Solutions to the wave equation
Solutions are characterized by quantum numbers
`
The principle quantum number,
n
, is a positive
integer that indicates the shell and relative size of
orbital(s)
orbital(s).
`
The angular momentum quantum number,
l
, is an
integer from zero to n-1. It defines the shape of the
orbital and subshell.
Value of l
0
1
2
3
4
Letter identifier
s
p
df
g
`
The magnetic quantum number,
m
l
, is an integer with a
value from -l to +l.
It defines the orientation of an
orbital in the space around the nucleus of an atom
orbital in the space around the nucleus of an atom.
`
The spin magnetic quantum number,
m
s
, is to account
for the two possible spin orientations.
The values for
m are +1/2 and
1/2
Roy A. Lacey, Stony Brook University;
Che 131, Fall 2011
3
m
s
are +1/2 and -1/2.
Quantum numbers
n
l
m
l
# orbitals
Quantum numbers are related to each other
1
0
0
1
20
0
1
1
-1 0 +1
3
-1,0,+1
30
0
1
1
-1,0,+1
3
2
-2.-1,0,+1,+2
5
40
0
1
1
-1,0,+1
3
2
-2.-1,0,+1,+2
5
Roy A. Lacey, Stony Brook University;
Che 131, Fall 2011
4
3
-3,-2.-1,0,+1,+2,+3
7
2-1
n total orbitals
n types of orbitals
=(n-1)