Principal Shell
Sub-level
n=
l=
ml =
1st
s
1
0
0
s
2
0
0
2nd
ppp
222
111
1 0+1
3rd
s
3
0
0
ppp
333
111
1 0+1
ddddd
33333
22222
- 2 1 0+1+2
s
4
0
0
ppp
444
111
1 0+1
4th
ddddd
44444
22222
- 2 1 0+1+2
Quantum Numbers
f f f f fff
4444444
3333333
- - 3 2 1 0+1+2+3
s
5
0
0
ppp
555
111
1 0+1
5th
ddddd
55555
22222
- 2 1 0+1+2
f f f f fff
5555555
3333333
- - 3 2 1 0+1+2+3
s
6
0
0
ppp
666
111
1 0+1
6th
ddddd
66666
22222
- 2 1 0+1+2
f f f f fff
6666666
3333333
- - 3 2 1 0+1+2+3
s
7
0
0
7th
ppp ddddd f f ff ff f
777 77777 7777777
111 22222 3333333
1 0+1 -2-1 0+1+2 -3-2-1 0+1+2+3
♦ A wave function with a given set of the four quantum numbers is called an atomic orbital. Atomic orbitals are mathematical expressions that we think of as geometric regions.
♦ An electron in an orbital is designated a set of four quantum numbers that describes it: {n, l, ml, ms} or {principal energy level, sublevel, orbital, spin}
State whether an electron can be described by the following set:
Example 1: {2, 1, -1, 1/2}; this set describes the electron in the 2nd principal energy level, the p-sublevel, in one of the 3 p-orbitals or p-values from –l to +l, spinning clockwise, therefore this set has all
allowed values. The electron it describes falls into the 5th position on the periodic table and therefore is the 5th electron in any element with 5 or more total electrons.
Example 2: {3, 1, -3, -1/2}; this set describes the electron in the 3rd principal energy level, the p-sublevel, in one of the 7 p-orbitals (which is impossible because p-sublevels have only 3 orbitals), spinning
counterclockwise, therefore this set is not possible or cannot describe an electron.
State whether an electron can be described by the following set. If the set is plausible, then state which electron it is (the 1st, 2nd, etc.). If a set is not possible, then state why it is not.
Quantum Number Set
1.
{2, 1, -2, 1/2}
2.
{3, 2, +2, 1/2}
3.
{4, 3, +3, 1/2}
4.
{5, 2, +3, -1/2}
5.
{0, 0, 0, 1/2}
Set is Plausible
Set is NOT Plausible. Why NOT?
Electron Number Described
Write ALL of the acceptable values for the missing quantum numbers in the following sets. Each time, state which electron it is that the set describes.
Quantum Number Set
1.
{?, 2, 0, ?}
2.
{2, ?, -1, -1/2}
3.
{4, ?, 2, ?}
4.
{?, 0, ?, 1/2}
5.
{?, ?, +3, ?}
© T. M. Chipi, Chemistry Instructor
Plausible Set/e- #
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1