UNIT 5
CH. 7
Quantum Mechanics
16
10/27/2002
THE 4 QUANTUM NUMBERS (
n, l, m
l
, m
s
)
THE PRINCIPAL QUANTUM NUMBER (
n
)
•
Designates the main energy level (floor) or shell.
•
Values: 1, 2, 3, …….
∞
.
n
= 7 is the highest number of shell used for the atoms
known.
•
Describes the
CLOUD SIZE
. The larger the value of
n
, the larger the cloud size.
•
Energy levels closer to the nucleus have lower energy. As
n
increases, the orbital
becomes larger and the electron spends more time farther from the nucleus. An
increase in
n
also means that the electron has a higher energy and is therefore less
tightly bound to the nucleus.
•
The larger n is, the greater the average distance of an electron in the orbital from the
nucleus and therefore the larger (and less stable) the orbital.
The maximum number of electrons possible in a given shell is 2
n
2
.
LEVEL
MAXIMUM
NO. OF
ELECTRONS
2n
2
n
= 1
2
n
= 2
8
n
= 3
18
n
= 4
32
n
= 5
50
n
= 6
72
n
= 7
98
In reality there are only 32 electrons in levels 5, 6, and 7 because of the number of different elements discovered or man-made.
ANGULAR MOMENTUM QUANTUM NUMBER (
l
)
•
Designates the sub-level (apartment) where the electron can be found.
•
Gives the
SHAPE OF THE ORBITALS
.
•
Values of l: from 0 to (
n
-1) for each value of n.
•
The value of
l
for a particular orbital is generally designated by the letters
s
,
p
,
d
, and
f
corresponding to l values of 0., 1, 2,
and 3.
for the known atoms, only
s, p, d
, and
f
exist.
Value of
l
0
1
2
3
4
5
Sub-level
s
p
d
f
g*
h*
*These sublevels are not used in the ground state of any known element.
•
Each sublevel is given a letter designation (like s) and a number designation (s = 0). This allows you to put these two
quantum numbers together to identify the shape and location of the atomic orbital.(1s, 4f, 3d etc.)
MAGNETIC QUANTUM NUMBER (m
l
)
•
Designates the orbital (room) where the electron can be found.
•
Gives the
DIRECTION IN SPACE
that the orbital takes.
•
m
l
specifies to which orbital within a subshell the electron is assigned. Orbitals in a given subshell differ only in their
orientation in space, not in their shape.
•
Values of m
l
:
from –
l
, ….0, ….+
l
.
•
The middle orbital of a subshell has a value of 0. Orbitals to the left of the middle orbital have negative numbers; to the
right, they have + numbers.
m