# Does the natural abundance of radioactive elements change?

Given that the half-lives differ between isotopes of a particular radioactive element, wouldn't the natural abundance change (fairly rapidly)?

For example, if we isolated a bunch of thorium, wouldn't the relative amount of the various isotopes of thorium in the sample differ over time, with the more slowly decaying isotope eventually making up the largest proportion?

Yes, you are right. The abundances of (radioactive and stable) nuclides change due to radioactive decay.

Regarding this, most environmental radionuclides can be divided into four categories:

Cosmogenic radionuclides are constantly produced by cosmic irradiation of the atmosphere. Therefore, their average concentrations in the atmosphere stay roughly constant even if their half-lives are short.

Primordial radionuclides have lifetimes comparable to the age of the earth. These nuclides have been formed at the time of the formation of the earth, the solar system, or even before. Their abundance is slowly decreasing due to radioactive decay. Therefore, the radiation exposure was higher some billion years ago when life evolved on earth than today. Furthermore, due to different half-lives, the relative abundance of these nuclides (e.g. the natural $\ce{^{235}U/^{238}U}$ isotopic ratio) also changes.

Radionuclides that are part of the natural decay chains of $\ce{^{238}U}$, $\ce{^{235}U}$ and $\ce{^{232}Th}$ are constantly reproduced by the radioactive decay of their mother nuclides. Therefore, their abundance is only slowly decreasing with the long half-life of $\ce{^{238}U}$, $\ce{^{235}U}$, or $\ce{^{232}Th}$ even if their own half-lives are short (this situation is called secular equilibrium).

Anthropogenic radionuclides are produced by modern technology. Since the discovery of nuclear fission, the activity concentrations of various anthropogenic radionuclides in the environment were increasing until the limited nuclear-test-ban treaty banned atmospheric tests of nuclear weapons. After that, the activity concentrations of most anthropogenic radionuclides decreased again.

If you isolate and chemically purify a radioactive sample, you remove any other mother or daughter nuclides and thus you disturb any decay chain or radioactive equilibrium. Thereby you start a radioactive clock.

For example, a solid rock sample may contain $\ce{^{226}Ra}$ $\left(t_{1/2}=1600\ \mathrm{a}\right)$ and its daughter nuclide $\ce{^{222}Rn}$ $\left(t_{1/2}=3.83\ \mathrm{d}\right)$ in a secular equilibrium. If you dissolve the sample and release the $\ce{^{222}Rn}$ (radon is a noble gas), the released $\ce{^{222}Rn}$ decays with its half-life of 3.83 days. If you purify the $\ce{^{226}Ra}$ and put it in a closed container, initially the container does not contain any $\ce{^{222}Rn}$, but new $\ce{^{222}Rn}$ is produced by radioactive decay of $\ce{^{226}Ra}$.

A similar thing occurs when natural minerals solidify. Radionuclides become trapped and decay. As they decay, decay products accumulate in the closed mineral.

By measuring the amount of mother and daughter nuclide, it is possible to calculate how long this sample has existed. This is the basis for nuclear dating.

If you isolate a sample that contains multiple radionuclides of the same chemical element, you can observe changing isotopic ratios – as you have expected in your question.

Your example, freshly purified thorium from a natural sample, mainly contains six different thorium nuclides:

$\ce{^{234}Th}$ $\left(t_{1/2}=24.10\ \mathrm{d}\right)$
$\ce{^{232}Th}$ $\left(t_{1/2}=1.405\cdot10^{10}\ \mathrm{a}\right)$
$\ce{^{231}Th}$ $\left(t_{1/2}=25.5\ \mathrm{h}\right)$
$\ce{^{230}Th}$ $\left(t_{1/2}=7.54\cdot10^{4}\ \mathrm{a}\right)$
$\ce{^{228}Th}$ $\left(t_{1/2}=1.91\ \mathrm{a}\right)$
$\ce{^{227}Th}$ $\left(t_{1/2}=18.7\ \mathrm{d}\right)$

The individual half-lives differ significantly; thus, the different thorium nuclides decay at different rates. The isotopic ratios change accordingly.
However, the calculation is slightly complicated since $\ce{^{234}Th}$ indirectly decays to $\ce{^{230}Th}$, $\ce{^{231}Th}$ indirectly decays to $\ce{^{227}Th}$, and $\ce{^{232}Th}$ indirectly decays to $\ce{^{228}Th}$.

Yes, you are correct; over time the proportion of the more stable isotopes (those with longer half-lives) increases. There can be alterations to this tendency if a less stable isotope happens to be continually replenished by the decay of a heavier element.

There is some very interesting physical proof of this. Consider uranium, whose dominant naturally-occurring isotopes are $\ce{^{238}U}$ and $\ce{^{235}U}$, with respective half-lives of $\mathrm{4.47\times 10^9\ yr}$ and $\mathrm{7.8\times 10^8\ yr}$. Currently, the uranium on Earth is composed of approximately 99.3% $\ce{^{238}U}$ and 0.7% $\ce{^{235}U}$. Given that $\ce{^{235}U}$ decays faster, we expect that in the distant past there was a higher proportion of $\ce{^{235}U}$ than we find now. Indeed that is the case - billions of years ago, the fraction of $\ce{^{235}U}$ in natural uranium was as high as 3%. It turns out that, due to its fissile nature, this concentration of $\ce{^{235}U}$ was high enough to sustain natural nuclear fission reactors. Nowadays, natural uranium contains too little of the fissile isotope to spontaneously form underground nuclear reactors, and so enrichment techniques must be used to obtain fissile uranium fuel, containing a higher proportion of $\ce{^{235}U}$.