October 30, 2009
• EXAM #3 HAS BEEN MOVED TO MONDAY,
N O V E M B E R 9 TH
The First Three Quantum Numbers
 n, l, and ml are integers
n
= principal quantum # = 1, 2, 3, …
n tells us the size/energy of the orbital
 l = angular momentum quantum # = 0, 1, 2, …, n-1
l tells us the shape of the orbital- s,p,d,f…
 ml = magnetic quantum number = –l to l
ml describes the orientation of the orbital
Hydrogen
Nodes
Orbital
(n,l)
Planar
Spherical
Total
1s
(1,0)
0
0
0
2s
(2,0)
0
1
1
2p
(2,1)
1
0
1
3s
(3,0)
0
2
2
3p
(3,1)
1
1
2
3d
(3,2)
2
0
2
4s
(4,0)
0
3
3
4p
(4,1)
1
2
3
4d
(4,2)
2
1
3
4f
(4,3)
3
0
3
Nodes, Revisited
# of planar nodes =
l
# of spherical nodes = n – l – 1
Total # nodes =
n–1
 Example: 3d orbital
What orbital has these quantum numbers?
n = 3, l = 2, ml = -1
1. 4p
2. 3d
63%
3. 3p
4. 1d
5. 2f
23%
8%
4%
3%
1
2
3
4
5
What are the quantum numbers for the 5dxy orbital?
1. n = 5, l = 2, ml = 0
2. n = 5, l = -2, ml = 3
51%
3. n = 4, l = 2, ml = 2
4. n = 5, l = 3, ml = 0
5. n = 5, l = 2, ml = -5
18%
11%
1
2
11%
10%
3
4
5
Which is not a valid set of quantum numbers?
1. n = 4, l = 1, ml = -1
42%
2. n = 1, l = 0, ml = 0
41%
3. n = 6, l = 5, ml = -5
4. n = 2, l = 2, ml = 1
5. n = 3, l = 2, ml = 2
7%
8%
3%
1
2
3
4
5
The representation 5d indicates which values for n and l?
1.
2.
3.
4.
n = 5; l = 0
n = 5; l = 1
n = 5; l = 2
n = 5; l = 3
77%
8%
1
10%
5%
2
3
4
What is the total number of nodes for the 5d orbital?
1.
2.
3.
4.
5.
0
1
2
3
4
57%
19%
14%
10%
0%
How many spherical nodes does a 5d orbital have?
1.
2.
3.
4.
5.
0
1
2
3
4
59%
16%
12%
10%
3%
1
2
3
4
5
How many planar nodes does a 5d orbital have?
1.
2.
3.
4.
5.
0
1
2
3
4
62%
19%
12%
4%
3%
1
2
3
4
5
The Fourth Quantum Number
 n, l, and ml are integers
n
= principal quantum # = 1, 2, 3, …
n tells us the size/energy of the orbital
 l = angular momentum quantum # = 0, 1, 2, …, n-1
l tells us the shape of the orbital- s,p,d,f…
 ml = magnetic quantum number = –l to l
ml describes the orientation of the orbital
 ms is not an integer
 ms=
spin quantum number = - ½ or ½
Electrons Spin
 Classical physics a spinning charge creates a
magnetic field
 Electron spin* is quantized; the two states are called
“spin up” and “spin down”
*Electrons are described by quantum physics and don’t really “spin”
Electron Spin is the Source of Magnetism in Materials
 Diamagnetic
 Paramagnetic
 Ferromagnetic (“real magnets”)