Mass Number

The mass number, conventionally represented by $A$, is the total number of protons and neutrons in an atomic nucleus. These particles are collectively called nucleons, so mass number is also known as nucleon number. It is an exact, dimensionless count rather than a measurement of mass. Together with the proton count, it identifies the nuclear composition of an atom and distinguishes different isotopes of an element. (goldbook.iupac.org)

Definition and notation

Mass number is defined by

where $Z$ is the atomic number, or number of protons, and $N$ is the neutron number. Consequently, the neutron count can be calculated as $N=A-Z$. For an atomic nucleus, $A$ is a positive integer. Hydrogen-1, whose nucleus consists of one proton and no neutrons, has $A=1$; carbon-14, with six protons and eight neutrons, has $A=14$. (goldbook.iupac.org)

A nucleus or atom with a specified nuclear composition is described as a nuclide. Its conventional notation is

where $\mathrm{X}$ is the symbol of the chemical element. The mass number appears as a left superscript and the atomic number as a left subscript. Thus carbon-14 is written ${}^{14}_{6}\mathrm{C}$. Because the element symbol already identifies $Z$, the subscript may be omitted, giving ${}^{14}\mathrm{C}$. In names, the mass number follows the element name after a hyphen, as in “carbon-14.” (iupac.org)

The number of electrons does not enter the definition. Removing or adding electrons produces an ion without changing $A$ or $Z$. Ionic charge is written separately as a right superscript: ${}^{13}\mathrm{C}^{+}$, for example, still has mass number 13. (goldbook.iupac.org)

Isotopes and isobars

Isotopes are nuclides of the same element with equal proton numbers but different neutron numbers, and therefore different mass numbers. Carbon-12, carbon-13, and carbon-14 all have $Z=6$, but their neutron counts are six, seven, and eight, respectively. An element consequently does not necessarily have a single mass number: the value belongs to a particular isotope, not to the element considered as an isotopic mixture. (openstax.org)

Different nuclides with the same mass number are called isobars. Equal $A$ means equal total nucleon counts, not identical nuclear composition. For example, carbon-14 and nitrogen-14 both contain 14 nucleons, but their proton and neutron counts differ. Mass number alone therefore cannot identify an element or uniquely specify a nuclide; atomic number is also required. (goldbook.iupac.org)

Difference from atomic mass and atomic weight

Despite its name, mass number is not atomic mass. Atomic mass is the measured mass of an individual atom, commonly expressed in the dalton or unified atomic mass unit, symbol $u$. This unit is defined through carbon-12: a neutral carbon-12 atom in its nuclear and electronic ground state has a mass of exactly $12\,u$. Other isotopic masses generally are not integers. Carbon-13, for example, has $A=13$, but its atomic mass is approximately $13.003355\,u$. (nist.gov)

The approximate correspondence between mass number and atomic mass reflects the roughly unit masses of protons and neutrons on this scale. Their masses are not exactly $1\,u$, however, and a bound nucleus has less mass than the sum of its separated nucleons. This difference is associated with nuclear binding energy through mass–energy equivalence. Electrons also contribute to the mass of an atom. None of these contributions changes the integer nucleon count. (openstax.org)

Relative atomic mass is a dimensionless ratio of atomic mass to the atomic mass constant. For an element in a sample, its atomic weight reflects the abundance-weighted mean of its isotopic masses. A carbon atomic weight near 12.011 therefore does not mean that a carbon nucleus contains 12.011 nucleons. Rounding an element’s atomic weight cannot, in general, determine the mass number of an unspecified isotope. (nist.gov)

Changes in radioactive decay

Mass-number bookkeeping is important in radioactive decay. In alpha decay, a nucleus emits a helium-4 nucleus containing two protons and two neutrons. The daughter nucleus has mass number $A-4$ and atomic number $Z-2$. (openstax.org)

In ordinary beta decay, one nucleon changes type without changing the total nucleon count. Beta-minus decay converts a neutron into a proton while emitting an electron and an electron antineutrino; $A$ remains unchanged and $Z$ increases by one. Beta-plus decay changes a proton into a neutron, decreasing $Z$ by one while preserving $A$. Emission of a gamma ray changes the nuclear energy state but not either nucleon count. (openstax.org)

Nuclear reactions and binding energy

In ordinary nuclear reactions, the total mass numbers of all participating nuclei and free nucleons balance between the initial and final states. For example, a fusion reaction between deuterium and tritium produces helium-4 and a neutron:

The nucleon-count balance is $2+3=4+1$. Likewise, fission equations must include emitted neutrons when balancing mass numbers. This accounting does not imply conservation of the summed rest masses: differences in rest mass can appear as released energy. (openstax.org)

In nuclear physics, dividing total binding energy by $A$ gives binding energy per nucleon, a useful quantity for comparing nuclei of different sizes. Mass number specifies how many nucleons are present, but their arrangement and interactions determine the binding energy; equal mass numbers do not guarantee equal masses or equal stability. (openstax.org)