The standard atomic weight of a
chemical element
A chemical element is a species of atoms that have a given number of protons in their nuclei, including the pure substance consisting only of that species. Unlike chemical compounds, chemical elements cannot be broken down into simpler sub ...
(symbol ''A''
r°(E) for element "E") is the
weighted arithmetic mean
The weighted arithmetic mean is similar to an ordinary arithmetic mean (the most common type of average), except that instead of each of the data points contributing equally to the final average, some data points contribute more than others. The ...
of the
relative isotopic masses of all
isotope
Isotopes are two or more types of atoms that have the same atomic number (number of protons in their nuclei) and position in the periodic table (and hence belong to the same chemical element), and that differ in nucleon numbers (mass numb ...
s of that element
weighted by each isotope's abundance on
Earth
Earth is the third planet from the Sun and the only astronomical object known to harbor life. While large volumes of water can be found throughout the Solar System, only Earth sustains liquid surface water. About 71% of Earth's surfa ...
. For example, isotope
63Cu (''A''
r = 62.929) constitutes 69% of the
copper
Copper is a chemical element with the symbol Cu (from la, cuprum) and atomic number 29. It is a soft, malleable, and ductile metal with very high thermal and electrical conductivity. A freshly exposed surface of pure copper has a pinkis ...
on Earth, the rest being
65Cu (''A''
r = 64.927), so
:
Because relative isotopic masses are
dimensionless quantities
A dimensionless quantity (also known as a bare quantity, pure quantity, or scalar quantity as well as quantity of dimension one) is a quantity to which no physical dimension is assigned, with a corresponding SI unit of measurement of one (or 1) ...
, this weighted mean is also dimensionless. It can be converted into a measure of mass (with
dimension
In physics and mathematics, the dimension of a mathematical space (or object) is informally defined as the minimum number of coordinates needed to specify any point within it. Thus, a line has a dimension of one (1D) because only one coor ...
) by multiplying it with the
dalton
Dalton may refer to:
Science
* Dalton (crater), a lunar crater
* Dalton (program), chemistry software
* Dalton (unit) (Da), the atomic mass unit
* John Dalton, chemist, physicist and meteorologist
Entertainment
* Dalton (Buffyverse), minor ch ...
, also known as the atomic mass constant.
Among various variants of the notion of
atomic weight
Relative atomic mass (symbol: ''A''; sometimes abbreviated RAM or r.a.m.), also known by the deprecated synonym atomic weight, is a dimensionless physical quantity defined as the ratio of the average mass of atoms of a chemical element in a giv ...
(''A''
r, also known as ''
relative atomic mass
Relative atomic mass (symbol: ''A''; sometimes abbreviated RAM or r.a.m.), also known by the deprecated synonym atomic weight, is a dimensionless physical quantity defined as the ratio of the average mass of atoms of a chemical element in a giv ...
'') used by scientists, the standard atomic weight is the most common and practical. The standard atomic weight of each chemical element is determined and published by the
Commission on Isotopic Abundances and Atomic Weights
The Commission on Isotopic Abundances and Atomic Weights (CIAAW) is an international scientific committee of the International Union of Pure and Applied Chemistry (IUPAC) under its Division of Inorganic Chemistry. Since 1899, it is entrusted wi ...
(CIAAW) of the
International Union of Pure and Applied Chemistry
The International Union of Pure and Applied Chemistry (IUPAC ) is an international federation of National Adhering Organizations working for the advancement of the chemical sciences, especially by developing nomenclature and terminology. It is ...
(IUPAC) based on natural, stable,
terrestrial
Terrestrial refers to things related to land or the planet Earth.
Terrestrial may also refer to:
* Terrestrial animal, an animal that lives on land opposed to living in water, or sometimes an animal that lives on or near the ground, as opposed to ...
sources of the element. The definition specifies the use of samples from many representative sources from the Earth, so that the value can widely be used as "the" atomic weight for substances as they are encountered in reality—for example, in pharmaceuticals and scientific research. Non-standardized atomic weights of an element are specific to sources and samples, such as the atomic weight of carbon in a particular bone from a particular archeological site. Standard atomic weight averages such values to the ''range of atomic weights'' that a chemist might expect to derive from many random samples from Earth. This range is the rationale for the ''interval notation'' given for some standard atomic weight values.
Of the 118 known chemical elements, 80 have stable isotopes and 84 have this Earth-environment based value. Typically, such a value is, for example helium: . The "(2)" indicates the uncertainty in the last digit shown, to read . IUPAC also publishes ''abridged values'', rounded to five significant figures. For helium, .
For thirteen elements the samples diverge on this value, because their sample sources have had a different decay history. For example, thallium (Tl) in sedimentary rocks has a different isotopic composition than in igneous rocks and volcanic gases. For these elements, the standard atomic weight is noted as an interval: . With such an interval, for less demanding situations, IUPAC also publishes a ''conventional value''. For thallium, .
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
The International Union of Pure and Applied Chemistry (IUPAC ) is an international federation of National Adhering Organizations working for the advancement of the chemical sciences, especially by developing nomenclature and terminology. It is ...
Commission on Atomic Weights and Isotopic Abundances'' (CIAAW).
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 (atomic weights) 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 (noted in brackets), or are an expectation interval (see example in illustration immediately above). This uncertainty reflects natural variability in isotopic distribution for an element, rather than uncertainty in measurement (which is much smaller with quality instruments).
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 element
A synthetic element is one of 24 known chemical elements that do not occur naturally on Earth: they have been created by human manipulation of fundamental particles in a nuclear reactor, a particle accelerator, or the explosion of an atomic bomb; ...
s 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 (i.e., the isotope with the longest half-life) 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
Lithium (from el, λίθος, lithos, lit=stone) is a chemical element with the symbol Li and atomic number 3. It is a soft, silvery-white alkali metal. Under standard conditions, it is the least dense metal and the least dense solid ...
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 Solar System Capitalization of the name varies. The International Astronomical Union, the authoritative body regarding astronomical nomenclature, specifies capitalizing the names of all individual astronomical objects but uses mixed "Solar ...
, 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
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(1).
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% (according to
solar wind
The solar wind is a stream of charged particles released from the upper atmosphere of the Sun, called the corona. This plasma mostly consists of electrons, protons and alpha particles with kinetic energy between . The composition of the sol ...
measurements), 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 (and related: precision) follows from its definition, the source being "terrestrial and stable". Systematic causes for uncertainty are:
# 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 (
fluorine-19
Fluorine (9F) has 18 known isotopes ranging from to (with the exception of ) and two isomers ( and ). Only fluorine-19 is stable and naturally occurring in more than trace quantities; therefore, fluorine is a monoisotopic and mononuclidic elem ...
) can be measured to the accuracy of eleven decimal places: . But a still more precise measurement system could become available, producing more decimals.
# Imperfect mixtures of isotopes. In the samples taken and measured the ''mix'' (relative abundance) 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. (Example: lead samples vary so much, it can not be noted more precise than four figures: )
# Earthly sources with a different history. A ''source'' is the greater area being researched, for example 'ocean water' or 'volcanic rock' (as opposed to a 'sample': the single heap of material being investigated). 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: ''A''
r°(Tl) =
For practical reasons, a simplified 'conventional' number is published too (for Tl: 204.38).
These three uncertainties are accumulative. The published value is a result of all these.
Determination of relative atomic mass
Modern relative atomic masses (a term specific to a given element sample) are calculated from measured values of atomic mass (for each nuclide) 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 element
A mononuclidic element or monotopic element is one of the 21 chemical elements that is found naturally on Earth essentially as a single nuclide (which may, or may not, be a stable nuclide). This single nuclide will have a characteristic atomic m ...
s (which are the same as the isotopic masses for each of the single naturally occurring nuclides of these elements) are known to especially high accuracy.
The calculation is exemplified for
silicon
Silicon is a chemical element with the symbol Si and atomic number 14. It is a hard, brittle crystalline solid with a blue-grey metallic luster, and is a tetravalent metalloid and semiconductor. It is a member of group 14 in the periodic ta ...
, 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% (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
Uncertainty refers to epistemic situations involving imperfect or unknown information. It applies to predictions of future events, to physical measurements that are already made, or to the unknown. Uncertainty arises in partially observable ...
is complicated,
especially as the
sample distribution is not necessarily symmetrical: the
IUPAC
The International Union of Pure and Applied Chemistry (IUPAC ) is an international federation of National Adhering Organizations working for the advancement of the chemical sciences, especially by developing nomenclature and terminology. It is ...
standard relative atomic masses 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. 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" (not to be confused with
atomic mass
The atomic mass (''m''a or ''m'') is the mass of an atom. Although the SI unit of mass is the kilogram (symbol: kg), atomic mass is often expressed in the non-SI unit dalton (symbol: Da) – equivalently, unified atomic mass unit (u). 1&nb ...
). The basic objection is that atomic weight is not a
weight
In science and engineering, the weight of an object is the force acting on the object due to gravity.
Some standard textbooks define weight as a vector quantity, the gravitational force acting on the object. Others define weight as a scalar qua ...
, that is the
force exerted on an object in a
gravitational field, measured in units of force such as the
newton or
poundal
The poundal (symbol: pdl) is a unit of force, introduced in 1877, that is part of the Absolute English system of units, which itself is a coherent subsystem of the foot–pound–second system.
:1\,\text = 1\,\text\text/\text^2
The poundal is de ...
.
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
Gravimetric analysis describes a set of methods used in analytical chemistry for the quantitative determination of an analyte (the ion being analyzed) based on its mass. The principle of this type of analysis is that once an ion's mass has been ...
) 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 (or
isotope
Isotopes are two or more types of atoms that have the same atomic number (number of protons in their nuclei) and position in the periodic table (and hence belong to the same chemical element), and that differ in nucleon numbers (mass numb ...
), 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
Power most often refers to:
* Power (physics), meaning "rate of doing work"
** Engine power, the power put out by an engine
** Electric power
* Power (social and political), the ability to influence people or events
** Abusive power
Power may a ...
quantity
**
molar concentration
Molar concentration (also called molarity, amount concentration or substance concentration) is a measure of the concentration of a chemical species, in particular of a solute in a solution, in terms of amount of substance per unit volume of sol ...
, which is not a molar quantity (a quantity expressed per unit amount of substance).
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 publishes one formal value for each stable element, called the ''standard atomic weight''.
Any updates are published biannually (in uneven years). In 2015, the atomic weight of ytterbium was updated.
Per 2017, 14 atomic weights were changed, including argon changing from single number to interval value.
The value published can have an uncertainty, like for neon: , or can be an interval, like for boron:
0.806, 10.821
Next to these 84 values, IUPAC also publishes ''abridged'' values (up to five digits per number only), and for the twelve interval values, ''conventional'' values (single number values).
Symbol ''A''
r is a relative atomic mass, for example from a specific sample. To be specific, the standard atomic weight can be noted as , where (E) is the element symbol.
Abridged atomic weight
The abridged atomic weight, also published by CIAAW, is derived from the standard atomic weight reducing the numbers to five digits (five significant figures). The name does not say 'rounded'.
Interval borders are rounded ''downwards'' for the first (lowmost) border, and ''upwards'' for the ''upward'' (upmost) 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 uncertainties are incorporated in the two numbers. For these elements, there is not an 'Earth average' constitution, and the 'right' value is not its middle (that would be 1.007975 for hydrogen, with an uncertainty of (±0.000135) that would make it just cover the interval). However, for situations where a less precise value is acceptable, CIAAW has published a single-number conventional atomic weight that can be used for example in trade. For hydrogen, .
A formal short atomic weight
By using the abridged value, and the conventional value for the thirteen interval values, a short IUPAC-defined value (5 digits plus uncertainty) can be given for all stable elements. In many situations, and in periodic tables, this may be sufficiently detailed.
List of atomic weights
In the periodic table
See also
*
International Union of Pure and Applied Chemistry
The International Union of Pure and Applied Chemistry (IUPAC ) is an international federation of National Adhering Organizations working for the advancement of the chemical sciences, especially by developing nomenclature and terminology. It is ...
(IUPAC)
*
Commission on Isotopic Abundances and Atomic Weights
The Commission on Isotopic Abundances and Atomic Weights (CIAAW) is an international scientific committee of the International Union of Pure and Applied Chemistry (IUPAC) under its Division of Inorganic Chemistry. Since 1899, it is entrusted wi ...
(CIAAW)
References
External links
IUPAC Commission on Isotopic Abundances and Atomic WeightsAtomic Weights of the Elements 2011
{{Authority control
Amount of substance
Chemical properties
Stoichiometry
Periodic table