Chemistry Reference
In-Depth Information
1
2
1
2
Because only two
m
s
values (
and
) are permitted, the maximum number
of electrons in a given orbital is two.
Practice Problem 4.11
What is the maximum number of electrons
that will fit into the first subshell of the second shell of an atom?
Even though the and values do not affect the energy of the electron,
it is still important to learn about them. The number of combinations of per-
mitted values of these quantum numbers determines the maximum number of
electrons in a given type of subshell. For example, in a subshell for which
can have five different values
m
/
m
s
/
2,
m
/
(
2,
1, 0,
1, and
2),
and
m
s
can
1
2
1
2
have two different values (
and
). The ten different combinations of
m
/
and
m
s
allow a maximum of ten electrons in any subshell for which
/
2.
EXAMPLE 4.12
How many electrons are permitted in a subshell for which (a)
/
0?
(b) for
/
3?
Solution
(a)
When Because has only one permitted value and
has two, there are two different combinations of and for this
subshell. Thus, it can be occupied by a maximum of two electrons.
/
0,
m
/
0.
m
/
m
s
m
/
m
s
(b)
Seven permitted
3) times two
permitted values ( and ) makes 14 combinations. A maximum of
14 electrons can occupy this subshell.
m
/
values (
3,
2,
1, 0,
1,
2,
and
1
2
1
2
m
s
Writing out each quantum number value for every electron in an atom is
very time-consuming. A more efficient method is to group all the electrons in
a given subshell. In this method, the following four lowercase letters represent
the possible
/
values:
Value of
/
Letter
0
s
1
p
2
d
3
f
Because only
n
and values affect the energies of electrons, the electrons with
the same
n
value and the same value all have the same energy. In other words,
all the electrons in a given subshell are degenerate. Each subshell is denoted by
its principal quantum number and the letter designation for For example, for
neon, with atomic number 10, the sets of quantum numbers for the 10 electrons
are listed in Table 4.2. We can group them as follows:
/
/
/
.
Number of
Subshell
Value of n
Value of
/
electrons
designation
1
0
2
1
s
2
0
2
2
s
2
1
6
2
p
