Atomic Number & Mass Number

Every atom is defined by two fundamental numbers: its atomic number (Z) and its mass number (A). These two integers encode the entire identity of an atom — what element it is, how many neutrons it contains, and how many electrons it carries when electrically neutral. Understanding Z and A is the foundation of all atomic chemistry, from writing chemical formulas to understanding radioactive decay. The atomic number Z equals the number of protons in the nucleus. Because protons carry a positive charge of +1e each, Z also determines the nuclear charge. More importantly, Z uniquely identifies the element: every carbon atom has Z = 6, every oxygen atom has Z = 8, and no two elements share the same atomic number. If you change Z, you change the element entirely — this is precisely what happens in nuclear reactions such as alpha decay or beta decay. The mass number A equals the total count of nucleons — that is, protons plus neutrons — in the nucleus. Electrons contribute negligible mass (about 1/1836 of a proton's mass), so A is essentially the integer approximation of an atom's mass in atomic mass units (u). Different atoms of the same element can have different values of A because the neutron count can vary; these variants are called isotopes. Together, Z and A allow chemists and physicists to distinguish every nuclide — every specific nuclear species — that exists.

Key takeaways

Define Atomic Number (Z)
Define Mass Number (A)
Calculate Number of Neutrons (N)
Electrons in a Neutral Atom
Nuclide Notation

Define Atomic Number (Z)

The atomic number Z is the number of protons in the nucleus of an atom. It is always a positive integer and is unique to each element. For example, hydrogen has Z = 1, carbon has Z = 6, and gold has Z = 79. The periodic table is arranged in order of increasing Z, which is why atomic number is sometimes called the 'identity number' of an element.

Define Mass Number (A)

The mass number A is the total number of protons and neutrons (collectively called nucleons) in the nucleus. It is always a positive integer. For example, a common carbon atom has 6 protons and 6 neutrons, so A = 12. A heavier carbon isotope has 6 protons and 8 neutrons, giving A = 14. Note that A is not the same as atomic mass (measured in u), which is a weighted average of all naturally occurring isotopes.

Calculate Number of Neutrons (N)

Once you know Z and A, you can find the number of neutrons using the simple relationship N = A − Z. For carbon-14: N = 14 − 6 = 8 neutrons. For uranium-238: N = 238 − 92 = 146 neutrons. Neutrons have no charge, so they do not affect the chemical identity of an element, but they do affect nuclear stability.

Electrons in a Neutral Atom

In a neutral (uncharged) atom, the number of electrons equals the number of protons, so the number of electrons = Z. Electrons occupy shells around the nucleus and are responsible for all chemical behavior. If electrons are added or removed, the atom becomes a negatively or positively charged ion (anion or cation), but Z does not change — the element remains the same.

Nuclide Notation

A nuclide is written using the symbol of the element with A as a superscript on the upper left and Z as a subscript on the lower left: ${}^{A}_{Z}\text{X}$ . For example, carbon-12 is written ${}^{12}_{6}\text{C}$ , carbon-14 is ${}^{14}_{6}\text{C}$ , and uranium-235 is ${}^{235}_{92}\text{U}$ . Because Z is already implied by the element symbol, it is sometimes omitted, leaving only the mass number as a superscript.

The Key Equation

A = Z + N

A — Mass Number (dimensionless (integer)): Total number of protons and neutrons (nucleons) in the nucleus; approximates atomic mass in unified atomic mass units (u).
Z — Atomic Number (dimensionless (integer)): Number of protons in the nucleus; uniquely identifies the element and equals the number of electrons in a neutral atom.
N — Neutron Number (dimensionless (integer)): Number of neutrons in the nucleus; calculated as N = A − Z. Varies between isotopes of the same element.

Worked Example

Problem. An atom of chlorine has the nuclide notation ${}^{37}_{17}\text{Cl}$ . Determine: (a) the number of protons, (b) the number of neutrons, (c) the number of electrons in the neutral atom, and (d) identify whether this is the same element as ${}^{35}_{17}\text{Cl}$ and explain why.

Z = 17,\quad N = A - Z = 37 - 17 = 20,\quad e^{-} = 17

Answer. Protons = 17, Neutrons = 20, Electrons = 17. Both ${}^{35}_{17}\text{Cl}$ and ${}^{37}_{17}\text{Cl}$ are chlorine isotopes (Z = 17 for both).

Figure

Diagram

Origins · 1 minErnest Rutherford and how this was discovered

Ernest Rutherford

1871–1937 · New Zealand–British

Rutherford's gold foil experiment (1909–1911) revealed that atoms have a tiny, dense, positively charged nucleus — overturning the 'plum pudding' model. He discovered the proton in 1917 and coined the term 'atomic number' in the context of nuclear charge. His nuclear model directly established that Z (the nuclear charge) uniquely identifies an element. He also predicted the existence of the neutron, which was later confirmed by James Chadwick in 1932. Rutherford famously said that all science is either physics or stamp collecting. He won the Nobel Prize in Chemistry (not Physics!) in 1908 — before he made his most famous discoveries about the nucleus.

Isotopes and Relative Atomic Mass — Isotopes are atoms with the same Z but different A (and thus different N). Understanding Z and A is a prerequisite for calculating weighted average atomic masses from isotopic abundances.
Electron Configuration and Shells — The number of electrons in a neutral atom equals Z. Knowing Z directly leads to writing electron configurations, which determine an element's chemical properties and position in the periodic table.
Radioactive Decay and Nuclear Equations — In nuclear equations, Z and A must balance on both sides. Alpha decay decreases Z by 2 and A by 4; beta decay increases Z by 1 with no change in A. These calculations rely entirely on the definitions of Z and A.
The Periodic Table and Periodicity — The periodic table is arranged by increasing atomic number Z. Each element's position (period and group) is determined by Z and the resulting electron configuration, linking subatomic particle counts to macroscopic chemical trends.