Notes III of III
Quantum Theory Notes
What is Heisenberg’s “Uncertainty Principle”?
What is Schrödinger’s “Wave Equation”?
Quantum Numbers
Quantum Numbers indicate:
Principal Quantum number (n):
 possible values:

What information do they give about the electron cloud?
Sublevel quantum number (ℓ):
 possible values:

What information do they give about the electron cloud?
Electron Configutration
 The arrangement of electrons in an atom

Each element has a different arrangement of electrons because
_____________________________________________

Electrons tend to assume arrangements that have the lowest possible energy levels
(ground state electron configuration.)
What is an orbital?
Notes III of III
Shapes of Electron Orbitals
The following are graphical representations of the shapes of the orbitals within atoms.
Remember these shapes do not exist but are mainly three-dimensional probabilities of
locating the electron. Also remember, a maximum of two electrons can occupy any of the
following shapes.
How many different kinds of orbitals does each energy level have?
n=1 (s)
n=2 (s and p)
n=3 (s,p,d)
n=4 (s,p,d,f)
s (sphere): 1 orbital, max 2 electrons
p (dumbbell): 3 orbitals, max 6 electrons
d: 5 orbitals, max 10 electrons
f: 7 orbitals, max 14 electrons
s-orbital (spherical)
The following picture shows the relative sizes of 1s, 2s, and 3s orbitals.
p-orbital (dumbbell)
3 orbitals: px py pz
Notes III of III
d-orbital (double dumbbell and dumbbell/donut)
5 orbitals
f-orbital (quadruple dumbbell and dumbbell/double donut)
7 orbitals
Notes III of III
Relative Energies of Orbitals
(Compare to arrangements of orbitals on periodic table)
Electrons are Placed into Orbitals According to 3 Basic Rules:
1.
Aufbau Principle
2. Pauli Exclusion Principle
3. Hund’s Rule
1. Aufbau Principle
 An electron occupies the ________________________ that can receive it
 The ____________________ always goes into the 1s orbital
 Notice that 4s is lower in energy than 3d
 According to the Aufbau principle, 4s will fill before 3d
 Compare the energy diagram to the periodic table (what changes do we have
to make – if any?)
2. Pauli Exclusion Principle
 No two electrons in the same atom can have the same set of 4 quantum numbers
 Electrons in the orbital must have ______________ (spin “up” and spin “down”)
3. Hund’s Rule
 Orbitals of equal energy are each occupied by one electron before any orbital is
occupied by a second electron
 For example:
Notes III of III
Orbital Notation
 Each electron is represented by a half-arrow
 When electrons share an orbital, opposite spins are represented by half-arrows
going in opposite directions
Examples: Write the orbital notation for the following atoms:
N (7 e-):
____
1s
____
2s
____ ____ ____
2p
P ( ___ e-):
Electron Configuration Notation
 Write the energy level and orbital (in increasing energy)
 Write the number of electrons in the sublevel with a superscript
Examples: Write the electron configuration notation for the following atoms:
N:
P:
Tc:
Electron Configuration Notation (Noble Gas Shorthand)
 Start with the noble gas “closet without going over” in brackets
 Continue normal electron configuration
Examples: Write the electron configuration notation for the following atoms (use the noble
gas shorthand):
N:
P:
Tc:
Lewis Dot Diagrams
 Valence electrons (e- in the outermost energy level) are the only electrons that are
lost or gained in ordinary chemical reactions
 Lewis Dot Diagrams only include electrons in valence (highest energy level)
 Write the letter and dots around the outside (2 on each side: maximum of 8)
Examples: Draw the Lewis Dot Diagram for:
N
Ca
Cl