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

proton A proton is a stable subatomic particle, symbol , Hydron (chemistry), H+, or 1H+ with a positive electric charge of +1 ''e'' (elementary charge). Its mass is slightly less than the mass of a neutron and approximately times the mass of an e ...

s and

neutron The neutron is a subatomic particle, symbol or , that has no electric charge, and a mass slightly greater than that of a proton. The Discovery of the neutron, neutron was discovered by James Chadwick in 1932, leading to the discovery of nucle ...

s (together known as

nucleon In physics and chemistry, a nucleon is either a proton or a neutron, considered in its role as a component of an atomic nucleus. The number of nucleons in a nucleus defines the atom's mass number. Until the 1960s, nucleons were thought to be ele ...

s) in an

atomic nucleus The atomic nucleus is the small, dense region consisting of protons and neutrons at the center of an atom, discovered in 1911 by Ernest Rutherford at the Department_of_Physics_and_Astronomy,_University_of_Manchester , University of Manchester ...

. It is approximately equal to the ''atomic'' (also known as ''isotopic'') mass of the

atom Atoms are the basic particles of the chemical elements. An atom consists of a atomic nucleus, nucleus of protons and generally neutrons, surrounded by an electromagnetically bound swarm of electrons. The chemical elements are distinguished fr ...

expressed in daltons. Since protons and neutrons are both

baryon In particle physics, a baryon is a type of composite particle, composite subatomic particle that contains an odd number of valence quarks, conventionally three. proton, Protons and neutron, neutrons are examples of baryons; because baryons are ...

s, the mass number ''A'' is identical with the

baryon number In particle physics, the baryon number (B) is an additive quantum number of a system. It is defined as B = \frac(n_\text - n_), where is the number of quarks, and is the number of antiquarks. Baryons (three quarks) have B = +1, mesons (one q ...

''B'' of the nucleus (and also of the whole atom or ion). The mass number is different for each

isotope Isotopes are distinct nuclear species (or ''nuclides'') of the same chemical element. They have the same atomic number (number of protons in their Atomic nucleus, nuclei) and position in the periodic table (and hence belong to the same chemica ...

of a given

chemical element A chemical element is a chemical substance whose atoms all have the same number of protons. The number of protons is called the atomic number of that element. For example, oxygen has an atomic number of 8: each oxygen atom has 8 protons in its ...

, and the difference between the mass number and the

atomic number The atomic number or nuclear charge number (symbol ''Z'') of a chemical element is the charge number of its atomic nucleus. For ordinary nuclei composed of protons and neutrons, this is equal to the proton number (''n''p) or the number of pro ...

''Z'' gives the number of neutrons (''N'') in the nucleus: . The mass number is written either after the element name or as a

superscript A subscript or superscript is a character (such as a number or letter) that is set slightly below or above the normal line of type, respectively. It is usually smaller than the rest of the text. Subscripts appear at or below the baseline, wh ...

to the left of an element's symbol. For example, the most common isotope of

carbon Carbon () is a chemical element; it has chemical symbol, symbol C and atomic number 6. It is nonmetallic and tetravalence, tetravalent—meaning that its atoms are able to form up to four covalent bonds due to its valence shell exhibiting 4 ...

carbon-12 Carbon-12 (12C) is the most abundant of the two stable isotopes of carbon ( carbon-13 being the other), amounting to 98.93% of element carbon on Earth; its abundance is due to the triple-alpha process by which it is created in stars. Carbon-1 ...

, 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: .

Mass number changes in radioactive decay

Different types of

radioactive decay Radioactive decay (also known as nuclear decay, radioactivity, radioactive disintegration, or nuclear disintegration) is the process by which an unstable atomic nucleus loses energy by radiation. A material containing unstable nuclei is conside ...

are characterized by their changes in mass number as well as

, according to the radioactive displacement law of Fajans and Soddy. For example,

uranium-238 Uranium-238 ( or U-238) is the most common isotope of uranium found in nature, with a relative abundance of 99%. Unlike uranium-235, it is non-fissile, which means it cannot sustain a chain reaction in a thermal-neutron reactor. However, it i ...

usually decays by

alpha decay Alpha decay or α-decay is a type of radioactive decay in which an atomic nucleus emits an alpha particle (helium nucleus). The parent nucleus transforms or "decays" into a daughter product, with a mass number that is reduced by four and an a ...

, where the nucleus loses two neutrons and two protons in the form of an

alpha particle Alpha particles, also called alpha rays or alpha radiation, consist of two protons and two neutrons bound together into a particle identical to a helium-4 nucleus. They are generally produced in the process of alpha decay but may also be produce ...

. Thus the atomic number and the number of neutrons each decrease by 2 (''Z'': 92 → 90, ''N'': 146 → 144), so that the mass number decreases by 4 (''A'' = 238 → 234); the result is an atom of

thorium-234 Thorium (90Th) has seven naturally occurring isotopes but none are stable. One isotope, 232Th, is ''relatively'' stable, with a half-life of 1.405×1010 years, considerably longer than the age of the Earth, and even slightly longer than the gen ...

and an alpha particle ():Suchocki, John. ''Conceptual Chemistry'', 2007. Page 119. : On the other hand,

carbon-14 Carbon-14, C-14, C or radiocarbon, is a radioactive isotope of carbon with an atomic nucleus containing 6 protons and 8 neutrons. Its presence in organic matter is the basis of the radiocarbon dating method pioneered by Willard Libby and coll ...

decays by

beta decay In nuclear physics, beta decay (β-decay) is a type of radioactive decay in which an atomic nucleus emits a beta particle (fast energetic electron or positron), transforming into an isobar of that nuclide. For example, beta decay of a neutron ...

, whereby one neutron is transmuted into a proton with the emission of an

electron The electron (, or in nuclear reactions) is a subatomic particle with a negative one elementary charge, elementary electric charge. It is a fundamental particle that comprises the ordinary matter that makes up the universe, along with up qua ...

and an

antineutrino A neutrino ( ; denoted by the Greek letter ) is an elementary particle that interacts via the weak interaction and gravity. The neutrino is so named because it is electrically neutral and because its rest mass is so small ('' -ino'') that it ...

. Thus the atomic number increases by 1 (''Z'': 6 → 7) and the mass number remains the same (''A'' = 14), while the number of neutrons decreases by 1 (''N'': 8 → 7). The resulting atom is

nitrogen-14 Natural nitrogen (7N) consists of two stable isotopes: the vast majority (99.6%) of naturally occurring nitrogen is nitrogen-14, with the remainder being nitrogen-15. Thirteen radioisotopes are also known, with atomic masses ranging from 9 to 23, ...

, with seven protons and seven neutrons: : Beta decay is possible because different isobarsAtoms with the same mass number. have mass differences on the order of a few

electron mass In particle physics, the electron mass (symbol: ) 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 or about , which has an energy ...

es. If possible, a nuclide will undergo beta decay to an adjacent isobar with lower mass. In the absence of other decay modes, a cascade of beta decays terminates at the isobar with the lowest atomic mass. Another type of radioactive decay without change in mass number is emission of a

gamma ray A gamma ray, also known as gamma radiation (symbol ), is a penetrating form of electromagnetic radiation arising from high energy interactions like the radioactive decay of atomic nuclei or astronomical events like solar flares. It consists o ...

from a

nuclear isomer A nuclear isomer is a metastable state of an atomic nucleus, in which one or more nucleons (protons or neutrons) occupy excited state levels (higher energy levels). "Metastable" describes nuclei whose excited states have Half-life, half-lives of ...

metastable In chemistry and physics, metastability is an intermediate energetic state within a dynamical system other than the system's state of least energy. A ball resting in a hollow on a slope is a simple example of metastability. If the ball is onl ...

excited state of an atomic nucleus. Since all the protons and neutrons remain in the nucleus unchanged in this process, the mass number is also unchanged.

Mass number and isotopic mass

The mass number gives an estimate of the isotopic mass measured in daltons (Da). For ¹²C, the isotopic mass is exactly 12, since the dalton is defined as 1/12 of the mass of ¹²C. For other isotopes, the isotopic mass is usually within of the mass number. For example, ³⁵Cl (17 protons and 18 neutrons) has a mass number of 35 and an isotopic mass of . The difference of the actual isotopic mass minus the mass number of an atom is known as the

mass excess The mass excess of a nuclide is the difference between its actual mass and its mass number in daltons. 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 ...

, which for ³⁵Cl is –0.03115. Mass excess should not be confused with mass defect, which is the difference between the mass of an atom and its constituent particles (namely

protons A proton is a stable subatomic particle, symbol , H+, or 1H+ with a positive electric charge of +1 ''e'' ( elementary charge). Its mass is slightly less than the mass of a neutron and approximately times the mass of an electron (the pro ...

, neutrons and

electrons The electron (, or in nuclear reactions) is a subatomic particle with a negative one elementary charge, elementary electric charge. It is a fundamental particle that comprises the ordinary matter that makes up the universe, along with up qua ...

). There are two reasons for mass excess: # The neutron is slightly heavier than the proton. This increases the mass of nuclei with more neutrons than protons relative to the dalton based on ¹²C with equal numbers of protons and neutrons. # Nuclear

binding energy In physics and chemistry, binding energy is the smallest amount of energy required to remove a particle from a system of particles or to disassemble a system of particles into individual parts. In the former meaning the term is predominantly use ...

varies between nuclei. A nucleus with greater binding energy has a lower total energy, and therefore a lower mass according to Einstein's

mass–energy equivalence In physics, mass–energy equivalence is the relationship between mass and energy in a system's rest frame. The two differ only by a multiplicative constant and the units of measurement. The principle is described by the physicist Albert Einstei ...

relation . For ³⁵Cl, the isotopic mass is less than 35, so this must be the dominant factor.

Relative atomic mass of an element

The mass number should also not be confused with the

standard atomic weight The standard atomic weight of a chemical element (symbol ''A''r°(E) for element "E") is the weighted arithmetic mean of the relative isotopic masses of all isotopes of that element weighted by each isotope's abundance on Earth. For example, ...

(also called

atomic weight Relative atomic mass (symbol: ''A''; sometimes abbreviated RAM or r.a.m.), also known by the deprecated synonym atomic weight, is a dimensionless physical quantity defined as the ratio of the average mass of atoms of a chemical element in a giv ...

) of an element, which is the ratio of the average atomic mass of the different isotopes of that element (weighted by abundance) to the

atomic mass constant The dalton or unified atomic mass unit (symbols: Da or u, respectively) is a unit of mass defined as of the mass of an unbound neutral atom of carbon-12 in its nuclear and electronic ground state and at rest. It is a non-SI unit accepted f ...

. The atomic weight is a ''mass'' ratio, while the mass number is a ''counted'' number (and so an integer). This weighted average can be quite different from the near-integer values for individual isotopic masses. For instance, there are two main isotopes of chlorine: chlorine-35 and chlorine-37. In any given sample of chlorine that has not been subjected to mass separation there will be roughly 75% of chlorine atoms which are chlorine-35 and only 25% of chlorine atoms which are chlorine-37. This gives chlorine a relative atomic mass of 35.5 (actually ). Moreover, the weighted average mass can be near-integer, but at the same time not corresponding to the mass of any natural isotope. For example,

bromine Bromine is a chemical element; it has chemical symbol, symbol Br and atomic number 35. It is a volatile red-brown liquid at room temperature that evaporates readily to form a similarly coloured vapour. Its properties are intermediate between th ...

has only two stable isotopes, ⁷⁹Br and ⁸¹Br, naturally present in approximately equal fractions, which leads to the standard atomic mass of bromine close to 80 (79.904 g/mol), even though the isotope ⁸⁰Br with such mass is unstable.

Mass number changes in radioactive decay

Mass number and isotopic mass

Relative atomic mass of an element

References

Further reading