Radiochemical dating and radioactive isotopes
Secular equilibrium is approached as the rate of loss (through decay) of the daughter comes to equal the rate of loss of the parent.Radioisotope ratios in whole otoliths can be interpreted if some rather problematic assumptions can be met.Knowing, for example, that the decay constant for \(\ce\) is 0.0247 yr does not give an immediate sense of how fast it disintegrates.On the other hand, knowing that its half-life is 28.1 y makes it clear that the concentration of \(\ce\) in a sample remains essentially constant over a short period of time.Therefore, this approach is best suited to species where the candidate age interpretations are widely divergent, such as in Sebastes or Hoplostethus. Examples of radiochemical dating as applied to age validation in temperate and tropical species are presented in Campana et al.
The most important difference between isotopes is their stability.
The nuclear configuration of a stable isotope remains constant with time.
Unstable isotopes, however, spontaneously disintegrate, emitting radioactive particles as they transform into a more stable form.
For first-order kinetics the half-life is \[t_ = \dfrac\label\] Because the half-life is independent of the number of radioactive atoms, it remains constant throughout the decay process.
For example, if 50% of the radioactive atoms remain after one half-life, then 25% remain after two half-lives, and 12.5% remain after three half-lives.