2 = exp(-Kt), and: ln(1/2) = -ln2 = -Kt, so t = ln2 / K So what we do in practice is determine the decay constant and calculate half life from it.
If the mineral contained 1 part per million Parentium-123 and 3 parts per million Daughterium-123, we could be sure all the Daughterium-123 was originally Parentium-123.
In other words there was originally 4 parts per million Parentium-123 and 0 parts per million Daughterium-123.