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Quantum Numbers

Quantum numbers describe the orbital occupied by an electron in terms of:

  • distance from the nucleus (energy level)
  • shape (type of orbital)
  • position with respect to 3-D
  • direction of spin in the orbital

Principal Quantum Number

The first quantum number, n, is the principal quantum number and describes the main energy level (shell) of the electron. This energy level is the probable distance the electron is from the nucleus.

The maximum number of electrons in any one energy level is 2n2. So as n increases, the energy and number of electrons in a level will increase.


n=1 → 2(1)2 = 2 electrons

∴ energy level one can have only 2 electrons maximum

n=2 → 2(2)2 = 8 electrons

∴ energy level one can have only 8 electrons maximum

The Angular Momentum Quantum Number

The second quantum number is the angular momentum quantum number and describes the shape or type of orbital. Within an energy level there are four possible sublevels each with a characteristic shape.

The value of the sublevels can be 0 to (n-1). However, it is a common practice to use the letters s, p, d, and f to represent these subshells instead of the numbers. An atom at ground state never has electrons higher than the f subshell, but excited electrons may go to higher levels and even out of the atom (n = ∞).

The number of sublevels or possible orbital shapes in any main energy level is equal to the value of n. If n = 1 then there is only one subshell, s. If n = 2 then there are two possible subshells, s and p, etc.


Magnetic Quantum Number


The third quantum numberis the magnetic quantum number and describes the electrons position in space with respect to the x, y, and z-axes.

  • the s subshell has only one possible position in space
  • the p subshell has three possible positions
  • the d subshell has five possible positions, and
  • the f subshell has seven possible positions.

Each possible position is an orbital and each orbital can have two electrons.


Spin Quantum Number

The fourth quantum number is the spin quantum number and describes the electron spin. If two negatively charged electrons occupy the same orbital, how do they keep from repelling one another?

It is possible the electrons spin in opposite directions and therefore, produce opposite magnetic fields that attract rather than repel one another. Scientist refer to these possible spins as (+1/2) and (-1/2).

The fact that each electron in an orbital must have different spin quantum numbers led Wolfgang Pauli to the conclusion that no two electrons in the same atom can have the same four quantum numbers. This conclusion still holds true and is known as the Pauli Exclusion Principle.

Now that the quantum numbers have been introduced, you can use them to describe the electron configurations of the elements.

electron configurations