What is atomic mass?
Atom
The actual mass of an atom at rest is often expressed using the unified atomic mass unit (u), also called dalton (Da). This unit is defined as a twelfth of the mass of a free neutral atom of carbon-12, which is approximately . Hydrogen-1 (the lightest isotope of hydrogen which is also the nuclide with the lowest mass) has an atomic weight of 1.007825 u. The value of this number is called the atomic mass. A given atom has an atomic mass approximately equal (within 1%) to its mass number times the atomic mass unit (for example the mass of a nitrogen-14 is roughly 14 u). However, this number will not be exactly an integer except in the case of carbon-12 (see below). The heaviest stable atom is lead-208, with a mass of .
Relative atomic mass
The relative "isotopic" mass is specifically the "ratio of" the mass of a single atom "to" the mass of a unified atomic mass unit. This value, too, is relative, and therefore dimensionless.
Molar mass
Molar mass is closely related to the relative molar mass ("M") of a compound, to the older term formula weight (F.W.), and to the standard atomic masses of its constituent elements. However, it should be distinguished from the molecular mass (also known as molecular weight), which is the mass of "one" molecule (of any "single" isotopic composition) and is not directly related to the atomic mass, the mass of "one" atom (of any "single" isotope). The dalton, symbol Da, is also sometimes used as a unit of molar mass, especially in biochemistry, with the definition 1 Da = 1 g/mol, despite the fact that it is strictly a unit of mass (1 Da = 1 u = 1.660 538 921(73)×10 kg).
Atomic mass
Here are some values of the ratio of atomic mass to mass number:
Direct comparison and measurement of the masses of atoms is achieved with mass spectrometry.
Atomic mass
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.
Whole number rule
During the 1920s, it was thought that the atomic nucleus was made of protons and electrons, which would account for the disparity between the atomic number of an atom and its atomic mass. In 1932, James Chadwick discovered an uncharged particle of approximately the mass as the proton, which he called the neutron. The fact that the atomic nucleus is composed of protons and neutrons was rapidly accepted and Chadwick was awarded the Nobel Prize in Physics in 1935 for his discovery.
Hydrogen atom
A hydrogen atom is an atom of the chemical element hydrogen. The electrically neutral atom contains a single positively charged proton and a single negatively charged electron bound to the nucleus by the Coulomb force. Atomic hydrogen constitutes about 75% of the baryonic mass of the universe.
Atomic ratio
The atomic ratio is a measure of the ratio of atoms of one kind (i) to another kind (j). A closely related concept is the atomic percent (or at.%), which gives the percentage of one kind of atom relative to the total number of atoms. The molecular equivalents of these concepts are the molar fraction, or molar percent.
Atomic mass
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.
Atomic mass
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.
Atomic mass
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.
Atomic mass constant
In practice, the atomic mass constant is determined as the ratio of the electron rest mass "m" to the electron relative atomic mass "A"(e) (that is, the mass of the electron on a scale where C = 12). The relative atomic mass of the electron can be measured in cyclotron experiments, while the rest mass of the electron can be derived from other physical constants.
The current uncertainty in the value of the atomic mass constant – one part in 20 million – is almost entirely due to the uncertainty in the value of the Planck constant.
Atomic mass unit
Despite this change, modern sources often still use the old term "amu" but define it as u ( of the mass of a carbon-12 atom), as mentioned in the article's introduction. Therefore, in general, "amu" likely does not refer to the old oxygen standard unit, unless the source material originates from the 1960s or before.
Relative atomic mass
The more common, and more specific quantity known as standard atomic weight ("A") 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.
Atomic mass
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%.
Atom
As even the most massive atoms are far too light to work with directly, chemists instead use the unit of moles. One mole of atoms of any element always has the same number of atoms (about ). This number was chosen so that if an element has an atomic mass of 1 u, a mole of atoms of that element has a mass close to one gram. Because of the definition of the unified atomic mass unit, each carbon-12 atom has an atomic mass of exactly 12 u, and so a mole of carbon-12 atoms weighs exactly 0.012 kg.
Chemistry
The atom is the basic unit of chemistry. It consists of a dense core called the atomic nucleus surrounded by a space occupied by an electron cloud. The nucleus is made up of positively charged protons and uncharged neutrons (together called nucleons), while the electron cloud consists of negatively charged electrons which orbit the nucleus. In a neutral atom, the negatively charged electrons balance out the positive charge of the protons. The nucleus is dense; the mass of a nucleon is approximately 1,836 times that of an electron, yet the radius of an atom is about 10,000 times that of its nucleus.
Atomic mass
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.
Atomic mass unit
The discovery of isotopic oxygen in 1929 led to a divergence in relative atomic mass representation, with isotopically weighted oxygen (i.e., naturally occurring oxygen relative atomic mass) given a value of exactly 16 atomic mass units (amu) in chemistry, while pure O (oxygen-16) was given the mass value of exactly 16 amu in physics.
Subatomic particle
The negatively charged electron has a mass equal to of that of a hydrogen atom. The remainder of the hydrogen atom's mass comes from the positively charged proton. The atomic number of an element is the number of protons in its nucleus. Neutrons are neutral particles having a mass slightly greater than that of the proton. Different isotopes of the same element contain the same number of protons but differing numbers of neutrons. The mass number of an isotope is the total number of nucleons (neutrons and protons collectively).
Mass (mass spectrometry)
The mass defect used in nuclear physics is different from its use in mass spectrometry. In nuclear physics, the mass defect is the difference in the mass of a composite particle and the sum of the masses of its component parts. In mass spectrometry the mass defect is defined as the difference between the exact mass and the nearest integer mass.
Atom
If the mass of the nucleus following a fusion reaction is less than the sum of the masses of the separate particles, then the difference between these two values can be emitted as a type of usable energy (such as a gamma ray, or the kinetic energy of a beta particle), as described by Albert Einstein's mass–energy equivalence formula, "E" = "mc", where "m" is the mass loss and "c" is the speed of light. This deficit is part of the binding energy of the new nucleus, and it is the non-recoverable loss of the energy that causes the fused particles to remain together in a state that requires this energy to separate.
Atomic mass unit
The former definition of the mole, an SI base unit, was accepted by the CGPM in 1971 as:
However, the first part of this definition will be changed on 20 May 2019 to:
Mass number
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 , 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: . This is technically redundant, as each element is defined by its atomic number, so it is often omitted.
Matter
In classical physics and general chemistry, matter is any substance that has mass and takes up space by having volume. All everyday objects that can be touched are ultimately composed of atoms, which are made up of interacting subatomic particles, and in everyday as well as scientific usage, "matter" generally includes atoms and anything made up of them, and any particles (or combination of particles) that act as if they have both rest mass and volume. However it does not include massless particles such as photons, or other energy phenomena or waves such as light or sound. Matter exists in various states (also known as phases). These include classical everyday phases such as solid, liquid, and gas – for example water exists as ice, liquid water, and gaseous steam – but other states are possible, including plasma, Bose–Einstein condensates, fermionic condensates, and quark–gluon plasma.
Relative atomic mass
The prevailing IUPAC definitions (as taken from the "Gold Book") are:
and
Here the "unified atomic mass unit" refers to of the mass of an atom of C "in its ground state".
Chemical element
Only about 4% of the total mass of the universe is made of atoms or ions, and thus represented by chemical elements. This fraction is about 15% of the total matter, with the remainder of the matter (85%) being dark matter. The nature of dark matter is unknown, but it is not composed of atoms of chemical elements because it contains no protons, neutrons, or electrons. (The remaining non-matter part of the mass of the universe is composed of the even more mysterious dark energy).
Stoichiometry
Different elements have a different atomic mass, and as collections of single atoms, molecules have a definite molar mass, measured with the unit mole (6.02 × 10 individual molecules, Avogadro's constant). By definition, carbon-12 has a molar mass of 12 g/mol. Thus, to calculate the stoichiometry by mass, the number of molecules required for each reactant is expressed in moles and multiplied by the molar mass of each to give the mass of each reactant per mole of reaction. The mass ratios can be calculated by dividing each by the total in the whole reaction.
Atomic mass
where formula_2 is the Molar mass constant and formula_3 is the Avogadro constant.
Molecular mass
In the example above the atomic mass of carbon is given as 12.011, not 12. This is because naturally occurring carbon is a mixture of the isotopes C, C and C which have relative atomic masses of 12, 13 and 14 respectively. Moreover, the proportion of the isotopes varies between samples, so 12.011 is an average value. By contrast, there is less variation in naturally occurring hydrogen so the average atomic mass is known more precisely. The precision of the molecular mass is determined by precision of the least precise atomic mass value, in this case that of carbon. In high-resolution mass spectrometry the isotopomers CH and CH are observed as distinct molecules, with molecular masses of 16 and 17, respectively. The intensity of the mass-spectrometry peaks is proportional to the isotopic abundances in the molecular species. C H H can also be observed with molecular mass of 17.
Atomic theory
From his own work and the work of his students Bohr and Henry Moseley, Rutherford knew that the positive charge of any atom could always be equated to that of an integer number of hydrogen nuclei. This, coupled with the atomic mass of many elements being roughly equivalent to an integer number of hydrogen atoms - then assumed to be the lightest particles - led him to conclude that hydrogen nuclei were singular particles and a basic constituent of all atomic nuclei. He named such particles protons. Further experimentation by Rutherford found that the nuclear mass of most atoms exceeded that of the protons it possessed; he speculated that this surplus mass was composed of previously-unknown neutrally charged particles, which were tentatively dubbed "neutrons".
Semi-empirical mass formula
The mass of an atomic nucleus is given by
where formula_2 and formula_3 are the rest mass of a proton and a neutron, respectively, and formula_4 is the binding energy of the nucleus. The semi-empirical mass formula states that the binding energy will take the following form:
Atomic mass
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.
Planck constant
The Avogadro constant "N" is determined as the ratio of the mass of one mole of electrons to the mass of a single electron; the mass of one mole of electrons is the "relative atomic mass" of an electron "A"(e), which can be measured in a Penning trap (), multiplied by the molar mass constant "M", which is defined as .
The dependence of the Avogadro constant on the Planck constant () also holds for the physical constants which are related to amount of substance, such as the atomic mass constant. The uncertainty in the value of the Planck constant limits the knowledge of the masses of atoms and subatomic particles when expressed in SI units. It is possible to measure the masses more precisely in atomic mass units, but not to convert them more precisely into kilograms.
Molar mass constant
The molar mass constant is important in writing dimensionally correct equations. It is common to see phrases such as
However, atomic weight, i.e., relative atomic mass, is a dimensionless quantity, and cannot take the units of grams per mole. Formally, the operation is the multiplication by a constant which has the value 1 g/mol, that is the molar mass constant.
Atomic mass
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 kilograms.
Atomic mass unit
Molecular masses of proteins are often expressed in kilodaltons (kDa or kD). For example, a molecule of a protein with molar mass has a mass of 64 kDa.
Avogadro constant
The Avogadro constant also enters into the definition of the unified atomic mass unit, u,
Nuclear binding energy
As seen above in the example of deuterium, nuclear binding energies are large enough that they may be easily measured as fractional mass deficits, according to the equivalence of mass and energy. The atomic binding energy is simply the amount of energy (and mass) released, when a collection of free nucleons are joined together to form a nucleus.
Relative atomic mass
Older (pre-1961) historical relative scales based on the atomic mass unit (symbol: "a.m.u." or "amu") used either the oxygen-16 relative isotopic mass or else the oxygen relative atomic mass (i.e., atomic weight) for reference. See the article on the history of the modern unified atomic mass unit for the resolution of these problems.
Relative atomic mass
Relative atomic mass is determined by the "average atomic mass", or the weighted mean of the atomic masses of all the atoms of a particular chemical element found in a particular sample, which is then compared to the atomic mass of carbon-12. This comparison is the quotient of the two weights, which makes the value dimensionless (no unit appended). This quotient also explains the word "relative": the sample mass value is considered relative to that of carbon-12..
Atomic number
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".
Electron rest mass
The electron relative atomic mass also enters into the calculation of all other relative atomic masses. By convention, relative atomic masses are quoted for neutral atoms, but the actual measurements are made on positive ions, either in a mass spectrometer or a Penning trap. Hence the mass of the electrons must be added back on to the measured values before tabulation. A correction must also be made for the mass equivalent of the binding energy "E". Taking the simplest case of complete ionization of all electrons, for a nuclide X of atomic number "Z",
As relative atomic masses are measured as ratios of masses, the corrections must be applied to both ions: the uncertainties in the corrections are negligible, as illustrated below for hydrogen 1 and oxygen 16.
Atom
Protons have a positive charge and a mass 1,836 times that of the electron, at . The number of protons in an atom is called its atomic number. Ernest Rutherford (1919) observed that nitrogen under alpha-particle bombardment ejects what appeared to be hydrogen nuclei. By 1920 he had accepted that the hydrogen nucleus is a distinct particle within the atom and named it proton.
Atomic mass
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.
Atomic radius
The atomic radius of a chemical element is a measure of the size of its atoms, usually the mean or typical distance from the center of the nucleus to the boundary of the surrounding cloud of electrons. Since the boundary is not a well-defined physical entity, there are various non-equivalent definitions of atomic radius. Three widely used definitions of atomic radius are: Van der Waals radius, ionic radius, and covalent radius.
Relative atomic mass
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.
Atomic mass unit
One consequence of this change is that the current defined relationship between the mass of the C atom, the dalton, the kilogram, and the Avogadro number will no longer be valid. One of the following must change:
The wording of the ninth SI Brochure implies that the first statement remains valid, which means that the second is no longer true. The molar mass constant, while still with great accuracy remaining 1 g/mol, is no longer exactly equal to that.
Given that the unified atomic mass unit is one twelfth the mass of one atom of carbon-12, meaning the mass of such an atom is 12 u, it follows that there are only approximately "N" atoms of carbon-12 in 0.012 kg of carbon-12. This can be expressed mathematically as
Atomic mass unit
The standard atomic weight (or atomic weight) scale has traditionally been a relative value, that is without a unit, with the first relative atomic mass basis suggested by John Dalton in 1803 as H. Despite the initial mass of H being used as the natural unit for relative atomic mass, it was suggested by Wilhelm Ostwald that relative atomic mass would be best expressed in terms of units of mass of oxygen (). This evaluation was made prior to the discovery of the existence of elemental isotopes, which occurred in 1912.
C-value
The relative molecular mass may be converted to an absolute value by multiplying it by the atomic mass unit (1 u) in picograms. Thus, 615.8771 is multiplied by 1.660539 × 10 pg. Consequently, the mean mass per nucleotide pair would be 1.023 × 10 pg, and 1 pg of DNA would represent 0.978 × 10 base pairs (978 Mbp).
Mass excess
The mass excess of a nuclide is the difference between its actual mass and its mass number in atomic mass units. It is one of the predominant methods for tabulating nuclear mass. The mass of an atomic nucleus is well approximated (less than 0.1% difference for most nuclides) by its mass number, which indicates that most of the mass of a nucleus arises from mass of its constituent protons and neutrons. Thus, the mass excess is an expression of the nuclear binding energy, relative to the binding energy per nucleon of carbon-12 (which defines the atomic mass unit). If the mass excess is negative, the nucleus has more binding energy than C, and vice versa. If a nucleus has a large excess of mass compared to a nearby nuclear species, it can radioactively decay, releasing energy.
Relative atomic mass
Apart from this uncertainty by measurement, some elements have variation over sources. That is, different sources (ocean water, rocks) have a different radioactive history and so different isotopic composition. To reflect this natural variability, the IUPAC made the decision in 2010 to list the standard relative atomic masses of 12 elements as an interval rather than a fixed number.
Atomic mass
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.
Mass in special relativity
The term "mass" in special relativity usually refers to the rest mass of the object, which is the Newtonian mass as measured by an observer moving along with the object. The "invariant mass" is another name for the "rest mass" of single particles. The more general invariant mass (calculated with a more complicated formula) loosely corresponds to the "rest mass" of a "system". Thus, invariant mass is a natural unit of mass used for systems which are being viewed from their center of momentum frame (COM frame), as when any closed system (for example a bottle of hot gas) is weighed, which requires that the measurement be taken in the center of momentum frame where the system has no net momentum. Under such circumstances the invariant mass is equal to the relativistic mass (discussed below), which is the total energy of the system divided by "c" (the speed of light squared).
Relative atomic mass
The definition deliberately specifies "An atomic weight…", as an element will have different relative atomic masses depending on the source. For example, boron from Turkey has a lower relative atomic mass than boron from California, because of its different isotopic composition. Nevertheless, given the cost and difficulty of isotope analysis, it is common practice to instead substitute the tabulated values of standard atomic weights, which are ubiquitous in chemical laboratories and which are revised biennially by the IUPAC's Commission on Isotopic Abundances and Atomic Weights (CIAAW).
Nuclear binding energy
The mass defect of a nucleus represents the amount of mass equivalent to the 
binding energy of the nucleus (E=mc), which is the difference between the mass of a nucleus and the sum of the individual masses of the nucleons of which it is composed.
Mass
This is a special case of the general rule, where unstable massive particles are formally described as having a complex mass, with the real part being their mass in the usual sense, and the imaginary part being the decay rate in natural units. However, in quantum field theory, a particle (a "one-particle state") is roughly defined as a state which is constant over time; i.e., an eigenvalue of the Hamiltonian. An unstable particle is a state which is only approximately constant over time; If it exists long enough to be measured, it can be formally described as having a complex mass, with the real part of the mass greater than its imaginary part. If both parts are of the same magnitude, this is interpreted as a resonance appearing in a scattering process rather than a particle, as it is considered not to exist long enough to be measured independently of the scattering process. In the case of a tachyon the real part of the mass is zero, and hence no concept of a particle can be attributed to it.
Law of definite proportions
A related early idea was Prout's hypothesis, formulated by English chemist William Prout, who proposed that the hydrogen atom was the fundamental atomic unit. From this hypothesis was derived the whole number rule, which was the rule of thumb that atomic masses were whole number multiples of the mass of hydrogen. This was later rejected in the 1820s and 30s following more refined measurements of atomic mass, notably by Jöns Jacob Berzelius, which revealed in particular that the atomic mass of chlorine was 35.45, which was incompatible with the hypothesis. Since the 1920s this discrepancy has been explained by the presence of isotopes; the atomic mass of any isotope is very close to satisfying the whole number rule, with the mass defect caused by differing binding energies being significantly smaller.
Atomic theory
In chemistry and physics, atomic theory is a scientific theory of the nature of matter, which states that matter is composed of discrete units called atoms. It began as a philosophical concept in ancient Greece and entered the scientific mainstream in the early 19th century when discoveries in the field of chemistry showed that matter did indeed behave as if it were made up of atoms.
Nuclear binding energy
For example, the atomic mass unit (1 u) is defined as 1/12 of the mass of a C atom—but the atomic mass of a H atom (which is a proton plus electron) is 1.007825 "u", so each nucleon in C has lost, on average, about 0.8% of its mass in the form of binding energy.
Isotope
The tabulated atomic masses of elements are averages that account for the presence of multiple isotopes with different masses. Before the discovery of isotopes, empirically determined noninteger values of atomic mass confounded scientists. For example, a sample of chlorine contains 75.8% chlorine-35 and 24.2% chlorine-37, giving an average atomic mass of 35.5 atomic mass units.
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 elements (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. For example, there is an uncertainty of only one part in 38 million for the relative atomic mass of fluorine, a precision which is greater than the current best value for the Avogadro constant (one part in 20 million).
Relative atomic mass
The IUPAC definition of relative atomic mass is:
Molar mass constant
The molar mass constant is unusual (but not unique) among physical constants by having an exactly defined value rather than being measured experimentally. It is fixed by the definitions of the mole and of relative atomic mass. From the definition of the mole, the molar mass of carbon 12 is exactly 12 g/mol. From the definition of relative atomic mass, the relative atomic mass of carbon 12, that is the atomic weight of a sample of pure carbon 12, is exactly 12. The molar mass constant is given by
The speed of light, the electric constant and the magnetic constant are other examples of physical constants whose values are fixed by the definitions of the International System of Units (SI), in these cases by the definitions of the metre and the ampere.
Mass spectrum
Early in mass spectrometry research the resolution of mass spectrometers did not allow for accurate mass determination. Francis William Aston won the Nobel prize in Chemistry in 1922. "For his discovery, by means of his mass spectrograph, of isotopes, in a large number of non-radioactive elements, and for his enunciation of the Whole Number Rule." In which he stated that all atoms (including isotopes) follow a whole-number rule This implied that the masses of atoms were not on a scale but could be expressed as integers. (In fact multiply charged ions were rare, so for the most part the ratio was whole as well.) There have been several suggestions (e.g. the unit thomson) to change the official mass spectrometry nomenclature formula_2 to be more internally consistent.
Synthetic element
Atomic mass for natural elements is based on weighted average abundance of natural isotopes that occur in Earth's crust and atmosphere. For "synthetic" elements, the isotope depends on the means of synthesis, so the concept of natural isotope abundance has no meaning. Therefore, for synthetic elements the total nucleon count (protons plus neutrons) of the most stable isotope, i.e. the isotope with the longest half-life—is listed in brackets as the atomic mass.
Mass (mass spectrometry)
The unified atomic mass unit (symbol: u) is the standard unit that is used for indicating mass on an atomic or molecular scale (atomic mass). The dalton (symbol: Da) is equivalent to the unified atomic mass unit. One unified atomic mass unit is approximately the mass of one a single proton or neutron. The unified atomic mass unit has a value of . The "amu" without the "unified" prefix is an obsolete unit based on oxygen, which was replaced in 1961.
Atomic mass unit
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.
Atomic units
Atomic units (au or a.u.) form a system of natural units which is especially convenient for atomic physics calculations. There are two different kinds of atomic units, Hartree atomic units and Rydberg atomic units, which differ in the choice of the unit of mass and charge. This article deals with Hartree atomic units, where the numerical values of the following four fundamental physical constants are all unity by definition:In Hartree units, the speed of light is approximately formula_5. Atomic units are often abbreviated "a.u." or "au", not to be confused with the same abbreviation used also for astronomical units, arbitrary units, and absorbance units in different contexts.
Mass–energy equivalence
For a system of particles going off in different directions, the invariant mass of the system is the analog of the rest mass, and is the same for all observers, even those in relative motion. It is defined as the total energy (divided by ) in the center of mass frame (where by definition, the system total momentum is zero). A simple example of an object with moving parts but zero total momentum is a container of gas. In this case, the mass of the container is given by its total energy (including the kinetic energy of the gas molecules), since the system total energy and invariant mass are the same in any reference frame where the momentum is zero, and such a reference frame is also the only frame in which the object can be weighed. In a similar way, the theory of special relativity posits that the thermal energy in all objects (including solids) contributes to their total masses and weights, even though this energy is present as the kinetic and potential energies of the atoms in the object, and it (in a similar way to the gas) is not seen in the rest masses of the atoms that make up the object.
Atomic mass unit
The unified atomic mass unit and the dalton are different names for the same unit of measure. As with other unit names such as watt and newton, "dalton" is not capitalized in English, but its symbol, Da, is capitalized. With the introduction of the name "dalton", there has been a gradual change towards using that name in preference to the name, "unified atomic mass unit":
Chemical element
The mass number of an element, "A", is the number of nucleons (protons and neutrons) in the atomic nucleus. Different isotopes of a given element are distinguished by their mass numbers, which are conventionally written as a superscript on the left hand side of the atomic symbol (e.g. U). The mass number is always a whole number and has units of "nucleons". For example, magnesium-24 (24 is the mass number) is an atom with 24 nucleons (12 protons and 12 neutrons).
Chemistry
A chemical element is a pure substance which is composed of a single type of atom, characterized by its particular number of protons in the nuclei of its atoms, known as the atomic number and represented by the symbol "Z". The mass number is the sum of the number of protons and neutrons in a nucleus. Although all the nuclei of all atoms belonging to one element will have the same atomic number, they may not necessarily have the same mass number; atoms of an element which have different mass numbers are known as isotopes. For example, all atoms with 6 protons in their nuclei are atoms of the chemical element carbon, but atoms of carbon may have mass numbers of 12 or 13.
Atomic mass
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 × 10.
Atomic mass
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 ).
Mass–energy equivalence
For things and systems made up of many parts, like an atomic nucleus, planet, or star, the relativistic mass is the sum of the relativistic masses (or energies) of the parts, because energies are additive in isolated systems. This is not true in open systems, however, if energy is subtracted. For example, if a system is "bound" by attractive forces, and the energy gained due to the forces of attraction in excess of the work done is removed from the system, then mass is lost with this removed energy. For example, the mass of an atomic nucleus is less than the total mass of the protons and neutrons that make it up, but this is only true after this energy from binding has been removed in the form of a gamma ray (which in this system, carries away the mass of the energy of binding). This mass decrease is also equivalent to the energy required to break up the nucleus into individual protons and neutrons (in this case, work and mass would need to be supplied). Similarly, the mass of the solar system is slightly less than the sum of the individual masses of the sun and planets.
Mass
In bound systems, the binding energy must often be subtracted from the mass of the unbound system, because binding energy commonly leaves the system at the time it is bound. The mass of the system changes in this process merely because the system was not closed during the binding process, so the energy escaped. For example, the binding energy of atomic nuclei is often lost in the form of gamma rays when the nuclei are formed, leaving nuclides which have less mass than the free particles (nucleons) of which they are composed.
Atomic mass
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.
Mass–energy equivalence
The difference between the rest mass of a bound system and of the unbound parts is the binding energy of the system, if this energy has been removed after binding. For example, a water molecule weighs a little less than two free hydrogen atoms and an oxygen atom. The minuscule mass difference is the energy needed to split the molecule into three individual atoms (divided by ), which was given off as heat when the molecule formed (this heat had mass). Likewise, a stick of dynamite in theory weighs a little bit more than the fragments after the explosion, but this is true only so long as the fragments are cooled and the heat removed. In this case the mass difference is the energy/heat that is released when the dynamite explodes, and when this heat escapes, the mass associated with it escapes, only to be deposited in the surroundings, which absorb the heat (so that total mass is conserved).
Atom
Every atom is composed of a nucleus and one or more electrons bound to the nucleus. The nucleus is made of one or more protons and typically a similar number of neutrons. Protons and neutrons are called nucleons. More than 99.94% of an atom's mass is in the nucleus. The protons have a positive electric charge, the electrons have a negative electric charge, and the neutrons have no electric charge. If the number of protons and electrons are equal, that atom is electrically neutral. If an atom has more or fewer electrons than protons, then it has an overall negative or positive charge, respectively, and it is called an ion.
Isotope
The mass number is a dimensionless quantity. The atomic mass, on the other hand, is measured using the atomic mass unit based on the mass of the carbon-12 atom. It is denoted with symbols "u" (for unified atomic mass unit) or "Da" (for dalton).
Mass (mass spectrometry)
The molecular mass (abbreviated M) of a substance, formerly also called molecular weight and abbreviated as MW, is the mass of one molecule of that substance, relative to the unified atomic mass unit u (equal to 1/12 the mass of one atom of C). Due to this relativity, the molecular mass of a substance is commonly referred to as the relative molecular mass, and abbreviated to M.
Atomic mass
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.
Relativistic mechanics
For isolated systems (closed to all mass and energy exchange), mass never disappears in the center of momentum frame, because energy cannot disappear. Instead, this equation, in context, means only that when any energy is added to, or escapes from, a system in the center-of-momentum frame, the system will be measured as having gained or lost mass, in proportion to energy added or removed. Thus, in theory, if an atomic bomb were placed in a box strong enough to hold its blast, and detonated upon a scale, the mass of this closed system would not change, and the scale would not move. Only when a transparent "window" was opened in the super-strong plasma-filled box, and light and heat were allowed to escape in a beam, and the bomb components to cool, would the system lose the mass associated with the energy of the blast. In a 21 kiloton bomb, for example, about a gram of light and heat is created. If this heat and light were allowed to escape, the remains of the bomb would lose a gram of mass, as it cooled. In this thought-experiment, the light and heat carry away the gram of mass, and would therefore deposit this gram of mass in the objects that absorb them.
Mass number
The mass number should also not be confused with the standard atomic weight (also called atomic weight) of an element, which is the ratio of the average atomic mass of the different isotopes of that element (weighted by abundance) to the unified atomic mass unit. The atomic weight is an actual "mass" (made relative, i.e., a ratio), while the mass number is a "counted" number (and so an integer).
Mass (mass spectrometry)
The whole number rule states that the masses of the isotopes are integer multiples of the mass of the hydrogen atom. The rule is a modified version of Prout's hypothesis proposed in 1815, to the effect that atomic weights are multiples of the weight of the hydrogen atom.
Isotope
The atomic mass ("m") of an isotope (nuclide) is determined mainly by its mass number (i.e. number of nucleons in its nucleus). Small corrections are due to the binding energy of the nucleus (see mass defect), the slight difference in mass between proton and neutron, and the mass of the electrons associated with the atom, the latter because the electron:nucleon ratio differs among isotopes.
Atomic mass unit
The atomic mass unit is not the unit of mass in the atomic units system, which is rather the electron rest mass ("m").
Mass (mass spectrometry)
The nominal mass for an element is the mass number of its most abundant naturally occurring stable isotope, and for an ion or molecule, the nominal mass is the sum of the nominal masses of the constituent atoms. Isotope abundances are tabulated by IUPAC: for example carbon has two stable isotopes C at 98.9% natural abundance and C at 1.1% natural abundance, thus the nominal mass of carbon is 12. The nominal mass is not always the lowest mass number, for example iron has isotopes Fe, Fe, Fe, and Fe with abundances 6%, 92%, 10%, and 2%, respectively, and a nominal mass of 56. For a molecule, the nominal mass is obtained by summing the nominal masses of the constituent elements, for example water has two hydrogen atoms with nominal mass 1 and one oxygen atom with nominal mass 16, therefore the nominal mass of HO is 18.
Isotope
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.
Atomic mass
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 (O, 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, C, met the physicists' need to base the scale on a pure isotope, while being numerically close to the chemists' scale.
Nuclear binding energy
Nuclear binding energy is the "minimum" energy that would be required to disassemble the nucleus of an atom into its component parts. These component parts are neutrons and protons, which are collectively called nucleons. The binding is always a positive number, as we need to spend energy in moving these nucleons, attracted to each other by the strong nuclear force, away from each other. The mass of an atomic nucleus is less than the sum of the individual masses of the free protons and neutrons, according to Einstein's equation E=mc. This 'missing mass' is known as the mass defect, and represents the energy that was released when the nucleus was formed.
Milli mass unit
The milli mass unit or (mmu) is used as a unit of mass by some scientific authors even though this unit is not defined by the IUPAP red book nor by the IUPAC green book. It is a short form of the tongue-breaking but formally more correct "milli unified atomic mass unit" (mu) and equivalent to 1/1000 of the unified atomic mass unit (u). A more modern name is the millidalton (mDa)
since the "unified atomic mass unit" is more and more displaced by the unit dalton. (1 Da = 1 u)
Standard atomic weight
The "standard" atomic weight is thus a more 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." (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.
Mass–energy equivalence
In nuclear reactions, typically only a small fraction of the total mass–energy of the bomb converts into the mass–energy of heat, light, radiation, and motion—which are "active" forms that can be used. When an atom fissions, it loses only about 0.1% of its mass (which escapes from the system and does not disappear), and additionally, in a bomb or reactor not all the atoms can fission. In a modern fission-based atomic bomb, the efficiency is only about 40%, so only 40% of the fissionable atoms actually fission, and only about 0.03% of the fissile core mass appears as energy in the end. In nuclear fusion, more of the mass is released as usable energy, roughly 0.3%. But in a fusion bomb, the bomb mass is partly casing and non-reacting components, so that in practicality, again (coincidentally) no more than about 0.03% of the total mass of the entire weapon is released as usable energy (which, again, retains the "missing" mass). See nuclear weapon yield for practical details of this ratio in modern nuclear weapons.
Atom
The electron is by far the least massive of these particles at , with a negative electrical charge and a size that is too small to be measured using available techniques. It was the lightest particle with a positive rest mass measured, until the discovery of neutrino mass. Under ordinary conditions, electrons are bound to the positively charged nucleus by the attraction created from opposite electric charges. If an atom has more or fewer electrons than its atomic number, then it becomes respectively negatively or positively charged as a whole; a charged atom is called an ion. Electrons have been known since the late 19th century, mostly thanks to J.J. Thomson; see history of subatomic physics for details.
Mass–energy equivalence
Once the nucleus was discovered, experimenters realized that the very high binding energies of the atomic nuclei should allow calculation of their binding energies, simply from mass differences. But it was not until the discovery of the neutron in 1932, and the measurement of the neutron mass, that this calculation could actually be performed (see nuclear binding energy for example calculation). A little while later, the Cockcroft–Walton accelerator produced the first transmutation reaction (), verifying Einstein's formula to an accuracy of ±0.5%.
In 2005, Rainville et al. published a direct test of the energy-equivalence of mass lost in the binding energy of a neutron to atoms of particular isotopes of silicon and sulfur, by comparing the mass lost to the energy of the emitted gamma ray associated with the neutron capture. The binding mass-loss agreed with the gamma ray energy to a precision of ±0.00004%, the most accurate test of to date.
Molar mass
The precision to which a molar mass is known depends on the precision of the atomic masses from which it was calculated. Most atomic masses are known to a precision of at least one part in ten-thousand, often much better (the atomic mass of lithium is a notable, and serious, exception). This is adequate for almost all normal uses in chemistry: it is more precise than most chemical analyses, and exceeds the purity of most laboratory reagents.
Kendrick mass
The Kendrick mass is defined by setting the mass of a chosen molecular fragment, typically CH, to an integer value in atomic mass units. It is different from the IUPAC definition, which is based on setting the mass of C isotope to exactly 12 u. The Kendrick mass is often used to identify homologous compounds differing only by a number of base units in high resolution mass spectra. This definition of mass was first suggested in 1963 by chemist Edward Kendrick, and it has been adopted by scientists working in the area of high-resolution mass spectrometry, environmental analysis, proteomics, petroleomics, metabolomics, polymer analysis, etc.
Milli mass unit
Since 1961 the unified atomic mass unit "u" has been defined as 1/12 the mass of C. Before that the atomic mass unit "amu" was defined as 1/16 the mass of O (physics) and as 1/16 the mass of O (chemistry). Thus the publication date in literature ought to be heeded when reading about the milli mass unit as its name does not reveal whether it refers to the old amu or the newer u.
Relative atomic mass
The IUPAC commission CIAAW maintains an expectation-interval value for relative atomic mass (or atomic weight) on Earth named standard atomic weight. Standard atomic weight requires the sources be terrestrial, natural, and stable with regard to radioactivity. Also, there are requirements for the research process. For 84 stable elements, CIAAW has determined this standard atomic weight. These values are widely published and referred to loosely as 'the' atomic weight of elements for real-life substances like pharmaceuticals and commercial trade.