An atomic orbital is specified first by three quantum numbers that are associated respectively, with the orbital’s size (energy), shape, orientation and, later, independent of these three quantum numbers, the electrons spin.

Three among the four quantum numbers characterize the orbitals in that atom. That is, they describe the orbital or the space the electron is supposed to occupy. The fourth quantum number is used to describe the spin of the electron that occupy the orbital.

Principal quantum number (n)
This quantum number is the one on which the energy of an electron in an atom principally depends. It can have any positive value 1, 2, 3, and so on. The smaller n is, the lower the energy. In the case of the hydrogen atom or single-electron atomic ions, such as Li²⁺ and He⁺, n is the only quantum number determining the energy. For other atoms, the energy also depends to a slight extent on the l quantum number. The size of an orbital also depends on n. Shells are sometimes designated by the following letters:

Angular momentum quantum number (l) (also called azimuthal quantum number)

This quantum number distinguishes orbitals of given n having different shapes; it can have any integer value from 0 to n. Within each shell of quantum number n, there are n different kinds of orbitals, each with a distinctive shape denoted by an l quantum number. For example, if an electron has a principal quantum number of 3, the possible values for l are 0, 1, and 2.

To denote a subshell within a particular shell, we write the value of the n quantum number for the shell, followed by the letter designation for the subshell. For example, 2p denotes a subshell with quantum numbers n = 2 and l = 1.

Magnetic Quantum Number (m_l)

This quantum number distinguishes orbitals of given n and l that is, of given energy and shape but having a different orientation in space; the allowed values are the integers from -l to +l. For l = 0 (s-subshell), the allowed m_l quantum number is 0 only; there is only one orbital in the s subshell. For l = 1 ( p-subshell), ml = -1, 0, and +1; there are three different orbitals in the p subshell.

Spin quantum number (m_s)

This quantum number refers to the two possible orientations of the spin axis of an electron; possible values are +1/2 and -1/2. An electron acts as though it were spinning on its axis like the earth.

The quantum numbers specify the energy states of the atom.

• The atom’s energy levels or shells are given by the n value.
• The atom’s sublevels or subshells are given by the n and l values. Each level contains sublevels that designate the shape of the orbital.
• The atom’s orbitals are specified by the n, l and m_l values. Thus, the three quantum numbers that describe an orbital express its size (energy), shape and spatial orientation. Each sublevel is designated by a letter:

l = 0, is an s sublevel
l = 1, is a p sublevel
l = 2, is a d sublevel
l = 3, is a f sublevel

General rules for assigning electrons to atomic orbitals.

Based on the preceding examples we can formulate some general rules for determining the maximum number of electrons that can be assigned to the various subshells and orbitals for a given value of n:

1. Each shell or principal level of quantum number n contains n subshells. For example, if n = 2, then there are two subshells (two values of l) of angular momentum quantum numbers 0 and 1.
2. Each subshell of quantum number l contains (2l+1) orbitals. For example, if, l = 1, then there are three p orbitals.
3. No more than two electrons can be placed in each orbital. Therefore, the maximum number of electrons is simply twice the number of orbitals that are employed.
4. A quick way to determine the maximum number of electrons that an atom can have in a principal level n is to use the formula 2n².