Electrons occupy discrete or separate energy levels within an atom. Each electron possesses a particular energy, with no more than two electrons in each atom having the same energy. This also implies that there is a discrete energy difference between any two energy levels.
Quantum Numbers
The energy level to which each electron belongs is determined by four quantum numbers. The numbers of possible energy levels is determined by the first three quantum numbers.
1. The principal quantum number n is assigned integral values 1, 2, 3, 4, 5, ... that refer to the quantum shell to which the electron belongs. Quantum shells are also assigned a letter; the shell for n = 1 is designated K, for n = 2, is L, for n = 3 is M, and so on.
2. The number of energy levels in each quantum shell is determined by the azimuthal quantum number l and the magnetic quantum number ml. The azimuthal quantum numbers are also assigned numbers: l = 0, 1, 2, ..., n - 1. If n = 2, then there are also two azimuthal quantum numbers, l = 0 and l = 1. The azimuthal quantum numbers are designated by lowercase letters:
s for l = 0
p for l = 1
d for l = 2
f for l = 3
The magnetic quantum number ml gives the number of energy levels, or orbitals, for each azimuthal quantum number. The total number of magnetic quantum numbers for each l is 2l + 1. The values for ml are given by whole numbers between -l and +l. For l = 2, there are 2(2) + 1 = 5 magnetic quantum numbers, with values -2, -1, 0, +1, and +2.
3. The Pauli exclusion principle specifies that no more than two electrons, with opposing electronic spins, may be present in each orbital. The spin quantum number ms is assigned values +1/2 and -1/2 to reflect the different spins.
The shorthand notation frequently used to denote the electronic structure of an atom combines the numerical value of the principal quantum number, the lowercase letter notation for the azimuthal quantum number, and a superscript showing the number of electrons in each orbital.