Electron shell

Overview
An electron shell, also known as a main energy level, is a group of atomic orbitals with the same value of the principal quantum number n. Electron shells are made up of one or more electron subshells, or sublevels, which have two or more orbitals with the same angular momentum quantum number l. Electron shells make up the electron configuration of an atom. It can be shown that the number of electrons that can reside in a shell is equal to $$2n^2$$.

History
The existence of electron shells was first observed experimentally in Charles Barkla's and Henry Moseley's X-ray absorption studies. Barkla labelled them with the letters K, L, M, etc. (The origin of this terminology was alphabetic. K for hypothetical spectral lines that were never discovered.) These letters were later found to correspond to the n-values 1, 2, 3, etc. They are used in the spectroscopic Siegbahn notation.

The name for electron shells originates from the Bohr model, in which groups of electrons were believed to orbit the nucleus at certain distances, so that their orbits formed "shells" around the nucleus.

Valence shell
The valence shell is the outermost shell of an atom in its uncombined state, which contains the electrons most likely to account for the nature of any reactions involving the atom and of the bonding interactions it has with other atoms. The outermost shell of an ion is not commonly termed valence shell. Electrons in the valence shell are referred to as valence electrons. The physical chemist Gilbert Lewis was responsible for much of the early development of the theory of the participation of valence shell electrons in chemical bonding. Linus Pauling later generalized and extended the theory while applying insights from quantum mechanics.

In a noble gas, an atom tends to have 8 electrons in its outer shell (except helium, which is only able to fill its shell with 2 electrons). This serves as the model for the octet rule which is mostly applicable to main group elements of the second and third periods. In terms of atomic orbitals, the electrons in the valence shell are distributed 2 in the single s orbital and 2 each in the three p orbitals.

For coordination complexes containing transition metals, the valence shell consists of electrons in these s and p orbitals, as well as up to 10 additional electrons, distributed as 2 into each of 5 d orbitals, to make a total of 18 electrons in a complete valence shell for such a compound. This is referred to as the eighteen electron rule.

Each shell (n=1, 2, 3, 4) can hold 2, 8, 18, or 32 electrons, or $$2n^2$$ electrons. It is important to note that the number of valence electrons is not necessarily equal to the total number of electrons in a given electron shell. For example, because the 3d subshell has a higher energy than the 4s subshell, the 3d electrons are considered to be part of the 4th valence shell. So, while the 3rd electron shell can contain a total of 18 electrons (2 in the 3s orbital, 6 in the 3p orbitals, and 10 in the 3d orbitals), the 3rd valence shell contains only 8 electrons as the 3d electrons are typically not part of the 3rd valence shell.