Radioactivity and geochronology

Geochronology: the determination of the time of geological events using radioactivity.

Radioactivity is the spontaneous change in the nuclear structure of an atomic nucleus usually accompanied by emission of subatomic particles and/or ionising radiation.

radioactive decay types

Radioactive decay is an attempt by a nucleus to reach the lowermost parts of a “valley of beta-stability”.

valley of beta stability

As protons have positive electrical charge and thus, repel each other, a nucleus would blow apart if the protons and neutrons weren’t “glued” together by the force-carrying gluon particles, which carry the “strong nuclear force”.

According to the Standard Model, neutrons and protons are each composed of three quarks; a neutron consists of 1 up-quark with 2 down-quarks (udd), whereas a proton consists of 2 up-quarks with 1 down-quark (uud).

The strong nuclear force binds quarks together because quarks have color charge. This attractive force opposes the repulsive electrical forces of the protons within the atomic nucleus. The valley of beta-stability is the locus along which the attractive forces acting on quarks within the nucleons are optimised against the repulsive electrical forces of the positively-charged protons.

When a neutron (udd) decays by beta-decay to a proton (uud), a down-quark converts to an up-quark releasing an electron and antineutrino. This reaction is known as a “quark flavor change”. As a result of the decay, the nucleus moves closer to the bottom of the valley of beta-stability.

Protons and neutrons can also migrate around within a nucleus and there is a small probability that two protons and two neutrons (forming a very stable alpha particle) can migrate outside the nucleus, resulting in alpha-decay.

During radioactive decay, the rate of change of the number of parent atoms is proportional to the number of atoms present.

radioactive decay law
Integrating over the total time t gives the following:

law of decay 2

Because we can’t measure parent atoms that have decayed, we need to express this in terms of daughter atoms, which we can measure. Number of daughter atoms formed is equal to number of parent atoms consumed, so:

law of decay 3

The above equation is fundamental to all geochronology methods using radioactive decay. The equation can be rearranged to solve for t. Rather than using absolute abundances, the equation is usually modified to refer to ratios of parent or daughter to a stable isotope, as such ratios are far easier to determine accurately (using a mass spectrometer) compared to absolute abundances.

The radioactive decay rate is not significantly effected by physical conditions commonly encountered on Earth.  The radioactive half-life provides an estimate of the time scale over which the decay scheme may be applied.

half life

In the Earth Sciences, the concept of a “date” has many meanings.  For example, what would a date obtained on a multiphase gneiss (composed of many igneous and sedimentary phases) that has been completely recrystallized to a metamorphic mineralogy, mean?  For radiometric dating methods, a date obtained usually relates to the last parent-daughter fractionation event (e.g. last event that has redistributed the parent 87Rb relative to its daughter 87Sr).  The chemical behaviour of the parent and daughter elements therefore determines what event the radiometric system can be used to date.