Atom Calculator — Protons & Electrons

Three integers describe an atom completely at this level of bookkeeping. The atomic number Z is the proton count and fixes the element: Z equal to 6 is carbon and nothing else, whatever the neutron count. The mass number A is protons plus neutrons, so neutrons equal A minus Z, and nuclides sharing Z but differing in A are isotopes. Electron count is Z minus the ionic charge, which is why an Fe3+ ion has 26 protons and 23 electrons. Stable nuclides run from a neutron-to-proton ratio near 1 for light elements up to about 1.5 for lead, and the belt of stability ends at bismuth; every element above Z equal to 83 is radioactive, and the periodic table currently stops at oganesson, Z equal to 118. Electron configurations here are filled by the Madelung or n plus l rule, which orders subshells 1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p and so on, subject to the Pauli exclusion principle limiting each orbital to two electrons of opposite spin and Hund rule of maximum multiplicity for degenerate orbitals. That ordering is an approximation with well-known exceptions: chromium is 3d5 4s1 and copper 3d10 4s1 rather than the predicted 3d4 4s2 and 3d9 4s2. Bulk quantities connect to atom counts through the Avogadro constant, fixed at exactly 6.02214076 times 10 to the 23rd per mole since the 2019 revision of the SI. The mass number used for grams-per-mole here is an integer nucleon count, not the isotope-averaged atomic weight from the periodic table, so the two differ slightly.

The nuclear picture assembled quickly in the early twentieth century. Ernest Rutherford interpreted the 1909 Geiger and Marsden alpha-scattering results as evidence for a tiny dense nucleus in 1911, replacing J. J. Thomson diffuse model. In 1913 Henry Moseley, working at Manchester, measured characteristic X-ray frequencies across the elements and showed they scaled with an integer that ordered the periodic table better than atomic weight did; that integer was recognised as nuclear charge, giving atomic number a physical meaning rather than a positional one. Moseley was killed at Gallipoli in 1915. Rutherford identified the proton in 1919, and James Chadwick established the neutron in 1932, which finally explained isotopes as nuclides differing only in neutron number. The electronic side developed in parallel. Niels Bohr proposed quantised electron shells in 1913 and used shell filling to rationalise periodicity. Wolfgang Pauli stated the exclusion principle in 1925, Friedrich Hund formulated his rules for degenerate orbitals the same year, and Erwin Schrodinger wave mechanics of 1926 replaced orbits with orbitals. The n plus l ordering rule is usually credited to Erwin Madelung in the 1930s, with Vsevolod Klechkovsky giving a theoretical justification in 1962. The mole and its associated constant, named after Amedeo Avogadro following Jean Perrin work of 1909, remained an experimentally determined quantity until the General Conference on Weights and Measures redefined it by fixing a numerical value in 2019.