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Quantum Theory and Electrons 111
The third quantum number is the magnetic quantum number (m l). It describes
the orientation of the orbital around the nucleus. The possible values of m l
depend upon the value of the l quantum number. The allowed values for m l are
l through 0 to l. For example, for l 3, the possible values of m l would be
3, 2, 1, 0, 1, 2, 3. This is why, for example, if l 1 (a p-orbital), there
are three p-orbitals (sublevels) corresponding to m l values of 1, 0, 1.
The fourth quantum number is the spin quantum number (m s) and indicates the
direction the electron is spinning. There are only two possible values for m s,
1 / 2 and 1 / 2. When two electrons are to occupy the same orbital, then one
must have an m s 1 / 2 and the other electron must have an m s 1 / 2. These
are spin-paired electrons.
In order to assign the four quantum numbers for a particular electron, first
begin with the electron in the lowest energy level, n 1. Assign the value of n,
then the corresponding values of l, m l, and finally m s. Once you have finished all
the possible electrons at n 1, repeat the procedure with n 2. Don’t forget
about Hund’s rule and the Pauli exclusion principle. The quantum numbers for
the six electrons in carbon would be:
Quantum First Second Third Fourth Fifth Sixth
Number Electron Electron Electron Electron Electron Electron
n 1 1 2 2 2 2
l 0 0 0 0 1 1
m l 0 0 0 0 1 0
m s 1 / 2 1 / 2 1 / 2 1 / 2 1 / 2 1 / 2
7-5 Electron Configuration
Quantum mechanics may be used to determine the arrangement of the electrons
within an atom if two specific principles are applied: the Pauli exclusion
principle and the Aufbau principle. The Pauli exclusion principle states that no
two electrons in a given atom can have the same set of the four quantum numbers.
For example, if an electron has the following set of quantum numbers:
n 1, l 0, m l 0, and m s 1/2, then no other electron may have the same
set. The Pauli exclusion principle limits all orbitals to only two electrons. For
example, the 1s-orbital is filled when it has two electrons, so that any additional
electrons must enter another orbital.
The second principle, the Aufbau principle, describes the order in which the
electrons enter the different orbitals and sublevels. The arrangement of electrons
builds up from the lowest energy level. The most stable arrangement of