Atomic mass

The atomic mass (ma) is the mass of an atom. Its unit is the unified atomic mass units (abbr. u) where 1 unified atomic mass unit is defined as ​112 of the mass of a single carbon-12 atom, at rest.[1] For atoms, the protons and neutrons of the nucleus account for nearly all of the total mass, and the atomic mass measured in u has nearly the same value as the mass number.

When divided by unified atomic mass units, or daltons (abbr. Da), to form a pure numeric ratio, the atomic mass of an atom becomes a dimensionless value called the relative isotopic mass (see section below). Thus, the atomic mass of a carbon-12 atom is 12 u (or 12 Da), but the relative isotopic mass of a carbon-12 atom is simply 12.

The atomic mass or relative isotopic mass refers to the mass of a single particle, and therefore is tied to a certain specific isotope of an element. The dimensionless standard atomic weight instead refers to the average (mathematical mean) of atomic mass values of a typical naturally-occurring mixture of isotopes for a sample of an element. Atomic mass values are thus commonly reported to many more significant figures than atomic weights. Standard atomic weight is related to atomic mass by the abundance ranking of isotopes for each element. It is usually about the same value as the atomic mass of the most abundant isotope, other than what looks like (but is not actually) a rounding difference.

The atomic mass of atoms, ions, or atomic nuclei is slightly less than the sum of the masses of their constituent protons, neutrons, and electrons, due to binding energy mass loss (as per E = mc2).[2]

Stylised atom with three Bohr model orbits and stylised nucleus
Stylized lithium-7 atom: 3 protons, 4 neutrons, and 3 electrons (total electrons are ~​14300th of the mass of the nucleus). It has a mass of 7.016 u. Rare lithium-6 (mass of 6.015 u) has only 3 neutrons, reducing the atomic weight (average) of lithium to 6.941.

Relative isotopic mass: the same quantity as atomic mass, but with different units

Relative isotopic mass (a property of a single atom) is not to be confused with the averaged quantity atomic weight (see above), that is an average of values for many atoms in a given sample of a chemical element.

Relative isotopic mass is similar to atomic mass and has exactly the same numerical value as atomic mass, whenever atomic mass is expressed in unified atomic mass units. The only difference in that case, is that relative isotopic mass is a pure number with no units. This loss of units results from the use of a scaling ratio with respect to a carbon-12 standard, and the word "relative" in the term "relative isotopic mass" refers to this scaling relative to carbon-12.

The relative isotopic mass, then, is the mass of a given isotope (specifically, any single nuclide), when this value is scaled by the mass of carbon-12, when the latter is set equal to 12. Equivalently, the relative isotopic mass of an isotope or nuclide is the mass of the isotope relative to 1/12 of the mass of a carbon-12 atom.

For example, the relative isotopic mass of a carbon-12 atom is exactly 12. For comparison, the atomic mass of a carbon-12 atom is exactly 12 daltons or 12 unified atomic mass units. Alternately, the atomic mass of a carbon-12 atom may be expressed in any other mass units: for example, the atomic mass of a carbon-12 atom is about 1.998467052 × 10−26 kilograms.

As in the case of atomic mass, no nuclides other than carbon-12 have exactly whole-number values of relative isotopic mass. As is the case for the related atomic mass when expressed in unified atomic mass units or daltons, the relative isotopic mass numbers of nuclides other than carbon-12 are not whole numbers, but are always close to whole numbers. This is discussed more fully below.

Similar terms for different quantities

The atomic mass and relative isotopic mass are sometimes confused, or incorrectly used, as synonyms of standard atomic weight (also known as atomic weight) and the standard atomic weight (a particular variety of atomic weight, in the sense that is a standardized atomic weight). However, as noted in the introduction, atomic weight and standard atomic weight represent terms for (abundance-weighted) averages of atomic masses in elemental samples, not for single nuclides. As such, atomic weight and standard atomic weight often differ numerically from relative isotopic mass and atomic mass, and they can also have different units than atomic mass when this quantity is not expressed in unified atomic mass units (see the linked article for atomic weight).

The atomic mass (relative isotopic mass) is defined as the mass of a single atom, which can only be one isotope (nuclide) at a time, and is not an abundance-weighted average, as in the case of relative atomic mass/atomic weight. The atomic mass or relative isotopic mass of each isotope and nuclide of a chemical element is therefore a number that can in principle be measured to a very great precision, since every specimen of such a nuclide is expected to be exactly identical to every other specimen, as all atoms of a given type in the same energy state, and every specimen of a particular nuclide, are expected to be exactly identical in mass to every other specimen of that nuclide. For example, every atom of oxygen-16 is expected to have exactly the same atomic mass (relative isotopic mass) as every other atom of oxygen-16.

In the case of many elements that have one naturally occurring isotope (mononuclidic elements) or one dominant isotope, the actual numerical similarity/difference between the atomic mass of the most common isotope, and the (standard) relative atomic mass or (standard) atomic weight can be small or even nil, and does not affect most bulk calculations. However, such an error can exist and even be important when considering individual atoms for elements that are not mononuclidic.

For non-mononuclidic elements that have more than one common isotope, the numerical difference in relative atomic mass (atomic weight) from even the most common relative isotopic mass, can be half a mass unit or more (e.g. see the case of chlorine where atomic weight and standard atomic weight are about 35.45). The atomic mass (relative isotopic mass) of an uncommon isotope can differ from the relative atomic mass, atomic weight, or standard atomic weight, by several mass units.

Atomic masses expressed in unified atomic mass units (i.e. relative isotopic masses) are always close to whole-number values, but never (except in the case of carbon-12) exactly a whole number, for two reasons:

  • protons and neutrons have different masses, and different nuclides have different ratios of protons and neutrons.
  • atomic masses are reduced, to different extents, by their binding energies.

The ratio of atomic mass to mass number (number of nucleons) varies from about 0.99884 for 56Fe to 1.00782505 for 1H.

Any mass defect due to nuclear binding energy is experimentally a small fraction (less than 1%) of the mass of equal number of free nucleons. When compared to the average mass per nucleon in carbon-12, which is moderately strongly-bound compared with other atoms, the mass defect of binding for most atoms is an even smaller fraction of a dalton (unified atomic mass unit, based on carbon-12). Since free protons and neutrons differ from each other in mass by a small fraction of a dalton (about 0.0014 u), rounding the relative isotopic mass, or the atomic mass of any given nuclide given in daltons to the nearest whole number always gives the nucleon count, or mass number. Additionally, the neutron count (neutron number) may then be derived by subtracting the number of protons (atomic number) from the mass number (nucleon count).

Mass defects in atomic masses

Binding energy curve - common isotopes
Binding energy per nucleon of common isotopes. A graph of the ratio of mass number to atomic mass would be similar.

The amount that the ratio of atomic masses to mass number deviates from 1 is as follows: the deviation starts positive at hydrogen-1, then decreases until it reaches a local minimum at helium-4. Isotopes of lithium, beryllium, and boron are less strongly bound than helium, as shown by their increasing mass-to-mass number ratios.

At carbon, the ratio of mass (in daltons) to mass number is defined as 1, and after carbon it becomes less than one until a minimum is reached at iron-56 (with only slightly higher values for iron-58 and nickel-62), then increases to positive values in the heavy isotopes, with increasing atomic number. This corresponds to the fact that nuclear fission in an element heavier than zirconium produces energy, and fission in any element lighter than niobium requires energy. On the other hand, nuclear fusion of two atoms of an element lighter than scandium (except for helium) produces energy, whereas fusion in elements heavier than calcium requires energy. The fusion of two atoms of He-4 to give beryllium-8 would require energy, and the beryllium would quickly fall apart again. He-4 can fuse with tritium (H-3) or with He-3, and these processes occurred during Big Bang nucleosynthesis. The formation of elements with more than seven nucleons requires the fusion of three atoms of He-4 in the so-called triple alpha process, skipping over lithium, beryllium, and boron to produce carbon.

Here are some values of the ratio of atomic mass to mass number:

Nuclide Ratio of atomic mass to mass number
1H 1.00782505
2H 1.0070508885
3H 1.0053497592
3He 1.0053431064
4He 1.0006508135
6Li 1.0025204658
12C 1
14N 1.0002195718
16O 0.9996821637
56Fe 0.9988381696
210Po 0.9999184462
232Th 1.0001640315
238U 1.0002133958

Measurement of atomic masses

Direct comparison and measurement of the masses of atoms is achieved with mass spectrometry.

Conversion factor between atomic mass units and grams

The standard scientific unit used to quantify the amount of a substance in macroscopic quantities is the mole (symbol: mol), which is defined arbitrarily as the amount of a substance which has as many atoms or molecules as there are atoms in 12 grams of the carbon isotope C-12. The number of atoms in a mole is called Avogadro's number, the value of which is approximately 6.022 × 1023.

One mole of a substance always contains almost exactly the standard atomic weight or molar mass of that substance; however, this may or may not be true for the atomic mass, depending on whether or not the element exists naturally in more than one isotope. For example, the standard atomic weight of iron is 55.847 g/mol, and therefore one mole of iron as commonly found on earth has a mass of 55.847 grams. The atomic mass of the 56Fe isotope is 55.935 u and one mole of 56Fe atoms would then in theory have a mass of 55.935 g, but such amounts of pure 56Fe have never been found (or separated out) on Earth. However, there are 22 mononuclidic elements of which essentially only a single isotope is found in nature (common examples are fluorine, sodium, aluminum and phosphorus) and for these elements the standard atomic weight and atomic mass are the same. Samples of these elements therefore may serve as reference standards for certain atomic mass values.

The formula used for conversion between atomic mass units and SI mass in grams for a single atom is:

where is the Molar mass constant and is the Avogadro constant.

Relationship between atomic and molecular masses

Similar definitions apply to molecules. One can compute the molecular mass of a compound by adding the atomic masses of its constituent atoms (nuclides). One can compute the molar mass of a compound by adding the relative atomic masses of the elements given in the chemical formula. In both cases the multiplicity of the atoms (the number of times it occurs) must be taken into account, usually by multiplication of each unique mass by its multiplicity.


The first scientists to determine relative atomic masses were John Dalton and Thomas Thomson between 1803 and 1805 and Jöns Jakob Berzelius between 1808 and 1826. Relative atomic mass (Atomic weight) was originally defined relative to that of the lightest element, hydrogen, which was taken as 1.00, and in the 1820s Prout's hypothesis stated that atomic masses of all elements would prove to be exact multiples of that of hydrogen. Berzelius, however, soon proved that this was not even approximately true, and for some elements, such as chlorine, relative atomic mass, at about 35.5, falls almost exactly halfway between two integral multiples of that of hydrogen. Still later, this was shown to be largely due to a mix of isotopes, and that the atomic masses of pure isotopes, or nuclides, are multiples of the hydrogen mass, to within about 1%.

In the 1860s Stanislao Cannizzaro refined relative atomic masses by applying Avogadro's law (notably at the Karlsruhe Congress of 1860). He formulated a law to determine relative atomic masses of elements: the different quantities of the same element contained in different molecules are all whole multiples of the atomic weight and determined relative atomic masses and molecular masses by comparing the vapor density of a collection of gases with molecules containing one or more of the chemical element in question.[3]

In the 20th century, until the 1960s chemists and physicists used two different atomic-mass scales. The chemists used a "atomic mass unit" (amu) scale such that the natural mixture of oxygen isotopes had an atomic mass 16, while the physicists assigned the same number 16 to only the atomic mass of the most common oxygen isotope (16O, containing eight protons and eight neutrons). However, because oxygen-17 and oxygen-18 are also present in natural oxygen this led to two different tables of atomic mass. The unified scale based on carbon-12, 12C, met the physicists' need to base the scale on a pure isotope, while being numerically close to the chemists' scale.

The term atomic weight is being phased out slowly and being replaced by relative atomic mass, in most current usage. This shift in nomenclature reaches back to the 1960s and has been the source of much debate in the scientific community, which was triggered by the adoption of the unified atomic mass unit and the realization that weight was in some ways an inappropriate term. The argument for keeping the term "atomic weight" was primarily that it was a well understood term to those in the field, that the term "atomic mass" was already in use (as it is currently defined) and that the term "relative atomic mass" might be easily confused with relative isotopic mass (the mass of a single atom of a given nuclide, expressed dimensionlessly relative to 1/12 of the mass of carbon-12; see section above).

In 1979, as a compromise, the term "relative atomic mass" was introduced as a secondary synonym for atomic weight. Twenty years later the primacy of these synonyms was reversed, and the term "relative atomic mass" is now the preferred term.

However, the term "standard atomic weights" (referring to the standardized expectation atomic weights of differing samples) has not been changed[4], because simple replacement of "atomic weight" with "relative atomic mass" would have resulted in the term "standard relative atomic mass."

See also


  1. ^ IUPAC, Compendium of Chemical Terminology, 2nd ed. (the "Gold Book") (1997). Online corrected version:  (2006–) "atomic mass". doi:10.1351/goldbook.A00496
  2. ^ Atomic mass, Encyclopædia Britannica on-line
  3. ^ Williams, Andrew (2007). "Origin of the Formulas of Dihydrogen and Other Simple Molecules". J. Chem. Educ. 84 (11): 1779. Bibcode:2007JChEd..84.1779W. doi:10.1021/ed084p1779.
  4. ^ De Bievre, P.; Peiser, H. S. (1992). "'Atomic weight': The name, its history, definition, and units" (PDF). Pure Appl. Chem. 64 (10): 1535. doi:10.1351/pac199264101535.

External links

Atomic Mass (band)

Atomic Mass were an English hard rock/heavy metal band from Sheffield, who formed in 1977 as part of the new wave of British heavy metal movement. The group's core members along with newly recruited singer Joe Elliott later became Def Leppard, eventually becoming one of the UK's top-selling hard rock bands.

Atomic mass unit

The unified atomic mass unit or dalton (symbol: u, or Da or AMU) is a standard unit of mass that quantifies mass on an atomic or molecular scale (atomic mass). One unified atomic mass unit is approximately the mass of one nucleon (either a single proton or neutron) and is numerically equivalent to 1 g/mol. It is defined as one twelfth of the mass of an unbound neutral atom of carbon-12 in its nuclear and electronic ground state and at rest, and has a value of 1.660539040(20)×10−27 kg, or approximately 1.66 yoctograms. The CIPM has categorised it as a non-SI unit accepted for use with the SI, and whose value in SI units must be obtained experimentally.The atomic mass unit (amu) without the "unified" prefix is technically an obsolete unit based on oxygen, which was replaced in 1961. However, many sources still use the term amu but now define it in the same way as u (i.e., based on carbon-12). In this sense, most uses of the terms atomic mass units and amu, today, actually refer to unified atomic mass unit. For standardization, a specific atomic nucleus (carbon-12 vs. oxygen-16) had to be chosen because the average mass of a nucleon depends on the count of the nucleons in the atomic nucleus due to mass defect. This is also why the mass of a proton or neutron by itself is more than (and not equal to) 1 u.

The atomic mass unit is not the unit of mass in the atomic units system, which is rather the electron rest mass (me).

Until the 2019 redefinition of SI base units, the number of daltons in a gram is exactly the Avogadro number by definition, or equivalently, a dalton is exactly equivalent to 1 gram/mol. Thereafter, these relationships will no longer be exact, but they will still be extremely accurate approximations.

Atomic number

The atomic number or proton number (symbol Z) of a chemical element is the number of protons found in the nucleus of an atom. It is identical to the charge number of the nucleus. The atomic number uniquely identifies a chemical element. In an uncharged atom, the atomic number is also equal to the number of electrons.

The sum of the atomic number Z and the number of neutrons, N, gives the mass number A of an atom. Since protons and neutrons have approximately the same mass (and the mass of the electrons is negligible for many purposes) and the mass defect of nucleon binding is always small compared to the nucleon mass, the atomic mass of any atom, when expressed in unified atomic mass units (making a quantity called the "relative isotopic mass"), is within 1% of the whole number A.

Atoms with the same atomic number Z but different neutron numbers N, and hence different atomic masses, are known as isotopes. A little more than three-quarters of naturally occurring elements exist as a mixture of isotopes (see monoisotopic elements), and the average isotopic mass of an isotopic mixture for an element (called the relative atomic mass) in a defined environment on Earth, determines the element's standard atomic weight. Historically, it was these atomic weights of elements (in comparison to hydrogen) that were the quantities measurable by chemists in the 19th century.

The conventional symbol Z comes from the German word Zahl meaning number, which, before the modern synthesis of ideas from chemistry and physics, merely denoted an element's numerical place in the periodic table, whose order is approximately, but not completely, consistent with the order of the elements by atomic weights. Only after 1915, with the suggestion and evidence that this Z number was also the nuclear charge and a physical characteristic of atoms, did the word Atomzahl (and its English equivalent atomic number) come into common use in this context.


Bismuth-209 is the isotope of bismuth with the longest known half-life of any radioisotope that undergoes α-decay (alpha decay). It has 83 protons and a magic number of 126 neutrons, and an atomic mass of 208.9803987 amu (atomic mass units). All of the primordial bismuth is of this isotope. It is also the β− daughter of lead-209.

20982Pb → 20983Bi + e− + ν


Carbon-12 (12C) is the more abundant of the two stable isotopes of carbon (Carbon-13 being the other), amounting to 98.93% of the element carbon; its abundance is due to the triple-alpha process by which it is created in stars. Carbon-12 is of particular importance in its use as the standard from which atomic masses of all nuclides are measured, thus, its atomic mass is exactly 12 daltons by definition. Carbon-12 is composed of 6 protons 6 neutrons and 6 electrons.

Electron rest mass

The electron rest mass (symbol: me) is the mass of a stationary electron, also known as the invariant mass of the electron. It is one of the fundamental constants of physics. It has a value of about 9.109×10−31 kilograms or about 5.486×10−4 atomic mass units, equivalent to an energy of about 8.187×10−14 joules or about 0.5110 MeV.


Eulim is a Chemistry library written in Ruby under the MIT license.

Eulim is a Ruby gem for Chemistry, which supports the calculation of molecular mass of compound, balancing chemical equations, efficient handling of states of chemical species and many more things.


Isotopes are variants of a particular chemical element which differ in neutron number, and consequently in nucleon number. All isotopes of a given element have the same number of protons but different numbers of neutrons in each atom.The term isotope is formed from the Greek roots isos (ἴσος "equal") and topos (τόπος "place"), meaning "the same place"; thus, the meaning behind the name is that different isotopes of a single element occupy the same position on the periodic table. It was coined by a Scottish doctor and writer Margaret Todd in 1913 in a suggestion to chemist Frederick Soddy.

The number of protons within the atom's nucleus is called atomic number and is equal to the number of electrons in the neutral (non-ionized) atom. Each atomic number identifies a specific element, but not the isotope; an atom of a given element may have a wide range in its number of neutrons. The number of nucleons (both protons and neutrons) in the nucleus is the atom's mass number, and each isotope of a given element has a different mass number.

For example, carbon-12, carbon-13 and carbon-14 are three isotopes of the element carbon with mass numbers 12, 13 and 14 respectively. The atomic number of carbon is 6, which means that every carbon atom has 6 protons, so that the neutron numbers of these isotopes are 6, 7 and 8 respectively.

Isotopes of cobalt

Naturally occurring cobalt (27Co) is composed of 1 stable isotope, 59Co. 28 radioisotopes have been characterized with the most stable being 60Co with a half-life of 5.2714 years, 57Co with a half-life of 271.8 days, 56Co with a half-life of 77.27 days, and 58Co with a half-life of 70.86 days. All of the remaining radioactive isotopes have half-lives that are less than 18 hours and the majority of these have half-lives that are less than 1 second. This element also has 11 meta states, all of which have half-lives less than 15 minutes.

The isotopes of cobalt range in atomic weight from 47Co to 75Co. The primary decay mode for isotopes with atomic mass unit values less than that of the most abundant stable isotope, 59Co, is electron capture and the primary mode of decay for those of greater than 59 atomic mass units is beta decay. The primary decay products before 59Co are iron isotopes and the primary products after are nickel isotopes.

Radioactive isotopes can be produced by various nuclear reactions. For example, the isotope 57Co is produced by cyclotron irradiation of iron. The principal reaction involved is the (d,n) reaction 56Fe + 2H → n + 57Co.

List of chemical elements

This is a list of the 118 chemical elements which have been identified as of 2019. A chemical element, often simply called an element, is a species of atoms which all have the same number of protons in their atomic nuclei (i.e., the same atomic number, or Z).Perhaps the most popular visualization of all 118 elements is the periodic table of the elements, a convenient tabular arrangement of the elements by their chemical properties that uses abbreviated chemical symbols in place of full element names, but the simpler list format presented here may also be useful. Like the periodic table, the list below organizes the elements by the number of protons in their atoms; it can also be organized by other properties, such as atomic weight, density, and electronegativity. For more detailed information about the origins of element names, see List of chemical element name etymologies.

Mass number

The mass number (symbol A, from the German word Atomgewicht (atomic weight), also called atomic mass number or nucleon number, is the total number of protons and neutrons (together known as nucleons) in an atomic nucleus. It determines the atomic mass of atoms. Because protons and neutrons both are baryons, the mass number A is identical with the baryon number B as of the nucleus as of the whole atom or ion. The mass number is different for each different isotope of a chemical element. This is not the same as the atomic number (Z) which denotes the number of protons in a nucleus, and thus uniquely identifies an element. Hence, the difference between the mass number and the atomic number gives the number of neutrons (N) in a given nucleus: .

The mass number is written either after the element name or as a superscript to the left of an element's symbol. For example, the most common isotope of carbon is carbon-12, or 12
, which has 6 protons and 6 neutrons. The full isotope symbol would also have the atomic number (Z) as a subscript to the left of the element symbol directly below the mass number: 12
. This is technically redundant, as each element is defined by its atomic number, so it is often omitted.

Mendeleev's predicted elements

Dmitri Mendeleev published a periodic table of the chemical elements in 1869 based on properties that appeared with some regularity as he laid out the elements from lightest to heaviest. When Mendeleev proposed his periodic table, he noted gaps in the table and predicted that as-then-unknown elements existed with properties appropriate to fill those gaps. He named them eka-boron, eka-aluminium and eka-silicon, with respective atomic masses of 44, 68, and 72.

Molar mass

In chemistry, the molar mass M is a physical property defined as the mass of a given substance (chemical element or chemical compound) divided by the amount of substance. The base SI unit for molar mass is kg/mol. However, for historical reasons, molar masses are almost always expressed in g/mol.

In simple terms, molar mass of a substance is the total weight of that substance (in either kilogram or gram) for one mole of that substance. That is, the weight of a substance for 6.02214076×10^23 molecules or atoms of that substance.

As an example, the molar mass of water: M(H2O) ≈ 18.015 g/mol.

Mole (unit)

The mole is the base unit of amount of substance in the International System of Units (SI). Effective 20 May 2019, the mole is defined as the amount of a chemical substance that contains exactly 6.02214076×1023 (Avogadro constant) constitutive particles, e.g., atoms, molecules, ions or electrons.This definition was adopted in November 2018, revising its old definition based on the number of atoms in 12 grams of carbon-12 (12C) (the isotope of carbon with relative atomic mass 12 Da by definition). The mole is an SI base unit, with the unit symbol mol.

The mole is widely used in chemistry as a convenient way to express amounts of reactants and products of chemical reactions. For example, the chemical equation 2H2 + O2 → 2H2O can be interpreted to mean that 2 mol dihydrogen (H2) and 1 mol dioxygen (O2) react to form 2 mol water (H2O). The mole may also be used to represent the number of atoms, ions, or other entities in a given sample of a substance. The concentration of a solution is commonly expressed by its molarity, defined as the amount of dissolved substance per unit volume of solution, for which the unit typically used is moles per litre (mol/l).

The term gram-molecule was formerly used for essentially the same concept. The term gram-atom has been used for a related but distinct concept, namely a quantity of a substance that contains an Avogadro's number of atoms, whether isolated or combined in molecules. Thus, for example, 1 mole of MgBr2 is 1 gram-molecule of MgBr2 but 3 gram-atoms of MgBr2.

Molecular mass

Relative molecular mass or molecular weight is the mass of a molecule. It is calculated as the sum of the relative atomic masses of each constituent element multiplied by the number of atoms of that element in the molecular formula. The molecular mass of small to medium size molecules, measured by mass spectrometry, determines stoichiometry. For large molecules such as proteins, methods based on viscosity and light-scattering can be used to determine molecular mass when crystallographic data are not available.

Relative atomic mass

Relative atomic mass (symbol: Ar) or atomic weight is a dimensionless physical quantity defined as the ratio of the average mass of atoms of a chemical element in a given sample to one unified atomic mass unit. The unified atomic mass unit (symbol: u or Da) is defined as being ​1⁄12 of the atomic mass of a carbon-12 atom. Since both values in the ratio are expressed in the same unit (u), the resulting value is dimensionless; hence the value is said to be relative.

For a single given sample, the relative atomic mass of a given element is the weighted arithmetic mean of the masses of the individual atoms (including their isotopes) that are present in the sample. This quantity can vary substantially between samples because the sample's origin (and therefore its radioactive history or diffusion history) may have produced unique combinations of isotopic abundances. For example, due to a different mixture of stable carbon-12 and carbon-13 isotopes, a sample of elemental carbon from volcanic methane will have a different relative atomic mass than one collected from plant or animal tissues.

The more common, and more specific quantity known as standard atomic weight (Ar, standard) is an application of the relative atomic mass values obtained from multiple different samples. It is sometimes interpreted as the expected range of the relative atomic mass values for the atoms of a given element from all terrestrial sources, with the various sources being taken from Earth. "Atomic weight" is often loosely and incorrectly used as a synonym for standard atomic weight (incorrectly because standard atomic weights are not from a single sample). Standard atomic weight is nevertheless the most widely published variant of relative atomic mass.

Additionally, the continued use of the term "atomic weight" (for any element) as opposed to "relative atomic mass" has attracted considerable controversy since at least the 1960s, mainly due to the technical difference between weight and mass in physics. Still, both terms are officially sanctioned by the IUPAC. The term "relative atomic mass" now seems to be replacing "atomic weight" as the preferred term, although the term "standard atomic weight" (as opposed to the more correct "standard relative atomic mass") continues to be used.

Rutherford model

The Rutherford model, also known as planetary model is a model which tried to describe an atom devised by Ernest Rutherford. Rutherford directed the famous Geiger–Marsden experiment in 1909 which suggested, upon Rutherford's 1911 analysis, that J. J. Thomson's plum pudding model of the atom was incorrect. Rutherford's new model for the atom, based on the experimental results, contained new features of a relatively high central charge concentrated into a very small volume in comparison to the rest of the atom and with this central volume also containing the bulk of the atomic mass of the atom. This region would be known as the "nucleus" of the atom.

Spontaneous fission

Spontaneous fission (SF) is a form of radioactive decay that is found only in very heavy chemical elements. The nuclear binding energy of the elements reaches its maximum at an atomic mass number of about 56; spontaneous breakdown into smaller nuclei and a few isolated nuclear particles becomes possible at greater atomic mass numbers.

Standard atomic weight

The standard atomic weight (Ar, standard, a relative atomic mass) is the atomic weight (Ar) of a chemical element, as appearing and met in the earthly environment. It reflects the variance of natural isotopes (and so weight differences) of an element. Values are defined by (restricted to) the IUPAC (CIAAW) definition of natural, stable, terrestrial sources. It is the most common and practical atomic weight used, for example to determine molar mass.

The specified definition is to use many representative sources (samples) from the Earth, so that the value can widely be used as 'the' atomic weight for real life substances—for example, in pharmaceuticals and scientific research. Atomic weights are specific to single sources and samples of an element, such as the atomic weight of carbon in a particular bone from a particular archeological site. Standard atomic weight generalizes such values to the range of atomic weights which a chemist might expect to derive from many random samples from Earth. This range is the cause of the interval notation in some standard atomic weight values.

Out of the 118 known chemical elements, 84 are stable and have this Earth-environment based value. Typically, such a value is, for example helium: Ar, standard(He) = 4.002602(2). The "(2)" indicates the uncertainty in the last digit shown, to read 4.002602 ±0.000002. IUPAC also publishes abridged values, rounded to five significant figures. For helium, Ar, abridged(He) = 4.0026.

For twelve 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: Ar, standard(Tl) = [204.38, 204.39]. With such an interval, for less demanding situations, IUPAC also publishes an conventional value. For thallium, Ar, conventional(Tl) = 204.38.

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