Atomic number, symbol (Z), is the number of protons in an atomic nucleus. It defines the identity of a chemical element: atoms with the same atomic number belong to the same element, regardless of differences in their neutron or electron counts. Also called the proton number, it provides the ordering principle of the modern periodic table. Unlike atomic mass, atomic number is an exact count rather than a measured mass or an average over isotopes. (goldbook.iupac.org)
Nuclear charge and electrons
Each proton carries one positive elementary charge, (e), so a nucleus containing (Z) protons has electric charge (+Ze). In an electrically neutral atom, this positive charge is balanced by (Z) negatively charged electrons. Consequently, atomic number specifies both the proton count and, for a neutral atom, the electron count. (openstax.org)
An ion has gained or lost electrons without necessarily changing its nucleus. If (n_e) is its electron count, its net charge is
[ q=(Z-n_e)e. ]
For example, neutral sodium has 11 electrons, whereas a sodium ion, (\mathrm{Na}^{+}), has 10; both have (Z=11). Electron removal through ionization therefore changes charge state, not elemental identity. Atomic number should not be confused with the charge displayed as a superscript on an ion symbol. (openstax.org)
Mass number, isotopes, and notation
Atomic number differs from mass number, (A), which counts both protons and neutrons. For an ordinary nucleus with neutron number (N),
[ A=Z+N,\qquad N=A-Z. ]
Atoms of the same element with different neutron counts are isotopes. Carbon-12 and carbon-14, for example, both have (Z=6), but contain six and eight neutrons respectively. Their differing mass numbers do not give them different positions in the periodic table. (openstax.org)
A nucleus or isotope is commonly represented as
[ {}^{A}_{Z}\mathrm{X}, ]
where (\mathrm{X}) is the element symbol. Thus ({}^{14}_{6}\mathrm{C}) identifies carbon-14. The subscript (Z) is often omitted because the element symbol already determines it. Relative atomic mass, by contrast, expresses mass relative to the atomic mass standard; values tabulated for elements generally reflect isotopic composition rather than a proton count. Atomic number and mass number are integers, whereas relative atomic mass generally is not. (openstax.org)
Historical development
Dmitri Mendeleev published his periodic system in 1869, principally arranging elements by atomic weight while using chemical similarities to resolve problematic placements. Atomic-weight ordering nevertheless produced exceptions, including tellurium and iodine: their chemical relationships required an order opposite to that suggested by their weights. (periodic-table.rsc.org)
The decisive experimental advance came from Henry Moseley in 1913–1914. Using spectroscopy, he measured characteristic X-rays emitted by elements and found systematic relationships between their frequencies and atomic numbers. His work established a measurable physical basis for the sequence of elements, connecting their positions with nuclear charge rather than atomic weight. It also exposed gaps corresponding to elements not yet discovered. (nist.gov)
For a particular series of characteristic X-ray lines, Moseley’s law can be expressed approximately as
[ \sqrt{\nu}=a(Z-b), ]
where (\nu) is frequency and (a) and (b) depend on the line series. This relationship resolved ordering anomalies such as cobalt and nickel and helped establish atomic number as the fundamental index of the periodic system. (nist.gov)
Electronic structure and periodicity
Atomic number fixes the nuclear charge and the electron count of a neutral atom. Together with the principles of quantum mechanics, these determine its electron configuration—the distribution of electrons among atomic orbitals. Orbital occupation follows rules including the Pauli exclusion principle, rather than a simple classical arrangement around the nucleus. (openstax.org)
As atomic number increases, recurring outer-electron configurations produce recurring chemical properties. Elements in the same periodic-table group commonly have similar valence-electron arrangements, explaining similarities in bonding and reactivity. Atomic number therefore underlies periodic classification, although chemical behavior depends on electronic structure and environment, not on proton count alone. (openstax.org)
Nuclear attraction is also partly screened by other electrons. Across a period, increasing effective nuclear attraction generally reduces atomic size and raises ionization energy, with exceptions associated with orbital occupation. Down a group, additional electron shells alter these trends. Atomic number is thus an organizing variable, not a guarantee that every property changes monotonically. (openstax.org)
Changes in nuclear processes
Ordinary chemical transformations rearrange electrons while preserving the atomic numbers of the participating nuclei. Nuclear transformations can change proton counts and thereby convert one element into another. In alpha decay, emission of a helium nucleus reduces (Z) by two and (A) by four. In beta-minus beta decay, a neutron becomes a proton, increasing (Z) by one without changing (A). Positron emission and electron capture reduce (Z) by one, likewise leaving (A) unchanged. Gamma emission changes neither number. (openstax.org)
In nuclear equations, the sums of mass-number labels and charge-number labels balance on both sides. Labels assigned to emitted electrons or positrons represent their charges, not proton counts: an electron written as ({}^{0}_{-1}\mathrm{e}) does not contain “negative one proton.” This notation distinguishes conservation of total electric charge from the possible change in the atomic number of an individual nucleus. (openstax.org)