Chemistry Reference
In-Depth Information
Each energy level is divided into sublevels, the number of which is equal
to the value of n. So, for example, the third energy level (n = 3) con-
tains 3 sublevels, whereas the fifth energy level (n = 5) would contain 5
sublevels.
l
The second quantum number, called the angular momentum quantum
number, is used to indicate the type of sublevel that the electron occu-
pies. The possible values for
l
refer to the types of sublevels, each of
which contain a certain number of orbitals. An orbital is a space that
can be occupied by up to two electrons, which occupy a specific three-
dimensional area. Depending on the course that you are in, you may or
may not need to know the shapes of the sublevels, but you are very
likely to need to know the number of orbitals and electrons that each
one holds. Values of
l
of 0, 1, 2, and 3 refer to sublevels, which are, in
turn, designated by the letters s, p, d, and f respectively. So, an electron
that has a value 3 for n (the first quantum number) and a value of 1 for
l
(the second quantum number) would be found in the third energy
level, in a “p” sublevel.
M
l
The third quantum number, called the magnetic quantum number, in-
dicates the spatial orientation of the orbital that the electron occupies.
The possible values of M
l
for an electron depend upon the value of the
electron's second quantum number (
l
). For any given electron, the pos-
l
,
including the value 0. So, in other
words, an electron with a value of 2 for
l
range from +
l
to -
sible values of M
l
would occupy a “d” sublevel,
and could have values of +2, +1, 0, -1, or -2 for M
l
.
M
s
The fourth quantum number, called the spin quantum number, indi-
cates the “spin” direction of the electron in a particular orbital. Pauli's
exclusion principle states that no two electrons in an atom can have the
exact same set of four quantum numbers. Electrons that are in the same
orbital have the same value for the first three quantum numbers (
n
,
l
,
l
), which means that they occupy the same energy level, sublevel,
and orbital. In order to satisfy the exclusion principle, electrons in the
same orbital must have a different value for M
s
. Each orbital can hold
up to two electrons, so only two values for M
s
are required. Those val-
ues have been designated as +1/2 and -1/2. Combined with the other
three quantum numbers, the fourth quantum number indicates the ac-
tual electron that you are studying.
The four quantum numbers are summarized in Figure 3-3a on page 84.
and M
