1. SCHRÖDINGER’S ATOMIC
MODEL

2. SCHRÖDINGER’S ATOMIC MODEL
Electrons occupy specific energy levels/shells in an atom.
The number of electrons in each level is governed by the
formula 2n2

3. SCHRÖDINGER’S ATOMIC MODEL
Erwin Schrödinger
Schrödinger proposed
that the atom was
arranged as "layers
within layers" in terms
of the electron shells.

4. SCHRÖDINGER’S ATOMIC MODEL
Schrödinger also
proposed that an
electron behaves in
a wave-like manner
rather than just as
particles.
Thus electrons are
both particles and
waves at the same
time.
Since electrons are
waves, they do not
remain localized in a
2-D orbit.

5. SCHRÖDINGER’S ATOMIC MODEL
Instead of being
organized in 2-D
orbits, electrons are
actually found in 3-D
orbitals.
Each orbital defines
an area where the
probability of finding
an electron is high.
These orbitals are
known as electron
“clouds”.

6. SCHRÖDINGER’S ATOMIC MODEL
Orbits Vs. Orbitals
2-D path 3-D path
Fixed distance from Variable distance from
nucleus nucleus
Circular or elliptical No path; varied shape of
path region
2n2 electrons per orbit 2 electrons per orbital

7. SCHRÖDINGER’S ATOMIC MODEL
Each orbital (containing 2 electrons) is further
classified under different categorizations based on
their shape
s
p
d
f

8. SCHRÖDINGER’S ATOMIC MODEL
Orbitals and Orbital Shapes
Each arrow
s Fits 2 electrons subshell
Increasing energy
represents an
orbital
electron
p Fits 6 electrons
px py pz
d Fits 10 electrons
dv dw dx dy dz
f Fits 14 electrons
dt du dv dw dx dy dz
Pauli exclusion principle: No
two electrons in an orbital have
the same direction

9. SCHRÖDINGER’S ATOMIC MODEL
RECALL: Schrödinger proposed that each energy
level/shell had a respective number of subshells.
s
s, p
s, p, d
What do you think these subshells are?

10. SCHRÖDINGER’S ATOMIC MODEL
Drawing an electron energy-level diagram
Example: Oxygen
How many electrons does oxygen have? 8
2p
2s Hund’s rule: No two electrons can
be put into the same orbital until one
1s
electron has been put into each of the
equal-energy orbitals
O
aufbau principle: An energy sublevel must be filled
before moving to the next higher sublevel

11. SCHRÖDINGER’S ATOMIC MODEL
Drawing an electron energy-level diagram
Example: Oxygen
How many electrons does oxygen have? 8
2p
2s
1s
O
aufbau principle: An energy sublevel must be filled
before moving to the next higher sublevel

12. SCHRÖDINGER’S ATOMIC MODEL
Drawing an electron energy-level diagram
Compare with its Bohr-
Example: Oxygen Rutherford diagram:
2p
2s
P=8
1s
N=8
O
Notice how the pairing of electrons in the Bohr-Rutherford
diagram matches the energy level diagram

13. SCHRÖDINGER’S ATOMIC MODEL
Drawing an electron energy-level diagram
Example: Iron How many electrons does iron have? 26
3d
3p
3s
2p
2s
Although the 3rd energy level
1s has 3 subshells, the “electron
filling” order is not as such
Fe

14. SCHRÖDINGER’S ATOMIC MODEL
Each energy level is
supposed to begin
with one s orbital,
and then three p
orbitals, and so forth.
There is often a bit of
overlap.
In this case, the 4s
orbital comes before
the 3d orbitals.

15. SCHRÖDINGER’S ATOMIC MODEL
aufbau diagram:
Start at the top and
add electrons in the
order shown by the
diagonal arrows.

16. SCHRÖDINGER’S ATOMIC MODEL
Drawing an electron energy-level diagram
Example: Iron How many electrons does iron have? 26
3d
4s
3p
3s
2p
2s
1s
Fe

17. SCHRÖDINGER’S ATOMIC MODEL
So why does bromine still have 7 valence electrons
despite how the 3rd energy level can hold 18 electrons?
4p
The last energy
3d level still has 7
electrons
4s
3p
3s
2p
2s
1s
Br

18. SCHRÖDINGER’S ATOMIC MODEL
Drawing an electron energy-level diagram
Example: sulfur vs sulfide ion
This explains why
Observe how there
sulfur gains 2
are two unpaired
electrons in ionic
electrons in sulfur
form
3p 3p
3s 3s
2p 2p
2s 2s This is despite
1s the fact that
1s
sulfur has 5
S S2- unfilled d
orbitals

19. SCHRÖDINGER’S ATOMIC MODEL
Drawing an electron energy-level diagram
Example: zinc vs zinc ion
3d 3d
4s 4s
3p 3p
3s 3s
The electrons
2p 2p
removed might
2s 2s not be from the
highest-energy
1s 1s orbitals. This is
based on
Zn Zn2+ experimental
evidence.

20. SCHRÖDINGER’S ATOMIC MODEL
Why is an electron energy-level diagram drawn as such?
The greater
the orbital
number, the
greater the
energy of
the
electrons
The nucleus
is located at
the bottom
of the
diagram

21. SCHRÖDINGER’S ATOMIC MODEL
Writing Electron Configurations
Electron configurations condense the information from
electron energy-level diagrams
Electron energy level diagram Electron configuration
O: 1s2 2s2 2p4
2p
2s
Energy level #
1s
O 2s 2
# of electrons
orbital in orbitals

22. SCHRÖDINGER’S ATOMIC MODEL
Writing Electron Configurations
Electron configurations:
Cl: 1s2 2s2 2p6 3s2 3p5
Sn: 1s2 2s2 2p6 3s2 3p6 4s2 3d10 4p6 5s2 4d10 5p2
S2-: 1s2 2s2 2p6 3s2 3p6
Fe: 1s2 2s2 2p6 3s2 3p6 4s2 3d6

23. SCHRÖDINGER’S ATOMIC MODEL
Writing Electron Configurations
Shorthand form of Electron configurations:
Same configuration as Neon
Cl: 1s2 2s2 2p6 3s2 3p5
Cl: [Ne] 3s2 3p5
Same configuration as krypton
Sn: 1s2 2s2 2p6 3s2 3p6 4s2 3d10 4p6 5s2 4d10 5p2
Sn: [Kr] 5s2 4d10 5p2
In the shorthand version, the “core electrons” of an
atom are represented by the preceding noble gas

24. SCHRÖDINGER’S ATOMIC MODEL
Writing Electron Configurations
Identify the element that has the following electron
configuration:
1s2 2s2 2p6 3s2 3p6 4s2 3d10 4p6 5s2 4d10 5p6 6s2 4f14 5d10 6p4
1s 1s
2s 2p
3s 3p
4s 3d 4p
5s 4d 5p It is the 4th
6s 5d 6p element from
7s 6d the left here
4f
5f
It is polonium (Po)

25. SCHRÖDINGER’S ATOMIC MODEL
Electrons cannot exist between orbitals?
Electrons
cannot exist
here or here…
2p
2s
1s
O or here…
Why?

26. SCHRÖDINGER’S ATOMIC MODEL
Since electrons are like waves around the nucleus, they
cannot have wavelengths that result in destructive
interference (which can collapse the wave).
mismatch
As a result, the wavelengths must be multiples of
whole numbers (n = 1, 2, 3, 4, …), which explains why
there are areas where electrons cannot exist.

27. SCHRÖDINGER’S ATOMIC MODEL
This causes electrons to be confined to certain
probabilities around the nucleus.