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The mass number (symbol ''A'', from the German word ''Atomgewicht'' tomic weight, also called atomic mass number or nucleon number, is the total number of
proton A proton is a subatomic particle, symbol or , with a positive electric charge of +1''e'' elementary charge and a mass slightly less than that of a neutron. Protons and neutrons, each with masses of approximately one atomic mass unit, are collecti ...

proton
s and
neutron The neutron is a subatomic particle, symbol or , which has a neutral (not positive or negative) charge, and a mass slightly greater than that of a proton. Protons and neutrons constitute the nuclei of atoms. Since protons and neutrons behav ...

neutron
s (together known as
nucleon In chemistry Chemistry is the study of the properties and behavior of . It is a that covers the that make up matter to the composed of s, s and s: their composition, structure, properties, behavior and the changes they undergo during ...
s) in an
atomic nucleus The atomic nucleus is the small, dense region consisting of s and s at the center of an , discovered in 1911 by based on the 1909 . After the discovery of the neutron in 1932, models for a nucleus composed of protons and neutrons were quickl ...
. It is approximately equal to the ''atomic'' (also known as ''isotopic'') mass of the
atom An atom is the smallest unit of ordinary 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 ato ...

atom
expressed in
atomic mass unit The dalton or unified atomic mass unit (symbols: Da or u) is a unit Unit may refer to: Arts and entertainment * UNIT, a fictional military organization in the science fiction television series ''Doctor Who'' * Unit of action, a discrete piece o ...
s. Since protons and neutrons are both
baryon In particle physics Particle physics (also known as high energy physics) is a branch of that studies the nature of the particles that constitute and . Although the word ' can refer to various types of very small objects (e.g. , gas partic ...
s, the mass number ''A'' is identical with the baryon number ''B'' of the nucleus (and also of the whole atom or
ion An ion () is an atom An atom is the smallest unit of ordinary 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 ...
). The mass number is different for each different
isotope Isotopes are two or more types of atoms that have the same atomic number 300px, The Rutherford–Bohr model of the hydrogen atom () or a hydrogen-like ion (). In this model it is an essential feature that the photon energy (or frequency) of ...
of a
chemical element In chemistry Chemistry is the study of the properties and behavior of . It is a that covers the that make up matter to the composed of s, s and s: their composition, structure, properties, behavior and the changes they undergo du ...
. Hence, the difference between the mass number and the
atomic number The atomic number or proton number (symbol ''Z'') of a chemical element In chemistry, an element is a pure Chemical substance, substance consisting only of atoms that all have the same numbers of protons in their atomic nucleus, nuclei. ...
 ''Z'' gives the number of neutrons (''N'') in a given 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, whil ...

superscript
to the left of an element's symbol. For example, the most common isotope of
carbon Carbon (from la, carbo "coal") is a with the C and 6. It is lic and —making four s available to form s. It belongs to group 14 of the periodic table. Carbon makes up only about 0.025 percent of Earth's crust. Three occur naturally, ...

carbon
is
carbon-12 Carbon-12 (12C) is the more abundant of the two Stable isotope, stable isotopes of carbon (carbon-13 being the other), amounting to 98.93% of the Periodic table, element carbon; its abundance is due to the triple-alpha process by which it is crea ...

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: .


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 consi ...

radioactive decay
are characterized by their changes in mass number as well as
atomic number The atomic number or proton number (symbol ''Z'') of a chemical element In chemistry, an element is a pure Chemical substance, substance consisting only of atoms that all have the same numbers of protons in their atomic nucleus, nuclei. ...
, according to the
radioactive displacement law of Fajans and Soddy The law of radioactive displacements, also known as Fajan's and Soddy's law, in radiochemistryRadiochemistry is the chemistry of radioactive materials, where radioactive isotopes of elements are used to study the properties and chemical reactions o ...
. For example,
uranium-238 Uranium-238 (238U or U-238) is the most common isotope Isotopes are two or more types of atoms that have the same atomic number 300px, The Rutherford–Bohr model of the hydrogen atom () or a hydrogen-like ion (). In this model it is an ...
usually decays by
alpha decay
alpha decay
, 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 proton A proton is a subatomic particle, symbol or , with a positive electric charge of +1''e'' elementary charge and a mass slightly less than that of a neutron. Proto ...

alpha particle
. 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 Thorium is a weakly radioactive decay, radioactive metallic chemical element with the Symbol (chemistry), symbol Th and atomic number 90. Thorium is silvery and tarnishes black when it is exposed to air, forming thorium dioxide; it is ...
and an alpha particle ():Suchocki, John. ''Conceptual Chemistry'', 2007. Page 119. : On the other hand,
carbon-14 Carbon-14 (14C), or radiocarbon, is a radioactive isotope A radionuclide (radioactive nuclide, radioisotope or radioactive isotope) is a nuclide that has excess nuclear energy, making it unstable. This excess energy can be used in one of three ...

carbon-14
decays by
beta decay In , beta decay (''β''-decay) is a type of in which a (fast energetic or ) is emitted from an , transforming the original to an of that nuclide. For example, beta decay of a transforms it into a by the emission of an electron accompanie ...

beta decay
, whereby one neutron is transmuted into a proton with the emission of an
electron The electron is a subatomic particle (denoted by the symbol or ) whose electric charge is negative one elementary charge. Electrons belong to the first generation (particle physics), generation of the lepton particle family, and are general ...

electron
and an
antineutrino A neutrino ( or ) (denoted by the Greek letter Nu (letter), ) is a fermion (an elementary particle with spin-1/2, spin of ) that interacts only via the weak interaction and gravity. The neutrino is so named because it is electric charge, electri ...
. 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 Nitrogen is the chemical element Image:Simple Periodic Table Chart-blocks.svg, 400px, Periodic table, The periodic table of the chemical elements In chemistry, an element is a pure substance consisting only of atoms tha ...

nitrogen-14
, 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 The electron rest mass (symbol: ''m''e) is the mass Mass is both a property Property (''latin: Res Privata'') in the Abstract and concrete, abstract is what belongs to or with something, whether as an attribute or as a component of said t ...
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 γ or \gamma), is a penetrating form of electromagnetic radiation In physics Physics is the natural science that studies matter, its Elementary particle, fundamental constituents, it ...
from a
nuclear isomer A nuclear isomer is a metastable In chemistry Chemistry is the science, scientific study of the properties and behavior of matter. It is a natural science that covers the Chemical element, elements that make up matter to the chemical c ...
or
metastable In chemistry and physics, metastability denotes an intermediate energetic state within a dynamical system other than the system's ground state, state of least energy. A ball resting in a hollow on a slope is a simple example of metastability. I ...

metastable
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
atomic mass unit The dalton or unified atomic mass unit (symbols: Da or u) is a unit Unit may refer to: Arts and entertainment * UNIT, a fictional military organization in the science fiction television series ''Doctor Who'' * Unit of action, a discrete piece o ...
s (u). For 12C, the isotopic mass is exactly 12, since the atomic mass unit is defined as 1/12 of the mass of 12C. For other isotopes, the isotopic mass is usually within 0.1 u of the mass number. For example, 35Cl (17 protons and 18 neutrons) has a mass number of 35 and an isotopic mass of 34.96885. The difference of the actual isotopic mass minus the mass number of an atom is known as the mass excess, which for 35Cl is –0.03115. Mass excess should not be confused with
mass defect Mass is both a property Property (''latin: Res Privata'') in the Abstract and concrete, abstract is what belongs to or with something, whether as an attribute or as a component of said thing. In the context of this article, it is one or mo ...
which is the difference between the mass of an atom and its constituent particles (namely
protons A proton is a subatomic particle, symbol or , with a positive electric charge Electric charge is the physical property of matter that causes it to experience a force when placed in an electromagnetic field. There are two types of electric cha ...

protons
,
neutrons The neutron is a subatomic particle In physical sciences, subatomic particles are smaller than atom An atom is the smallest unit of ordinary matter In classical physics and general chemistry, matter is any substance that has mass ...

neutrons
and
electrons The electron is a subatomic particle In physical sciences, subatomic particles are smaller than atom An atom is the smallest unit of ordinary matter In classical physics and general chemistry, matter is any substance that has m ...

electrons
). 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 atomic mass unit scale 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 In physics Physics is the that studies , its , its and behavior through , and the related entities of and . "Physical science is that department of know ...

binding energy
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 Physics is the that studies , its , its and behavior through , and the related entities of and . "Physical science is that department of knowledge which relates to the order of nature, or, in other words, to the regular ...
relation ''E'' = ''mc''2. 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 (''A''r, standard(E)) of a chemical element In chemistry Chemistry is the study of the properties and behavior of . It is a that covers the that make up matter to the composed of s, s and s: their c ...
(also called
atomic weight Relative atomic mass (symbol: ''A'') or atomic weight is a dimensionless physical quantity A physical quantity is a physical property of a material or system that can be Quantification (science), quantified by measurement. A physical quantity ...
) 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 dalton or unified atomic mass unit (symbols: Da or u) is a unit of measurement, unit of mass widely used in physics and chemistry. It is defined as of the mass of an chemical bond, unbound neutral atom of carbon-12 in its nuclear and electro ...
. 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). 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 Chlorine is a chemical element Image:Simple Periodic Table Chart-blocks.svg, 400px, Periodic table, The periodic table of the chemical elements In chemistry, an element is a pure substance consisting only of atoms that al ...
: 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 35.4527 g/ mol). 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 In chemistry, an element is a pure Chemical substance, substance consisting only of atoms that all have the same numbers of protons in their atomic nucleus, nuclei. Unlike chemical compounds, chemical elemen ...

bromine
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.


References


Further reading

* {{cite book , last=Bishop , first=Mark , title=An Introduction to Chemistry , url=http://preparatorychemistry.com , access-date=2008-07-08 , publisher=Chiral Publishing , isbn=978-0-9778105-4-3 , pages=93 , chapter=The Structure of Matter and Chemical Elements (ch. 3) , chapter-url=http://preparatorychemistry.com/Bishop_Book_atoms_3.html __NOTOC__ Nuclear chemistry Chemical properties