Chemical element hydrogen and deuterium). Thus, all carbon isotopes have nearly identical chemical properties because they all have six protons and six electrons, even though carbon atoms may, for example, have 6 or 8 neutrons. That is why the atomic number, rather than mass number or atomic weight, is considered the identifying characteristic of a chemical element. The symbol for atomic number is "Z". Isotopes are atoms of the same element (that is, with the same number of protons in their atomic nucleus), but having "different" numbers of neutrons. Thus, for example, there are three main isotopes of carbon. All carbon atoms
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