Orbital Diagrams
• Orbitals are the places where electrons
are placed.
• Orbitals reside outside of the nucleus
• Orbitals possess energy
• The orbital angular momentum is balanced with
the electrical forces of attraction between the
electrons and protons
• This balance keeps the electron in the orbit
Orbital Diagrams are based on
the SchrÖdinger Equation
Solutions for the SchrÖdinger
Equation have 3 variables
• First variable is called n, principle quantum
number and has positive integer values of
1, 2, 3, ….
• Second variable is called l, and has positive
values of 0, 1, 2,…(n-1); this variable
describes the shape of the orbital
• Third variable is called m, and has both
positive and negative values of – l 0 + l
Orbital Diagrams
• Main Energy Levels – Rows in the
periodic table (quantum designation, n)
• Each row contains orbital types
(shapes, quantum designation, l)
• Orbital types come in 4 styles
•
•
•
•
s – “basketball shape” (l =0)
p – “dumbell shape
(l =1)
d – complex shape
(l =2)
f – even more complex shape (l =3)
Orbital Diagrams
• Ground Rules
– Each row represents a different energy
level (like the floors in an apartment
building)
– Within each row there are a different
number of kinds of orbitals
– Orbitals also have different energy levels
with the lowest being the s and the highest
being the f
Orbital Diagrams
• The number of different kinds of orbitals
in an energy level is given by the row
number.
•
•
•
•
•
Row 1 has 1 kind of orbital, s
Row 2 has 2 kinds of orbitals, s and p
Row 3 has 3 kinds of orbitals, s, p, and d
Row 4 has 4 kinds of orbitals, s, p, d, and f
How many kinds of orbital and what would they
be called for Row 5?
Orbital Diagrams
• How many kinds of orbital and what
would they be called for Row 5?
• There would be 5 kinds of orbitals, s, p, d, f,
and g
• Do any known elements have electron(s) in the
g suborbit? None that are presently known.
Orbital Diagrams
• How are electrons placed in the energy
levels of an atom?
• Electrons are always placed in the lowest
possible energy level available. This means
that the first electron is always placed in the
first energy level (n=1)
• Electrons are always placed in the lowest
energy suborbital s<p<d<f
Orbital Diagrams
• There is a “trick” in determining the
lowest energy state using the numerical
value for n and l.
• Add (n+ l)
• Lowest sum is the lowest energy level and the
place where electrons are placed next
• If it is a “tie”, then the lowest value of n is the
lower energy state
Orbital Diagrams
• How many orbitals of each kind can be
present in an energy level?
– s, one (1)
– p, three (3)
– d, five (5)
– f, seven (7)
Orbital Diagrams
• How many electrons can be placed in any
single orbital? TWO (2) This means that
the total number of electrons that can be
placed in each suborbital is:
•
•
•
•
s, 2 electrons
p, 6 electrons
d, 10 electrons
f, 14 electrons
Orbital Diagrams
• Do I really have to know all of these things so
that I can write electron configurations?
• No; the periodic table is written in such a way
that all of these rules can be simplified. Also,
there is an easy pneumonic to assist in
writing electron configurations.
Summary of Orbital Diagrams
Energy
Level
Suborbitals
1
s
2
s
p
s
p
d
3
# of
Orbital
number electrons
l=
l=0
2
l=0
l=1
l=0
l=1
l=2
2
6
2
6
10
Total # of
electrons
2
2n
2
8
18
Summary of Orbital Diagrams
Energy
Level
Suborbitals
# of
Orbital
number electrons
l=
Total #
of
electron
s
2
2n
4
s
p
d
f
0
1
2
3
2
6
10
14
32
5
s
p
d
F
g
0
1
2
3
4
2
6
10
14
18
50
1s
2s 2p
These are
3s 3p 3d
not used
4s 4p 4d 4f
5s 5p 5d 5f 5g
6s 6p 6d 6f 6g 6h
7s 7p 7d 7f 7g 7h 7i
Orbital Diagram for A Nitrogen
Atom
N

1s

2s


2p

3s
Orbital Diagram for A Nitrogen
Atom
N





1s 2s
2p
3s
Why do the arrows point in opposite
directions? They represent paired electrons
with opposite “spin”.
Orbital Diagram for A Nitrogen
Atom
N





1s 2s
2p
3s
Why are the 3/2p electrons written in
separate orbitals? This is an example of
Hund’s rule of maximum multiplicity.
Orbital Diagram for A Nitrogen
Atom
N





1s 2s
2p
3s
Which means? Electrons are negatively
charged. They don’t like to get together
unless it is absolutely necessary.
Orbital Diagram for A Nitrogen
Atom
N





1s 2s
2p
3s
The 2p is the lowest available energy state so all
three electrons must be placed here. But there
are 3 places open and each one is equivalent
(scientific word is “degenerate”)
Orbital Diagram for A Nitrogen
Atom
N





1s 2s
2p
3s
So, an electron is placed in the lowest
available space until each space has one
electron. Only then will electrons begin to
pair.
Orbital Diagram for A Fluorine
Atom
F

1s

2s

2p


3s
Orbital Diagram for A
Magnesium Atom
Mg

1s

2s

2p



3s
Writing Orbital Diagrams
Write the orbital diagram for the
electrons in an oxygen atom.
Solution
Write the orbital diagram for the
electrons in an oxygen atom.


1s
2s


2p

3s
Writing Orbital Diagrams
Write the orbital diagram for the
electrons in an iron atom.
Solution
Write the orbital diagram for the electrons in an
iron atom.
 
1s
  
2s
2p
   
3d

3s

  
3p

4s
Solution
• Note that the 4s level is filled before the
3d. Why is that? Remember the n + l
rule?
– For the 4s level, n+ l = 4 + 0 = 4
– For the 3d level, n+ l = 3 + 2 = 5
– That means the 4s is lower in energy than
the 3d, so the 4s is filled first.
– What happens if there is a “tie”? Then the
lower value of n “wins”.