Now on to quantum
numbers…
Quantum Numbers
• PRINCIPAL: n energy level,
the distance the orbital is from the nucleus
(1, 2, 3, 4…)
• ANGULAR MOMENTUM: l
(s = 0, p = 1, d = 2, f = 3)
shape
• MAGNETIC: ml spatial orientation
(0 for s; -1, 0, +1 for p; -2, -1, 0, +1, +2 for d, etc.)
• SPIN: ms spin (+1/2 or -1/2)
Review
•
•
•
•
•
•
Atomic number = # electrons
Electrons occupy orbitals defined by n, l, m
Each orbital can hold two electrons
Orbitals  diffuse electron cloud
“lower energy electron”  closer to nucleus
Outer electrons: “valence” most reactive
Numbers
• The principalQuantum
quantum number
has the symbol n.
n = 1, 2, 3, 4, ...... “shells”
(n = K, L, M, N, ......)
The electron’s energy depends principally on n .
1
2
3
Quantum Numbers
• The angular momentum quantum number has
the symbol .
 = 0, 1, 2, 3, 4, 5, .......(n-1)
 = s, p, d, f, g, h, .......(n-1)
•  tells us the shape of the orbitals.
• These orbitals are the volume around the atom
that the electrons occupy 90-95% of the time.
Quantum Numbers
• The symbol for the magnetic quantum number is
m, representing the spatial orientation.
m = -  , (-  + 1), (-  +2), .....0, ......., ( -2), ( -1), 
• If  = 0 (or an s orbital), then m = 0.
• If  = 1 (or a p orbital), then m = -1,0,+1.
y
z
x
• If  = 2 (or a d orbital), then m = -2,-1,0,+1,+2.
• If  = 3 (or an f orbital), then m = -3,-2,1,0,+1,+2, +3.
• Theoretically, this series continues on to g,h,i, etc
Spin quantum number
• The last quantum number is the spin
quantum number which has the symbol ms.
• The spin quantum number only has two
possible values.
– ms = +1/2 or -1/2
Spin of electron
• Spin quantum number effects:
– Every orbital can hold up to two electrons.
• Consequence of the Pauli Exclusion Principle.
– The two electrons are designated as having
– one spin up  and one spin down 
• Spin describes the direction of the electron’s
magnetic fields.
Re-Cap: Quantum Numbers
• PRINCIPAL: n energy level, distance from
nucleus (1, 2, 3, 4…)
• ANGULAR MOMENTUM: l
(s = 0, p = 1, d = 2, f = 3)
shape
• MAGNETIC: ml spatial orientation
(0 for s; -1, 0, +1 for p; -2, -1, 0, +1, +2 for d, etc.)
• SPIN: ms spin (+1/2 or -1/2)
Atomic Orbitals: s, p, d, f
• Atomic orbitals are regions of space where
the probability of finding an electron about
an atom is highest.
• s orbital properties:
– There is one s orbital per n level.
=0
and only one value of m = 0
• s orbitals are spherically symmetric
For every s orbital:
= 0 and ml = 0
The only thing that
changes for s orbitals is
n.
1s orbital of
hydrogen
Distance from nucleus
Probability
densities for
finding an
electron at a
given radius
1s, 2s, and 3s
orbitals for
hydrogen
Three
dimensional
depictions of
electron
distribution
p orbitals
• p orbital properties:
– The first p orbitals appear in the n = 2 shell.
• p orbitals are peanut or dumbbell shaped volumes.
• There are 3 p orbitals per n level.
– The three orbitals are named px, py, pz.
 = 1 for all p orbitals.
m = -1,0,+1 (designate the three orientations)
• p orbitals are peanut or dumbbell shaped.
l=1
• p orbitals are peanut or dumbbell shaped.
l=1
m = -1,0,+1
2p orbital
d orbital properties:
– The first d orbitals appear in the n = 3 shell.
• The five d orbitals have two different shapes:
– 4 are clover leaf shaped.
– 1 is peanut shaped with a doughnut around it.
– The orbitals lie directly on the Cartesian axes or are
rotated 45o from the axes.
There
are 5 d orbitals per n level.
d xy , d yz , d xz , d x 2 - y2 , d z 2
–The five orbitals are named:
have an  = 2.
–m = -2,-1,0,+1,+2 (5 values of m )
–They
=2
m = -2,1,0,+1,+2
• d orbital shapes
=2
m = -2,1,0,+1,+2
f orbital properties:
– The first f orbitals appear in the n = 4 shell.
• The f orbitals have the most complex
shapes.
• There are seven f orbitals per n level.
– The f orbitals have complicated names.
– They have an  = 3
– m = -3,-2,-1,0,+1,+2, +3
7 values
=3
m = -3,-2,-1,0,+1,+2, +3
values
7
• f orbital shapes
Quantum Numbers
• PRINCIPAL: n energy level, distance from
orbital (1, 2, 3, 4…)
• ANGULAR MOMENTUM: l
(s = 0, p = 1, d = 2, f = 3)
shape
• MAGNETIC: ml spatial orientation
(0 for s; -1, 0, +1 for p; -2, -1, 0, +1, +2 for d, etc.)
• SPIN: ms spin (+1/2 or -1/2)
s, p
and d
s and p
only s
Recall that Shrodinger’s equations derives the orbitals!
s, p, and d shells of
a hydrogen atom
• Pauli Exclusion Principle
– No two electrons in an atom can have the same
set of 4 quantum numbers.
• The Aufbau Principle describes the electron filling
order in atoms.
4s
3p
3s
2p
2s
1s
paired
parallel spins
• Electron Configurations
The order of orbital levels is:
1s 2s 2p 3s 3p 4s 3d 4p 5s 4d 5p 6s 4f 5d 6p 7s …..
Know configurations up to Ba!
Electron Configurations
2p
2p
2p
2p
2s
2s
2s
2s
1s
1s
1s
1s
B
C
N
O
5
6
7
8
2. Or you can use the periodic chart .
1
2
3
4
5
6
2. Or you can use the periodic chart .
Ge
Ge = 1s22s22p63s23p64s23d104p2
or [Ar] 4s23d104p2
or [Ar]3d10 4s24p2
1
2
3
4
5
6
•Hund’s rule tells us that the electrons will fill the
p orbitals by placing electrons in each orbital
singly and with same spin until half-filled. Then
the electrons will pair to finish the p orbitals.
• 3rd row elements
3s
3p
Configurat ion
11 Na Ne 
12
Mg Ne 
13
Al
14
Si
15
P
16
S
17
Cl
18
Ar
Ne
Ne
Ne
Ne
Ne
Ne



 

  

  

  

  
Ne 3s1
Ne 3s2
Ne 3s2 3p1
Ne 3s2 3p2
Ne 3s2 3p3
Ne 3s2 3p4
Ne 3s2 3p5
Ne 3s2 3p6
Fourth row
3d
4s
19 K Ar 

20
Ca Ar 

Sc Ar  

22
Ti Ar   

23
V Ar    

Cr Ar      

21
24
4p
Configurat ion
Ar  4s1
Ar  4s2
Ar  4s2 3d1
Ar  4s2 3d 2
Ar  4s2 3d 3
Ar  4s1 3d5
There is an extra measure of stability associated
with half - filled and completely filled orbitals.
Fourth row
3d
25 Mn Ar      
26
27
28
29
Fe Ar      
Co Ar      
Ni Ar      
4s




Cu Ar       
Another exception like Cr!
4p
Configurat ion
Ar  4s 2 3d 5
Ar  4s 2 3d 6
Ar  4s 2 3d 7
Ar  4s 2 3d 8
Ar  4s1 3d10
Fourth row
3d
25 Mn Ar      
26
27
28
29
30
4s

Fe Ar      

Co Ar      

Ni Ar      

Cu Ar       
Zn Ar       
4p
Configurat ion
Ar  4s2 3d5
Ar  4s2 3d 6
2
7
Ar  4s 3d
Ar  4s2 3d8
Ar  4s1 3d10
Ar  4s2 3d10
Fourth row
3d
4s
31 Ga Ar        
4p
Configurat ion
Ar  4s2 3d10 4p1
2
10
2




Ge
Ar








Ar
4s
3d
4p
32
2
10
3




As
Ar









Ar
4s
3d
4p
33
2
10
4




Se
Ar









Ar
4s
3d
4p
34
2
10
5




Br
Ar









Ar
4s
3d
4p
35
2
10
6




Kr
Ar









Ar
4s
3d
4p
36
Specific quantum numbers for
each electron
1st e-
n

m
1
0
0
ms
 1/2
Specific quantum numbers for each electron
n

m
1
0
0
2 nd e - 1
0
0
3rd e -
2
0
0
4 th e -
2
0
0
5th e -
2
1
6 th e -
2
1
7 th e -
2
1
8th e -
2
1
9 th e -
2
1
10 th e -
2
1
11th e -
3
0
1st e -
ms
 1/2 
1 s electrons
 1/2 
 1/2 
2 s electrons
 1/2 
 1/2 

0
 1/2 
 1  1/2 

2 p electrons
 1  1/2 
0
 1/2 

 1  1/2 

0
 1/23 s electron
-1
How to deal with ions?
S vs S2-
Cl vs Cl+
What type of ion would be expected to be
favored for each element?
Na
F
Na+ or NaF+ or F-
What are the electron configurations of the
two C isotopes?
12C
13C
Chemical properties  Valence electrons