Chemical element their atomic nucleus; so the atomic number of carbon is 6. Carbon atoms may have different numbers of neutrons; atoms of the same element having different numbers of neutrons are known as isotopes of the element. The number of protons in the atomic nucleus also determines its electric charge, which in turn determines the number of electrons of the atom in its non-ionized state. The electrons are placed into atomic orbitals that determine the atom's various chemical properties. The number of neutrons in a nucleus usually has very little effect on an element's chemical properties (except in the case of
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