Half-Life

An illustration for the half-life of an unspecified nucleus undergoing radioactive decay. Artwork: NaturPhilosophie with AI

The half-life t1/2 is the time required for a quantity to reduce to half its initial value.  It describes how quickly unstable atoms undergo, or how long stable atoms survive, radioactive decay.

However, the half-life usually describes the decay of discrete entities.

A half-life period is defined in terms of probability.

A table listing the half-life of isotopes used in Surface Exposure Dating: Tritium, Beryllium-10, Carbon-14, Fluorine-18, Aluminium-26 and Chloride-36.

The radioactive decay equation is

N(t)=N_0 (\frac{1}{2})^{\frac{t}{{t^{1/2}}}}

or

N(t)=N_0 e^-{\lambda t}

where

N_0 is the initial number of nuclei,

\lambda is the decay constant,

t is the time elapsed and

e is Euler’s number (~ 2.718).

The basic principle is that isotopes/radionuclides are produced at a known rate and also decay at a known rate.

The half-life formula is then

t^{1/2} = \frac{ln_2}{\lambda}

The larger the decay constant \lambda the shorter the half-life.

Accordingly, measuring the concentration of these cosmogenic nuclides in a rock sample and accounting for the flux of the cosmic rays and the half-life of the nuclide, makes it possible to estimate how long the sample has been exposed to the cosmic rays.