Isotopic abundance

Relative abundance of elements in the Earth's upper crust

In physics, isotopic abundance is the amount of one particular isotope of a chemical element as a fraction of all the atoms in that element in a sample. In a sample representing the naturally occurring isotopes, it is called the natural isotopic abundance, or natural abundance (NA) when the context is clear. 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 billion 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 that allowed a natural nuclear fission reactor 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).

Standards body

The Commission on Isotopic Abundances and Atomic Weights (CIAAW) part of the International Union of Pure and Applied Chemistry (IUPAC) compiles and publishes tables of isotopic abundance. These tables provide data for standard atomic weights also published by this commission. They report data derived from normal material which they define as

“The material is a reasonably possible source for this element or its compounds in commerce, for industry or science; the material is not itself studied for some extraordinary anomaly and its isotopic composition has not been modified significantly in a geologically brief period.”

Experimentally the isotopic abundance in different samples of normal material varies and as a consequence the commission reports a range of values called intervals for the isotopic abundance. The latest report was published in 2013.

Relation to relative atomic mass

The average mass of an atom of an element is the result of averaging over each isotope mass, weighted by its abundance in a material. The relative atomic mass (aka atomic weight) is the average mass expressed as a ratio to the atomic mass unit, $1/12$ the mass of ¹²C. This atomic weight ($A$) in any given material ($P$) is derived from the isotopic abundances of that element ($E$) in the material via $$A(E)=\sum _{i}x_{P}(^{i}E)A(^{i}E)$$ where $x_{P}(^{i}E)$ is the isotopic abundance of the isotope $^{i}E$ in the material. When applied to normal terrestrial material (as defined by CIAAW), the result is called the standard atomic weight. The sum runs over all the stable isotopes of an element and any radioactive isotopes with long half-lives which normally appear in measurements.

Measuring differences

Main article: Isotope analysis

High precision measurements of isotopic abundance is difficult due to instrumental fluctations over time. Consequently analytic applications of isotopic abundance measure isotopic ratios as differences from a standard sample measured at the same time. For example, Vienna Standard Mean Ocean Water is distilled ocean water distributed by the International Atomic Energy Agency in Vienna, Austria. These measurements are widely used in many fields including geochemistry and archaeology.

Deviations from natural abundance

It is now known from study of the Sun and primitive meteorites that the Solar System was initially almost homogeneous in isotopic composition. Deviations from the (evolving) galactic average, locally sampled around the time that the Sun's nuclear burning began, can generally be accounted for by mass fractionation (see the article on mass-independent fractionation) plus a limited number of nuclear decay and transmutation processes. There is also evidence for injection of short-lived (now-extinct) isotopes from a nearby supernova explosion that may have triggered solar nebula collapse. Hence deviations from natural abundance on Earth are often measured in parts per thousand (per mille or ‰) because they are less than one percent (%).

An exception to this lies with the presolar grains found in primitive meteorites. These small grains condensed in the outflows of evolved ("dying") stars and escaped the mixing and homogenization processes in the interstellar medium and the solar accretion disk (also known as the solar nebula or protoplanetary disk). As stellar condensates ("stardust"), these grains carry the isotopic signatures of specific nucleosynthesis processes in which their elements were made. In these materials, deviations from "natural abundance" are sometimes measured in factors of 100.

Some natural isotope abundances

The next table gives the terrestrial isotope distributions for some elements. Some elements, such as phosphorus and fluorine, only exist as a single isotope, with a natural abundance of 100%.

Natural isotope abundance

Isotope	% abundance	atomic mass
1H	99.985	1.007825
2H	0.015	2.0140
12C	98.89	12 (formerly by definition)
13C	1.11	13.00335
14N	99.64	14.00307
15N	0.36	15.00011
16O	99.76	15.99491
17O	0.04	16.99913
18O	0.2	17.99916
28Si	92.23	27.97693
29Si	4.67	28.97649
30Si	3.10	29.97376
32S	95.0	31.97207
33S	0.76	32.97146
34S	4.22	33.96786
35Cl	75.77	34.96885
37Cl	24.23	36.96590
79Br	50.69	78.9183
81Br	49.31	80.9163

History

In 1919, Fred Aston invented the mass spectrometric detector and quickly was able to determine that some elements had many isotopes. By 1931 Harold Urey and Charles A. Bradley, Jr. showed that different isotopes show slightly different chemistry, allowing chemistry to alter isotopic abundance.

See also

• Abundance of the chemical elements
• Decay product
• Isotope
• Presolar grains
• Radionuclide

External links

• Berkeley Isotopes Project Interactive Table (archived 2015)
• Exact Masses of the Elements and Isotopic Abundances, Scientific Instrument Services
• Tools to compute low- and high-precision isotopic distribution (archived 2011)