Isotopic ratio

In physics, natural abundance (NA) refers to the abundance of isotopes of a chemical element as naturally found on a planet. The relative atomic mass (a weighted average, weighted by mole-fraction abundance figures) of these isotopes is the atomic weight listed for the element in the periodic table. The abundance of an isotope varies from planet to planet, and even from place to place on the Earth, but remains relatively constant in time (on a short-term scale).

As an example, uranium has three naturally occurring isotopes: ²³⁸U, ²³⁵U and ²³⁴U. Their respective natural mole-fraction abundances are 99.2739–99.2752%, 0.7198–0.7202%, and 0.0050–0.0059%. For example, if 100,000 uranium atoms were analyzed, one would expect to find approximately 99,274 ²³⁸U atoms, approximately 720 ²³⁵U atoms, and very few (most likely 5 or 6) ²³⁴U atoms. This is because ²³⁸U is much more stable than ²³⁵U or ²³⁴U, as the half-life of each isotope reveals: 4.468 × 10⁹ years for ²³⁸U compared with 7.038 × 10⁸ years for ²³⁵U and 245,500 years for ²³⁴U.

Exactly because the different uranium isotopes have different half-lives, when the Earth was younger, the isotopic composition of uranium was different. As an example, 1.7 billion years ago the NA of ²³⁵U was 3.1% compared with today's 0.7%, and for that reason a natural nuclear fission reactor was able to form, something that cannot happen today.

However, the natural abundance of a given isotope is also affected by the probability of its creation in nucleosynthesis (as in the case of samarium; radioactive ¹⁴⁷Sm and ¹⁴⁸Sm are much more abundant than stable ¹⁴⁴Sm) and by production of a given isotope as a daughter of natural radioactive isotopes (as in the case of radiogenic isotopes of lead).

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