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Quantum Mechanics
 The application of quantum theory to explain
the properties of matter, particularly electrons
in atoms
Schrodinger’s Standing Waves
 Louis De Broglie developed
a theory that matter
can have wave-like properties
 Schrodinger extended this theory to electrons
bound to a nucleus
 Postulated that electrons resembled a
standing wave
 Certain orbitals exist at whole wavelengths of
electron vibrations
Orbitals - Redefined
 Orbital: region around the nucleus where there
is a high probability of finding an electron
 As per wave model of Schrodinger – because
things are vibrating
Heisenberg Uncertainty
Principle
Heisenberg Uncertainty
Principle

Heisenberg studied statistics and developed matrix
algebra

Developed a statistical approach to explaining how
electrons works and realized…

IT IS IMPOSSIBLE TO KNOW THE EXACT
POSITION AND SPEED OF ELECTRON AT A GIVEN
TIME
 At best, we can describe the probability of
finding it at a specific place
 Wave functions: the mathematical probability of
finding an electron in a certain region of space
 Wave functions give us:
 Electron probability densities: the probability of
finding an electron at a given location, derived
from wave equations
Homework
Quantum Numbers
 Quantum Numbers: numbers that describe the
quantum mechanical properties (energies) of
orbitals
 From the solutions to Schrodinger’s equation
 The most stable energy states is called the
ground state
Principal Quantum Number (n)
 Integer number (n)
used to level the main
shell or energy level of
the electron
 Describes size and
energy of the atomic
orbital
 Increase number =
increase energy, bigger
Secondary Quantum Number, l
 Describes the shape of the orbital within each
shell
 Each energy level contains several sublevels
 Relates to the shape of the orbital
 Can be any integer from 0 to (n-1)
Values of l
Value
0
1
2
3
4
Letter
Used
s
p
d
f
g
Name
sharp
principal
diffuse
fundamental
 Each orbital is given a code:
 Example
 If n = 1, l = 0 then we call it a 1s orbital
 If n = 3, l = 2 then we call it a 3d orbital
Magnetic Quantum Number, ml
 Describes the orientation of the orbital in 3-
space
 Can be whole number integers from – l to + l
 Example: if l = 1, then ml can be -1, 0, +1
 There are 3 possible p orbitals
 px, py, and pz
 What are possible values for ml if l is:
0
1
2
3
Spin Quantum Number
 Electrons are basically little magnetics spin
around when placed in magnetic fields, they can
have spin ‘up’ or spin ‘down’
 ms can be either +1/2 or – 1/2
Homework
Electron Configurations and
Energy Level Diagrams
 The four quantum numbers tell us about the
energies of electrons in each atom
 Unless otherwise stated were are talking about
ground state energies
Energy Diagrams
 Describe how electrons fill orbitals using
quantum numbers
 Electrons fill the lowest energy level orbitals
first
 Each shell is (for the most part) filled before
moving to higher shells
Rules
 Use circles (or boxes) to represent each orbital
in any given energy level and arrows for
electrons
 Unoccupied circles imply that there are no
electrons in it
 A circle can have at most two electrons in it;
only if the arrows are pointing in opposite
directions
Rules to Remember
 Pauli exclusion Principle: no two electrons
can have the same 4 quantum numbers.
Electrons in the same orbital can’t have the
same spin
 Hund’s Rule: One electron occupies each of
sub-orbitals in the same energy level before a
second can occupy the same sub-orbital
 Aufbau Principle: each electron is added to the
lowest energy orbital available
Building Orbital Diagrams
Practice
 H, B, C, Ne
 Mg, P, Ar
 Ca, Mn, Zn, Ge, Kr
Electron Configurations
 Condensed versions of orbital diagrams
 Write the electron configuration for each of the
atoms above
Exceptions to the Rules
 Examine the allowed
charges for Chromium and
Copper
 Write the electron configuration for chromium
and copper
What actually happens?
 Why? Evidence suggests that half-filled and
filled orbitals are more stable than other
orbitals, so electrons rearrange to give these
configurations
Explaining Ion Charges
 In order to get particular charges, entire energy
levels or sublevels get cleared first.
 Use electron configuration theory to explain
why:
 Zn  Zn2+
 Pb  Pb2+ or Pb4+
Explaining Trends in the
Periodic Table
 Atomic Radius: size of the atom
 Ionization Energy: energy needed to remove an
electron from the outermost energy level from
an electron in the gaseous state
 Electron Affinity: change in energy that occurs
when an electron is added to a gaseous atom