Chemistry Reference
In-Depth Information
Solution
(a)
/
0, 1, 2,
or 3, but no higher
(b)
/
0
or 1 (
/
cannot be as high as
n
)
Note that the value of
/
is not necessarily equal to
(
n
1)
but can vary from
zero up to
(
n
1).
Practice Problem 4.4
How many
different values of
/
are permitted
for an electron with (a)
n
4
and (b)
n
2?
For each value of the angular momentum quantum number the
mag-
netic quantum number
has values ranging from through zero to
in integral steps. The value of does not ordinarily affect the energy of an
electron, but it does determine the orientation in space of the volume that can
contain the electron (Section 4.6).
(
/
),
(
m
/
)
/
/
m
/
EXAMPLE 4.5
What values of
m
/
are permitted for an electron with (a)
/
2
and (b)
/
0?
Solution
Section Row Seat
RFLD 109A 12
(a)
m
/
2,
1, 0, 1, or 2
(b)
m
/
0
Rock Concert
Practice Problem 4.5
How many
different values of
m
/
are permit-
ted for an electron with (a)
/
2
and (b)
/
0?
EXAMPLE 4.6
Date
SATURDAY
APRIL 22, 2006
1:15PM
Can we tell what values of
m
/
are permitted for an electron with
n
3?
Solution
TICKET
Z25511123421
PRICE (TAX INCLUDED)
$14.00
T
The permitted values of
m
/
depend on the value of
/
,
not on the value of
n
. The
most we can say in this case is that
/
is limited to 0, 1, or 2, so
m
/
must be 0 if
ADMIT ONE SUBJECT O CONDITIONS ON BA
CK
/
0,
it may be
1,
0, or
1
if
/
1,
and it may be
2,
1,
0, 1, or 2 if
/
2.
Practice Problem 4.6
What is the lowest value of
m
/
permitted for
APRIL 22, 2006
any electron with
n
4?
PRICE (TAX INCLUDED)
$14.00
Section Row Seat
RFLD 109A 12
1
2
1
2
The
spin quantum number
may have values of or only. The
value of does not depend on the value of any other quantum number. The spin
value gives the orientation of the magnetic field associated with the electron.
Another important limitation on the quantum numbers of electrons in atoms,
in addition to those listed in Table 4.1, is the
Pauli exclusion principle.
This
principle states that no two electrons in an atom can have the same set of four
quantum numbers. This is like the business law that states that no two tickets
to a rock concert can have the same set of date and section, row, and seat num-
bers (Figure 4.7). The row number may depend on the section number, and the
(
m
s
)
m
s
Ticket to Rock
Figure 4.7
Concert
No two tickets from the same concert
hall can have the same set of section
designation, row number, seat
number, and date.
