atomic weight

atomic weight

atomic weight, mean (weighted average) of the masses of all the naturally occurring isotopes of a chemical element, as contrasted with atomic mass, which is the mass of any individual isotope. Although the first atomic weights were calculated at the beginning of the 19th cent., it was not until the discovery of isotopes by F. Soddy (c.1913) that the atomic mass of many individual isotopes was determined, leading eventually to the adoption of the atomic mass unit as the standard unit of atomic weight.

Effect of Isotopes in Calculating Atomic Weight

Most naturally occurring elements have one principal isotope and only insignificant amounts of other isotopes. Therefore, since the atomic mass of any isotope is very nearly a whole number, most atomic weights are nearly whole numbers, e.g., hydrogen has atomic weight 1.00797 and nitrogen has atomic weight 14.007. However, some elements have more than one principal isotope, and the atomic weight for such an element—since it is a weighted average—is not close to a whole number; e.g., the two principal isotopes of chlorine have atomic masses very nearly 35 and 37 and occur in the approximate ratio 3 to 1, so the atomic weight of chlorine is about 35.5. Some other common elements whose atomic weights are not nearly whole numbers are antimony, barium, boron, bromine, cadmium, copper, germanium, lead, magnesium, mercury, nickel, strontium, tin, and zinc.

Atomic weights were formerly determined directly by chemical means; now a mass spectrograph is usually employed. The atomic mass and relative abundance of the isotopes of an element can be measured very accurately and with relative ease by this method, whereas chemical determination of the atomic weight of an element requires a careful and precise quantitative analysis of as many of its compounds as possible.

Development of the Concept of Atomic Weight

J. L. Proust formulated (1797) what is now known as the law of definite proportions, which states that the proportions by weight of the elements forming any given compound are definite and invariable. John Dalton proposed (c.1810) an atomic theory in which all atoms of an element have exactly the same weight. He made many measurements of the combining weights of the elements in various compounds. By postulating that simple compounds always contain one atom of each element present, he assigned relative atomic weights to many elements, assigning a weight of 1 to hydrogen as the basis of his scale. He thought that water had the formula HO, and since he found by experiment that 8 weights of oxygen combine with 1 weight of hydrogen, he assigned an atomic weight of 8 to oxygen. Dalton also formulated the law of multiple proportions, which states that when two elements combine in more than one proportion by weight to form two or more distinct compounds, their weight proportions in those compounds are related to one another in simple ratios. Dalton's work sparked an interest in determining atomic weights, even though some of his results—such as that for oxygen—were soon shown to be incorrect.

While Dalton was working on weight relationships in compounds, J. L. Gay-Lussac was experimenting with the chemical reactions of gases, and he found that, when under the same conditions of temperature and pressure, gases react in simple whole-number ratios by volume. Avogadro proposed (1811) a theory of gases that holds that equal volumes of two gases at the same temperature and pressure contain the same number of particles, and that these basic particles are not always single atoms. This theory was rejected by Dalton and many other chemists.

P. L. Dulong and A. T. Petit discovered (1819) a specific-heat method for determining the approximate atomic weight of elements. Among the first chemists to work out a systematic group of atomic weights (c.1830) was J. J. Berzelius, who was influenced in his choice of formulas for compounds by the method of Dulong and Petit. He attributed the formula H2O to water and determined an atomic weight of 16 for oxygen. J. S. Stas later refined many of Berzelius's weights. Stanislao Cannizzaro applied Avogadro's theories to reconcile atomic weights used by organic and inorganic chemists.

The availability of fairly accurate atomic weights and the search for some relationship between atomic weight and chemical properties led to J. A. R. Newlands's table of "atomic numbers" (1865), in which he noted that if the elements were arranged in order of increasing atomic weight "the eighth element, starting from a given one, is a kind of repetition of the first." He called this the law of octaves. Such investigations led to the statement of the periodic law, which was discovered independently (1869) by D. I. Mendeleev in Russia and J. L. Meyer in Germany. T. W. Richards did important work on atomic weights (after 1883) and revised some of Stas's values.

Ratio of the average mass of a chemical element's atoms to 112 the mass of an atom of the carbon-12 isotope. The original standard of atomic weight, established in the 19th century, was hydrogen, with a value of 1. From circa 1900 until 1961, the reference standard was oxygen, with a value of 16, and the unit of atomic mass was defined as 116 the mass of an oxygen atom. Oxygen, however, contains small amounts of two isotopes that are heavier than the most abundant one, and 16 is actually a weighted average of the masses of the three isotopes of oxygen. Therefore, the standard was changed to one based on carbon-12. The new scale required only minimal changes to the values that had been used for chemical atomic weights.

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Atomic weight (symbol: A) is a dimensionless physical quantity, the ratio of the average mass of atoms of an element (from a given source) to 1/12 of the mass of an atom of carbon-12. The term is usually used, without further qualification, to refer to the standard atomic weights published at regular intervals by the International Union of Pure and Applied Chemistry (IUPAC) and which are intended to be applicable to normal laboratory materials. These standard atomic weights are reprinted in a wide variety of textbooks, commercial catalogues, wallcharts etc, and in the table below. The term "relative atomic mass" may also used to describe this physical quantity, and indeed the continued use of the term "atomic weight" has attracted considerable controversy since at least the 1960s (see below).

Atomic weights, unlike atomic masses (the masses of individual atoms), are not physical constants and vary from sample to sample. Nevertheless, they are sufficiently constant in "normal" samples to be of fundamental importance in chemistry.


The IUPAC definition of atomic weight is:
An atomic weight (relative atomic mass) of an element from a specified source is the ratio of the average mass per atom of the element to 1/12 of the mass of an atom of C.

The definition deliberately specifies "An atomic weight…", as an element will have different atomic weights depending on the source. For example, boron from Turkey has a lower atomic weight than boron from California, because of its different isotopic composition. Nevertheless, given the cost and difficulty of isotope analysis, it is usual to use the tabulated values of standard atomic weights which are ubiquitous in chemical laboratories.

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, or just 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.

In reply, supporters of the term "atomic weight" point out (among other arguments) 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 (that is by gravimetric analysis) and that the name of a physical quantity shouldn't 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 (or isotope), while "atomic weight" be used for the weighted mean of the relative atomic mass 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

It could be added that atomic weight is often not truly "atomic" either, as it doesn't correspond to the property of any individual atom. The same argument could be made against "relative atomic mass" used in this sense.

Determination of atomic weight

Modern atomic weights are calculated from measured values of relative atomic mass (for each nuclide) and isotopic composition. Highly accurate relative atomic masses are avalable 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 atomic weights of the twenty-two mononuclidic elements are known to especially high accuracy – an uncertainty of only one part in 38 million in the case of fluorine, a precision which is greater than the current best value for the Avogadro constant (one part in 20 million).

Isotope Relative atomic mass Abundance
Standard Range
Si 27.976 926 532 46(194) 92.2297(7)% 92.21–92.25%
Si 28.976 494 700(22) 4.6832(5)% 4.69–4.67%
Si 29.973 770 171(32) 3.0872(5)% 3.10–3.08%
The calculation is exemplified for silicon, whose atomic weight is especially important in metrology. Silicon exists in nature as a mixture of three isotopes: Si, Si and Si. The relative atomic masses of these nuclides are known to a precision of one part in 14 billion for Si and about one part 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% (see table). The calculation is
A(Si) = (27.97693 × 0.922297) + (28.97649 × 0.046832) + (29.97377 × 0.030872) = 28.0854
The estimation of the uncertainty is complicated, especially as the sample distribution is not necessarily symmetrical: the IUPAC standard atomic weights are quoted with estimated symmetrical uncertainties, and the value for silicon is 28.0855(3). The relative standard uncertainty in this value is 1 or 10 ppm.

Standard atomic weights (to four figures)


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