Marc Daniels
Chemistry 591
Lesson Plan (50-45 minutes):
Quantum Numbers and Orbitals
Goals: (written on corner of board and discussed for about 5 minutes)
 To learn about the Principal Quantum Number (n)
 To learn about the Angular Momentum Quantum Number (l)
 To learn about the Magnetic Quantum Number (ml)
 How to define orbitals using these three properties using the proper notation
 How to determine n,l,m given information about the orbital
Introduction to Quantum Numbers (30-35 minutes):
 When using the Schrodinger equation for a H atom, we find many orbital that satisfy it. We use
a series of numbers called quantum numbers to describe the properties of the orbital.
Principal Quantum Number (n)
 The principal quantum number (n) has values that range from 1 to infinity (1, 2, 3, 4,.……..).
 This number refers to the size and energy of the orbital
 As (n) increases the orbital becomes larger and the electron spends more time away from the
nucleus.
 This also correlates to a higher energy, since the electron is less tightly bound to the nucleus
(energy is less negative)

For example an orbital with n=2 is smaller and has less energy than an orbital with n=4
(short question to ask students, which has a larger energy, n=5 or n=8? Why? May ask before
explaining to see if students are connecting concepts previously discussed.)
Principal Quantum Number Notation
 This is relatively simple the notation of n is just n, so for an orbital with n=1, we note this as a 1
orbital. (For n=3, this is a 3 orbital)
Angular Momentum Quantum Number (l)
 The angular momentum quantum number (l) has the values of 0 to n-1 for each value of n.
(This means that an orbital with n=2 has two (l) values, that of l=1 and l=0. For n=4, l can be
equal
to 3, 2, 1, and/or 0)
 The quantum number is related to the shape of atomic orbital.
Angular Momentum Quantum Number Notation
 For l=0 we assign the letter s, for l=1 we assign p, for l=2 we assign the letter d, for l=3 we assign
the letter f, for l=5 and so on we follow the alphabet from f, (l=4 would be g, l=5 would be h,
l=6 would be h)
 A way for remembering the order s.p.d.f (Spiffy People Dress Fresh…..ask students for
suggestions)
For example what would the quantum numbers (n,l) be for an orbital called 2s, 3p, 5f? (Done alone in
class for a few minutes then open up for discussion)
Answers: n=2 and l=0, n=3 and l=1, n=5 and l=3
Magnetic Quantum Number (ml)
 This has values that range from l to -l (this includes 0).
 This value is related to the orientation of the orbital in space relative to the other orbital in the
atom.
 What’s great about this!?!? NO NOTATION FOR IT (though it is important to know possible
orbital given values of n and l, or how to find l and n, given the range of m.
For example for m that ranges from -2 to 2 suggests that the orbital has an angular momentum
quantum number of 2, which tells us that n must be 3. (how to do this, m=-l….,0.…,l, n= l-1, and l=n+1).
Can a 1p orbital exist?
Answer: No, since n=1 then l can only be equal to 0 which suggests that it is a 1s orbital. If it were a 1p
orbital l would have to be equal to 1, but it is limited by n.
Table to have students fill out (done for the remainder of classroom time/turns into a homework
assignment)
Hints:
n=1, 2,3,…….
l=0,1,…..(n-1)
m = -l,…..,0,…..,l
For Students
n
l
1
2
2
3
3
4
4
4
5
5
5
5
5
0
1
0
2
0
1
3
0
1
2
Notation
1s
2s
3s
3p
3d
4s
4d
4f
5s
5p
5f
4
m
0
-1,0,1
0
-1,0,1
0
-1,0,1
-2,-1,0,1,2
0
-1,0,1
-2,-1,0,1,2
-3,-2,-1,0,1,2,3
Number of Orbitals
1
1
3
1
3
5
1
3
5
7
1
3
5
7
9
Can you see a correlation between the number of orbitals and the notation for l?
Answers
n
l
1
2
3
4
5
0
0
1
0
1
2
0
1
2
3
0
1
2
3
4
Notation
1s
2s
2p
3s
3p
3d
4s
4p
4d
4f
5s
5p
5d
5f
5g
Answer for question above:
s=1 orbital
p=3 orbital
d=5 orbital
f=7 orbital
g=9 orbital
h=11 orbital
And so on…..
m
0
0
-1,0,1
0
-1,0,1
-2,-1,0,1,2
0
-1,0,1
-2,-1,0,1,2
-3,-2,-1,0,1,2,3
0
-1,0,1
-2,-1,0,1,2
-3,-2,-1,0,1,2,3
-4,-3,-2,-1,0,1,2,3,4
Number of Orbitals
1
1
3
1
3
5
1
3
5
7
1
3
5
7
9