Quantum
Mechanics
Electron Density
Based on Heisenberg uncertainty principle and Schrodinger wave equation
Representation of the electron density
distribution surrounding the nucleus in
the hydrogen atom; shows a high
probability of finding the electron closer
to the nucleus
• Gives the probability that
an electron will be found
in a particular region of
an atom
• Regions of high electron
density represent a high
probability of locating the
electron
Atomic Orbital
• Way to distinguish Bohr’s model from
the current quantum mechanical
model
• Probability of locating the electron in
3D space around the nucleus
• Has a characteristic energy
Quantum numbers
used to describe atomic orbitals and to
label electrons that reside in them
• Principle quantum number (n)
• Angular momentum quantum number
• Magnetic quantum number
• Electron spin quantum number
Principal Quantum
Number n
n = 1, 2, 3, 4, ….
distance of e- from the nucleus
n=1
n=2
n=3
5
Energy levels are like rungs of a
ladder. You cannot be in
between a rung
Energy levels in an atom’s
electron are unequally spaced.
The higher energy levels are
closer together.
Angular Momentum
Quantum Number
Shape of the “volume” of space that the e- occupies
s orbital
p orbital
d orbital
f orbital
smart people do fine
Magnetic
Quantum Number
•Describes the orientation of the orbitals in space
•All orientations are identical in energy
s orbital
Sphere
p orbital
3 orientations
dumbbell
d orbital
5 orientations
Double dumbbell
f orbital
7 orientations
Electron Spin
Quantum Number
•Electrons are
thought to be
spinning on their own
axes-clockwise, or
counterclockwise.
•The up and down
arrows denote the
direction of the spin.
Energy of Orbitals
depends on
principle and
angular
momentum
quantum
numbers
Shielding Effect
• Why is the 2s orbital
lower in energy than the
2p?
• “shielding” reduces the
electrostatic attraction
• Energy difference also
depends on orbital shape
Electron Configuration vs
Orbital diagram
number of electrons
in the orbital
1s1
principal quantum
number n
Shape
Orbital diagram
H
1s1
Aufbau Principle
“fill up” the lowest
energy level first
Orbitals in the Periodic Table
Pauli Exclusion Principle
• No two electrons can have the same 4 quantum
numbers
• Only two electrons may occupy the same atomic
orbital, and these electrons must have opposite
spins
• Electrons that have opposite spins are said to
be paired
Orbital name
s
p
d
f
# of orientations Total # of electrons
Hund’s Rule
•The most stable
arrangement of
electrons in an
orbital is the one
with the greatest
number of parallel
spins
•e- will occupy
singly before filling
with opposite spins
Practice
Fill in the orbital diagram, and write the electron
configuration for the following atoms
Example of Exceptions to
the Rules
Element
Copper
Should be
1s22s22p63s23p63d44s2
Chromium 1s22s22p63s23p63d94s2
Actually is
1s22s22p63s23p63d54s1
1s22s22p63s23p63d104s1
•These are not the only two exceptions.
•The rules are violated because half-filled
sublevels are not as stable as filled sublevels,
but they are more stable than other
configurations
Noble Gas Configuration
What is the electron configuration for Ne?
Ne:
What is the electron configuration for Mg?
Mg:
What do both electron configurations have in
common?
To figure out which noble gas to use find the
noble gas that is closest to the element without
going over in atomic number
Which noble gas is closest without going over?
Rb
Cl
Ra
Practice
Write the noble gas electron configuration for the
following atoms:
Na:
Mn:
Co:
Sn:
Valence Electrons
• Electrons in the outermost s and p orbitals
(highest n shell)
• These electrons participate in chemical
reactions