# Atomic mass

Stylized lithium-7 atom: 3 protons, 4 neutrons, & 3 electrons (total electrons are ~1/4300th 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 u.

The atomic mass (ma) is the mass of an atomic particle, sub-atomic particle, or molecule. It may be expressed in unified atomic mass units, which by International agreement is 1/12 mass of a single carbon-12 atom at rest.[1] When expressed in such units, the atomic mass is called the relative isotopic mass (see section below).

The atomic mass of atomic particles is slightly less than the total mass of its constituting protons, neutrons, or electrons due to binding energy mass loss (as per E=mc2).[2]

## Relative isotopic mass, the same term with different units

Relative isotopic mass (not to be confused with relative atomic mass) has exactly the same numerical value as atomic mass when atomic mass is expressed in unified atomic mass units. The only difference is that relative isotopic mass differs is a pure number with no units. The loss of units results from this term's use in a scale ratio with respect to a carbon-12 standard.

Thus, the relative isotopic mass is the relative mass of a given isotope (specifically, any single nuclide), scaled by the mass of carbon-12, which on this scale is set equal to 12. Equivalently, the relative isotopic mass of an isotope 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 carbon-12 is exactly 12, but (as in the case of atomic mass) no nuclides other than carbon-12 have exactly whole-number values in this scale. As is the case for the related atomic mass when expressed in unified atomic mass units, 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 synonyms of relative atomic mass (atomic weight) and standard atomic weight. However, the latter terms for elements are averages of isotopic abundances. As such, they often differ numerically from relative isotopic mass, and 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 and relative isotopic mass are 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. 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 relative atomic mass or (standard) atomic weight can be small or even nil, and does affect most bulk calculations. However, such an error can be critical 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. the case of chlorine). The atomic mass of an uncommon isotope can differ from the relative atomic mass or 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. The difference from whole numbers for these values is due to two factors: [1] the different mass of neutrons and protons acting to change the total mass in nuclides that have a proton:neutron ratios other than the 1:1 ratio of carbon-12; and [2] an exact whole-number will not be obtained if there exists a loss/gain of mass signifying a difference in mean binding energy relative to the mean binding energy for carbon-12. This is always the case.

Any mass defect due to binding energy is a small fraction (less than 1%) compared to the mass of a nucleon, and even less compared to the average mass per nucleon in carbon-12, which is moderately strongly-bound compared with other atoms. Since protons and neutrons differ in mass from each by an even smaller fraction (about 0.0014 u), the practice of rounding the atomic mass of any given nuclide or isotope to the nearest whole number, always gives the simple whole number total nucleon count, or mass number. The neutron count (neutron number) may then be derived by subtracting the number of protons (atomic number).

## Mass defects in atomic masses

Binding energy per nucleon of common isotopes.

The amount that the atomic masses deviate from their mass numbers is as follows: the deviation starts positive at hydrogen-1, becomes negative until a minimum is reached at iron-56, iron-58 and nickel-62, then increases to positive values in the heavy isotopes, with increasing atomic number. This corresponds to the following: nuclear fission in an element heavier than iron produces energy, and fission in any element lighter than iron requires energy. The opposite is true of nuclear fusion reactions: fusion in elements lighter than iron produces energy, and fusion in elements heavier than iron requires energy.

## 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 for dealing with atoms in macroscopic quantities is the mole (symbol: mol), which is defined arbitrarily as the amount of a substance with as many atoms or other units as there are 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 mol−1.

One mole of a substance always contains almost exactly the relative atomic mass or molar mass of that substance (which is the concept of molar mass), expressed in grams; 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 relative atomic mass 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 weigh 55.935 g, but such amounts of pure 56Fe have never been found on Earth. However, there exist in nature 22 mononuclidic elements for which essentially only a single isotope is found in nature (common examples are fluorine, sodium, aluminum and phosphorus), and for these elements the relative atomic mass and atomic mass are the same. Samples of these elements therefore may serve as reference standards for certain atomic mass values.

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

$1\ {\rm{u}}={M_{\rm{u}} \over N_{\rm A}}\ = {{1\ \rm{g/mol}} \over N_{\rm A}}$

where $M_{\rm u}$ is the Molar mass constant and $N_{\rm A}$ 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.

## History

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 taken as 1.00, and in the 1820s Prout's hypothesis stated that atomic masses of all elements would prove via a whole number rule to be exact multiples of this hydrogen relative atomic mass. Berzelius, however, soon proved that this hypothesis did not always hold even approximately, and in some elements, such as chlorine, relative atomic mass falls almost exactly between two multiples of the hydrogen relative atomic mass. Still later, as noted, this was shown to be an isotope effect, 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 early twentieth century, up until the 1960s chemists and physicists used two different atomic mass scales. The chemists used a scale such that the natural mixture of oxygen isotopes had an atomic mass 16, while the physicists assigned the same number 16 to the atomic mass of the most common oxygen isotope (containing eight protons and eight neutrons). However, because oxygen-17 and oxygen-18 are also present in natural oxygen this led to 2 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. The history of this shift in nomenclature reaches back to the 1960s and has been the source of much debate in the scientific community. The debate was largely created 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" was in some ways redundant. In 1979, in a compromise move, the definition was refined and the term "relative atomic mass" was introduced as a secondary synonym. Twenty years later the primacy of these synonyms was reversed and the term "relative atomic mass" is now the preferred term; however the "standard atomic weights" have maintained the same name.[4]