Rutherford's gold foil experiment, performed in conjunction with Geiger and Marsden, provided evidence for the nucleus due to the scattering of alpha particles. The repulsion of some alpha particles suggested that the nucleus is positively charged, containing protons. Further work by Chadwick revealed the existence of neutrons within the nucleus of the atom. The atomic number describes the number of protons in the nucleus. For a neutral atom this is also the number of electrons outside the nucleus. Subtracting the atomic number from the atomic mass number gives the number of neutrons in the nucleus. Isotopes are atoms of the same element (i.e., they have the same number of protons, or the same atomic number) which have a different number of neutrons in the nucleus. Isotopes of an element have similar chemical properties. Radioactive isotopes are called radioisotopes. Most of the elements in the periodic table have several isotopes, found in varying proportions for any given element. The average atomic mass of an element takes into account the relative proportions of its isotopes found in nature. A nuclear binding force holds the nucleus of the atom together. The nuclear mass defect, a slightly lower mass of the nucleus compared to the sum of the masses of its constituent matter, is due to the nuclear binding energy holding the nucleus together. The mass defect can be used to calculate the nuclear binding energy, with E = mc². The average binding energy per nucleon is a measure of nuclear stability. The higher the average binding energy, the more stable the nucleus.

The Bohr's model of the atom described the electrons as orbiting in discrete, precisely defined circular orbits. Electrons can only occupy certain allowed orbitals. For an electron to occupy an allowed orbit, a certain amount of energy must be available. Each orbit is assigned a quantum number, with the lowest quantum numbers being assigned to those orbitals closest to the nucleus. Only a specified maximum number of electrons can occupy an orbital. Under normal circumstances, electrons occupy the lowest energy level orbitals closest to the nucleus. By absorbing additional energy, electrons can be promoted to higher orbitals, and release that energy when they return back to lower energy levels. The Bohr's model of the atom helped to offer one possible explanation for the emission spectrum formed by hydrogen and other gases. Photons are used to describe the wave-particle duality of light. The energy of a photon depends upon its frequency. This helps to explain the photoelectric effect; only photons having a sufficiently high energy are capable of dislodging an electron from the illuminated surface. E = hv where E is the photon energy in J, v is the photon frequency in Hz, and h is Planck's constant, 6.626 × 10^-34 J / Hz. Quantum theory offers a mathematical model to help explain the nature of the atom. Quantum theory describes a region surrounding the nucleus which has the highest probability of locating an electron. These orbital "clouds" have some unusual and interesting shapes.