An electron shell (or atomic shell) is the region of space around an atom in which an electron with a particular amount of energy can reside. Electron shells are denoted using principle atomic numbers n=1, 2, 3,... with each higher number indicating a higher energy region and are further away from the nucleus. Each shell can hold 2n2 electrons. The outer part of the atomic shells, the Valence shell, is responsible for the chemical bonds in particular.
Amazingly, the energy levels in the basic analysis of hydrogen depend only on the principal quantum number and not the azimuthal or magnetic quantum numbers (See quantum number). When the energy is expressed in electron volts, the energy of the nth is:
This can be generalized to partially ionized atoms that have only one electron with atomic number z:
The sole dependence of the energy on the principal quantum number is a property of potentials that only depend on the inverse of the radius and not on either the polar or azimuthal angles. In derivation of this energy, the only potential considered is the Coulomb attraction between the positive nucleus and negative electron. This means the potential only depends on r. When other effects such as spin-orbit coupling, Lamb shift and electron-nuclear spin interaction s are included, this inverse dependence is broken. This results in the splitting of energy energy levels, so that they do depend on other quantum numbers.