Standard atomic weight



Definition

The standard atomic weight is a special value of the relative atomic mass. It is defined as the "recommended values" of relative atomic masses of sources in the local environment of the Earth's crust and atmosphere as determined by the IUPAC Commission on Atomic Weights and Isotopic Abundances. In general, values from different sources are subject to natural variation due to a different radioactive history of sources. Thus, standard atomic weights are an expectation range of atomic weights from a range of samples or sources. By limiting the sources to terrestrial origin only, the CIAAW-determined values have less variance, and are a more precise value for relative atomic masses actually found and used in worldly materials.
The CIAAW-published values are used and sometimes lawfully required in mass calculations. The values have an uncertainty, or are an expectation interval. This uncertainty reflects natural variability in isotopic distribution for an element, rather than uncertainty in measurement.
Although there is an attempt to cover the range of variability on Earth with standard atomic weight figures, there are known cases of mineral samples which contain elements with atomic weights that are outliers from the standard atomic weight range.
For synthetic elements the isotope formed depends on the means of synthesis, so the concept of natural isotope abundance has no meaning. Therefore, for synthetic elements the total nucleon count of the most stable isotope is listed in brackets, in place of the standard atomic weight. When the term "atomic weight" is used in chemistry, usually it is the more specific standard atomic weight that is implied. It is standard atomic weights that are used in periodic tables and many standard references in ordinary terrestrial chemistry.
Lithium represents a unique case where the natural abundances of the isotopes have in some cases been found to have been perturbed by human isotopic separation activities to the point of affecting the uncertainty in its standard atomic weight, even in samples obtained from natural sources, such as rivers.

Terrestrial definition

An example of why "conventional terrestrial sources" must be specified in giving standard atomic weight values is the element argon. Between locations in the Solar System, the atomic weight of argon varies as much as 10%, due to extreme variance in isotopic composition. Where the major source of argon is the decay of [potassium-40|] in rocks, will be the dominant isotope. Such locations include the planets Mercury and Mars, and the moon Titan. On Earth, the ratios of the three isotopes 36Ar : 38Ar : 40Ar are approximately 5 : 1 : 1600, giving terrestrial argon a standard atomic weight of 39.948.
However, such is not the case in the rest of the universe. Argon produced directly, by stellar nucleosynthesis, is dominated by the alpha-process nuclide. Correspondingly, solar argon contains 84.6%, and the ratio of the three isotopes 36Ar : 38Ar : 40Ar in the atmospheres of the outer planets is 8400 : 1600 : 1. The atomic weight of argon in the Sun and most of the universe, therefore, would be only approximately 36.3.

Causes of uncertainty on Earth

Famously, the published atomic weight value comes with an uncertainty. This uncertainty follows from its definition, the source being "terrestrial and stable". Systematic causes for uncertainty are:
  1. Measurement limits. As always, the physical measurement is never finite. There is always more detail to be found and read. This applies to every single, pure isotope found. For example, today the mass of the main natural fluorine isotope can be measured to the accuracy of eleven decimal places:. But a still more precise measurement system could become available, producing more decimals.
  2. Imperfect mixtures of isotopes. In the samples taken and measured the mix of those isotopes may vary. For example, copper. While in general its two isotopes make out 69.15% and 30.85% each of all copper found, the natural sample being measured can have had an incomplete 'stirring' and so the percentages are different. The precision is improved by measuring more samples of course, but there remains this cause of uncertainty.
  3. Earthly sources with a different history. A source is the greater area being researched, for example 'ocean water' or 'volcanic rock'. It appears that some elements have a different isotopic mix per source. For example, thallium in igneous rock has more lighter isotopes, while in sedimentary rock it has more heavy isotopes. There is no Earthly mean number. These elements show the interval notation: Ar° = . For practical reasons, a simplified 'conventional' number is published too.
These three uncertainties are accumulative. The published value is a result of all these.

Determination of relative atomic mass

Modern relative atomic masses are calculated from measured values of atomic mass and isotopic composition of a sample. Highly accurate atomic masses are available for virtually all non-radioactive nuclides, but isotopic compositions are both harder to measure to high precision and more subject to variation between samples. For this reason, the relative atomic masses of the 22 mononuclidic elements are known to especially high accuracy.
The calculation is exemplified for silicon, whose relative atomic mass is especially important in metrology. Silicon exists in nature as a mixture of three isotopes: Si, Si and Si. The atomic masses of these nuclides are known to a precision of one part in 14 billion for Si and about one part in one billion for the others. However the range of natural abundance for the isotopes is such that the standard abundance can only be given to about ±0.001%.
The calculation is
The estimation of the uncertainty is complicated, especially as the sample distribution is not necessarily symmetrical: the IUPAC standard relative atomic masses are quoted with estimated symmetrical uncertainties, and the value for silicon is 28.0855. The relative standard uncertainty in this value is 1 or 10 ppm. To further reflect this natural variability, in 2010, IUPAC made the decision to list the relative atomic masses of 10 elements as an interval rather than a fixed number.

Naming controversy

The use of the name "atomic weight" has attracted a great deal of controversy among scientists. Objectors to the name usually prefer the term "relative atomic mass". The basic objection is that atomic weight is not a weight, that is the force exerted on an object in a gravitational field, measured in units of force such as the newton or poundal.
In reply, supporters of the term "atomic weight" point out that:
  • the name has been in continuous use for the same quantity since it was first conceptualized in 1808;
  • for most of that time, atomic weights really were measured by weighing and the name of a physical quantity should not change simply because the method of its determination has changed;
  • the term "relative atomic mass" should be reserved for the mass of a specific nuclide, while "atomic weight" be used for the weighted mean of the atomic masses over all the atoms in the sample;
  • it is not uncommon to have misleading names of physical quantities which are retained for historical reasons, such as
  • * electromotive force, which is not a force
  • * resolving power, which is not a power quantity
  • * molar concentration, which is not a molar quantity.
It could be added that atomic weight is often not truly "atomic" either, as it does not correspond to the property of any individual atom. The same argument could be made against "relative atomic mass" used in this sense.

Published values

IUPAC, through its Commission on Isotopic Abundances and Atomic Weights, publishes a formal value, called the standard atomic weight for each element that has at least one stable isotope or a well-characterised terrestrial isotopic composition. Updates are made only when justified by new high-precision measurements; they are no longer issued on a fixed biennial schedule. The most recent revisions affected three elements: gadolinium, lutetium, and zirconium.
The published value may be given with an uncertainty, e.g. neon:, or as an interval, e.g. boron: .
Currently 83 elements have an assigned standard atomic weight. In addition to the full-precision values, CIAAW publishes abridged standard atomic weights and, for the twelve elements whose atomic weights are expressed as intervals, single-number conventional atomic-weight values for use when isotopic variation is unimportant.
The symbol Ar denotes the relative atomic mass of a particular sample of element E, whereas the standard atomic weight is denoted .

Abridged atomic weight

The abridged atomic weight, also published by CIAAW, is derived from the standard atomic weight, reducing the numbers to five digits. The name does not say 'rounded'.
Interval borders are rounded downward for the first border, and upward for the upward border. This way, the more precise original interval is fully covered.
Examples:
  • Calcium: →
  • Helium: →
  • Hydrogen: →

Conventional atomic weight

Fourteen chemical elements – hydrogen, lithium, boron, carbon, nitrogen, oxygen, magnesium, silicon, sulfur, chlorine, argon, bromine, thallium, and lead – have a standard atomic weight that is defined not as a single number, but as an interval. For example, hydrogen has. This notation states that the various sources on Earth have substantially different isotopic constitutions, and that the uncertainties in all of them are just covered by the two numbers. For these elements, there is not an 'Earth average' constitution, and the 'right' value is not its middle. However, for situations where a less precise value is acceptable, for example in trade, CIAAW has published a single-number conventional atomic weight. For hydrogen,.

A formal short atomic weight

By using the abridged value, and the conventional value for the fourteen interval values, a short IUPAC-defined value can be given for all stable elements. In many situations, and in periodic tables, this may be sufficiently detailed.