Download Quantum Mechanics

Chemistry- Unit 3
Section II - Chapter 7
(7.6-7.8, 7.11)
Quantum Mechanics
Atomic Review
What subatomic particles do you get to “play” with?
Protons
→ NO! It would change the element
Neutrons → Don’t Care - isotopes: only mass is different
Electrons → What we “play with” in chemistry
Bohr Model of the Atom
• electrons must circle the nucleus of an atom in
certain paths
• Developed the concept of Energy Levels
Bohr Model of the Atom
• The model correctly fits the quantized energy
levels of the hydrogen atom and postulates only
certain allowed circular orbits for the electron
• Bohr’s model is incorrect. This model only works
for hydrogen
• Electrons do not move around the nucleus in
circular orbits
Quantum Mechanics
• Quantum (definition from Webster’s)
1) quantity, amount
2) any of the very small increments or parcels into
which many forms of energy are subdivided
• Quantum Theory
-describes mathematically the wave properties of
electrons and other very small particles
*electrons were determined to have a dual waveparticle nature
*uses two principles
Quantum Mechanics
• Heisenberg uncertainty principle
 it is impossible to determine simultaneously both the
position and velocity of an electron or any other
particle
• Schrodinger Wave Equation
 treats electrons as waves around the nucleus
Together these two principles determine the
probability of finding electrons
We do not know the detailed pathway of an electron
Quantum Mechanics
Orbital
 three-dimensional region around the nucleus that
indicates the probable location of an electron
To describe orbitals, we use…..
Quantum Numbers
 specify the properties of atomic orbitals and the
properties of electrons in orbitals
there are 4 quantum numbers
Quantum Numbers
• Principal quantum number (n)
– size and energy of the orbital
– the main energy level occupied by the electron
• positive integers
• ranges from 1 to 7
• equal to the period
Quantum Numbers
• Angular momentum quantum number (l or l)
– shape of atomic orbitals
– sometimes called a subshell
• Orbitals possible is equal to n
• Values of l are all integers less than l = n-1
Quantum Numbers
• Angular momentum quantum number (l or l)
l
0
1
2
3
subshell
s
p
d
f
Quantum Numbers
• Angular momentum quantum number (l or l)
Concept Check
For principal quantum level n = 3, determine
the number of allowed subshells (different
values of l), and give the designation of each.
# of allowed subshells = 3
l=0
3s
l=1
3p
l=2
3d
Quantum Numbers
• Magnetic quantum number (ml)
– orientation of the orbital in space relative to
the other orbitals around the nucleus
– ml = ±l
• each subshell has a specific shape
– s subshell has 1 orbital  one shape
– p subshell has 3 orbitals  three shapes
– d subshell has 5 orbitals  five shapes
– f subshell has 7 orbitals  seven shapes
• Assign each family magnetic quantum number
then repeat if needed
You do NOT need to know the shapes
Quantum Mechanics
• Electron spin quantum number (ms)
– an orbital can hold only two electrons, and
they must have opposite spins
– can be -½ or +½
• Each electron must be distinguishable
(different) from all others
• Start with the negative spin first
Quantum Mechanics
Quantum Numbers for the First Four Levels of Orbitals in the
Hydrogen Atom
Quantum Mechanics
1s Orbital
Quantum Mechanics
Two Representations
of the Hydrogen 1s,
2s, and 3s Orbitals
Quantum Mechanics
2px Orbital
Quantum Mechanics
2py Orbital
Quantum Mechanics
2pz Orbital
Quantum Mechanics
The Boundary Surface Representations of All Three 2p Orbitals
Quantum Mechanics
3dx -y Orbital
2
2
Quantum Mechanics
3dxy Orbital
Quantum Mechanics
3dxz Orbital
Quantum Mechanics
3dyz Orbital
Quantum Mechanics
3d z 2
Orbital
Quantum Mechanics
The Boundary Surfaces of All of the 3d Orbitals
Quantum Mechanics
Representation of the 4f Orbitals in Terms of Their Boundary
Surfaces
Concept Check
For l = 2, determine the magnetic quantum
numbers (ml) and the number of orbitals.
magnetic quantum numbers = –2, – 1, 0, 1, 2
number of orbitals = 5
Quantum Mechanics
Identify the four quantum number for the following
elements:
Element
Lithium
Bromine
Silver
Uranium
n
2
4
5
7
l
0
1
2
3
ml
0
0
1
-1
ms
-½
+½
+½
-½
Concept Check
Identify the four quantum number for the following
elements:
Element
Platinum
Silicon
Chlorine
Radium
n
6
3
3
7
l
2
1
1
0
ml
0
0
0
0
ms
+½
-½
+½
+½
Concept Check
Identify the four quantum number for the following
elements:
Element
Potassium
Iron
Arsenic
Tungsten
n
4
4
4
6
l
0
2
1
2
ml
0
-2
1
1
ms
-½
+½
-½
-½
Quantum Mechanics
Electron Configurations
• the arrangement of electrons in an atom
 based on 3 rules
• Aufbau principle
– electrons occupy the lowest energy level
they can
• Pauli exclusion principle
– in a given atom, no two electrons can have
the same set of four quantum numbers
Quantum Mechanics
Electron Configurations
• Hund’s Rule
– the lowest energy configuration for an atom is
the one having the maximum number of
unpaired electrons allowed by the Pauli
principle in a particular set of degenerate
(same energy) orbitals
• orbitals of equal energy are each occupied by one
electron before any orbital is occupied by a second
electron
• all electrons in singularly occupied orbitals must
have the same spin
Quantum Mechanics
Orbital Energies
Quantum Mechanics
Orbital Energies
Quantum Mechanics
The Orbitals Being Filled for Elements in Various Parts of the
Periodic Table
Quantum Mechanics
Electron Configuration Notation
• The order that electrons fill orbitals
1s2 2s2 2p6 3s2 3p6 4s2 3d10 4p6 5s2 4d10 5p6
6s2 4f14 5d10 6p6 7s2 5f14 6d10 7p6
Quantum Mechanics
Electron Configuration Notation
What is the electron configuration for oxygen?
1s2 2s2 2p4
What is the electron configuration for bromine?
1s2 2s2 2p6 3s2 3p6 4s2 3d10 4p5
Quantum Mechanics
Electron Configuration Notation
• Instead of using the Periodic Table, you can
make this chart to write electron configurations.
Quantum Mechanics
Electron Configuration Notation
What is the electron configuration for Strontium?
1s2 2s2 2p6 3s2 3p6 4s2 3d10 4p6 5s2
What is the electron configuration for Erbium (Er)?
1s2 2s2 2p6 3s2 3p6 4s2 3d10 4p6 5s2 4d10 5p6
6s2 4f12
Review page 315 and 316 in book
Quantum Mechanics
Noble Gas Configuration Notation
• You can also use Noble Gases to show electron
configurations since they have a fulfilled Octet Rule
 To do this, go backwards from your element to
the closest Noble Gas and list it in brackets [ ]
 Starting from that point, list the electron
configuration to your element
• It is really the same thing; it just shortens the
configuration up.
• Don’t use a Noble Gas Configuration unless asked
to do so.
Quantum Mechanics
Noble Gas Configuration Notation
What is the Noble Gas configuration for Chlorine?
[Ne] 3s2 3p5
What is the Noble Gas configuration for Einsteinium
(Es)?
[Rn] 7s2 5f11
Quantum Mechanics
Orbital Diagram
• A notation that shows how many electrons an
atom has in each of its occupied electron
orbitals.
• Always draw up arrows (-½ spin) first
Oxygen: 1s22s22p4
Oxygen:
1s
2s
2p
Quantum Mechanics
Orbital Diagram
• Draw an orbital diagram for sulfur.
Sulfur: 1s22s22p63s23p4
3s
2s
1s
2p
3p
Concept Check
Determine the expected electron configurations
for each of the following.
a) S
1s22s22p63s23p4
b) Ba
1s22s22p63s23p64s23d104p65s24d105p66s2
c) Eu
1s22s22p63s23p64s23d104p65s24d105p66s24f7
Concept Check
Determine the expected Noble Gas
configurations for each of the following.
a) S
[Ne]3s23p4
b) Sr
[Kr]5s2
c) Au
[Xe]6s24f145d9
Concept Check
Draw an Orbital Diagram for Aluminum.
3s
2s
1s
2p
3p
Quantum Mechanics
Valence Electrons
• The electrons in the outermost principal
quantum level of an atom
1s2 2s22p6 (valence electrons = 8)
• The elements in the same group on the periodic
table have the same valence electron
configuration
• Only going to be responsible for Main Group
elements
• Range is from 1 to 8
Quantum Mechanics
Valence Electrons
• Chlorine – 1s22s22p6 3s23p5
[Ne] 3s23p5
7 valence electrons
• The number of valence electrons is equal to
the group number minus 10 (unless it is a
single digit, then it is the number of valence
electrons)
Concept Check
Determine the valence electrons for the
following elements:
a) S
6
b) Sr
2
c) B
3
Unit 3
Homework Set #2
pg 332: #67, 68, 70, 75, 76, 77, 79, 84,
89, 92, 132
(11)