History of subatomic physics the mostly empty volume of atoms. In 1918, Rutherford confirmed that the hydrogen nucleus was a particle with a positive charge, which he named the proton. By then, Frederick Soddy's researches of radioactive elements, and experiments of J. J. Thomson and F.W. Aston conclusively demonstrated existence of isotopes, whose nuclei have different masses in spite of identical atomic numbers. It prompted Rutherford to conjecture that all nuclei other than hydrogen contain chargeless particles, which he named the neutron. Evidences that atomic nuclei consist of some smaller particles (now called "nucleons") grew; it became obvious that, while protons repulse each other
Atomic orbital polynomial series, and exponential and trigonometric functions. (see hydrogen atom). For atoms with two or more electrons, the governing equations can only be solved with the use of methods of iterative approximation. Orbitals of multi-electron atoms are "qualitatively" similar to those of hydrogen, and in the simplest models, they are taken to have the same form. For more rigorous and precise analysis, numerical approximations must be used. A given (hydrogen-like) atomic orbital is identified by unique values of three quantum numbers: , , and . The rules restricting the values of the quantum numbers, and their energies (see below), explain