New unit !
Quantum
Mechanical Model
and Periodicity

DeBroglie  duality

treated the electron as a function of a wave (Bohr treated as a particle)




Differs from Bohr model in several ways

2 of particular note



“If waves of energy have some properties of particles, perhaps particles of matter
have some properties of waves.”
Combined E=mc2 with E=h x nu
Distinction between both particle and wave disappears at the atomic level
The kinetic energy of an electron is inversely related to the volume of the
region to which it is confined (more common – electrostatic energy decreases
as kinetic energy increases creating a balance )
It is impossible to specify the precise position of an electron in an atom at a
given instant (the best that can be done is estimate the “probability” of finding
an electron in a particular region
Schrodinger

Wave function of electron


Certain allowed amounts of energy due to the allowed wave-like motion of an
electron
Electron cloud
Quantum Mechanical Model
Each electron has it’s own region within the atom and has a number designation describing that region
1.
Principle quantum number (n)
~ main energy level or shell
~ represented by whole number
integers (1, 2, 3 ...the period number on the p-table)
~ number indicates the distance from the
nucleus (the > the ‘pqn’ the farther the
electrons are from the nucleus)
~ specifies the size of the ORBITAL
Sublevels, sublevels, sublevels
2. Azimuthal quantum #
~ represented by the letter ‘l ’
~ shape of the electron cloud
~ the # of sublevels is equal to
the value of the ‘pqn’
(‘pqn’ = 2, then there are 2
sublevels)
Sublevels are?
s..p..d..f..g..h..so on
l = integer from 0
to… (n-1)
l = 0, 1, 2, 3…
Ex. 1 – 1 = 0 (#
representing the “s” sublevel)
 Atomic

Orbital Shapes and Sizes
Names derived from the characteristics of their
spectroscopic lines: sharp, principle, diffuse, and
fundamental
s
p
d
f
 and
so on…g, h, …
ORBITALS
http://chemed.chem.wisc.edu/chempaths/GenChem-Textbook/Orbitals-896.html
 Within sublevels each electron pair has a different place in space.

This space is called an orbital.
3. Magnetic Quantum number ( ml )
Orbital-orientation quantum #
Max. 2 electrons
per orbital
• the quantum number that represents the
appropriate orbital
ml = - l to + l
s-sublevel----1 orbital----- ml = 0
p-sublevel ----3 orbitals ----- ml = -1, 0, +1
d-sublevel ----5 orbitals ----- ml = -2, -1, 0, +1, +2
f-sublevel ----7 orbitals ----- ml = -3, -2, -1, 0, +1, +2, +3
4. Spin Quantum Number (ms)
~ NOT a property of the orbital
~ describes a property of the electron itself
~ indicates the direction of the electron spin
ms= +1/2 or -1/2
Main
Energy
Level
• represented by a whole
number
• represented by the periods
on the periodic table
• the size of the orbital
Sublevels
• represented
by s, p, d, f
• the shape of
the orbital
•
Orbitals
the different
ways the
orbital aligns
around the x,
y, z axis
Spin of
electron
* the distribution of electrons
within the orbitals of an
element’s atoms
* determines
behavior and
chemical properties
and reactivity
of the elements
Electron Configurations
Orbital notation
# = main energy level (pqn, 1, 2, 3 etc…)
letter = sublevel (s, p, d, f)
= orbital
3s
2p
2s
= electrons
1s
2p 2p
Starting order of energy
level with sublevel and
orbital
Here electron, come on boy!
 Aufbau principle
 Pauli exclusion
~ electrons are added one
principle
at a time
~ an orbital can hold a
~ you begin with the
maximum of 2
lowest energy
electrons
~ you add electrons until ~ paired and unpaired
all electrons are
accounted for
More assigning of electrons
 Hund’s rule
~ all orbitals within a sublevel
must have at least one electron
before a paired electron can be
used
 It doesn’t matter which one
gets an electron first, but…
1. Each electron MUST have the
SAME SPIN as the others in
unfilled orbitals! (up or down)
2. NO electron pairs are allowed
until every orbital in that
sublevel has one electron!
4p
4p
4p
3d
4s
3p
3p
3p
2p
2p
2p
3s
2s
1s
3d
3d
3d
3d
Electron “Promotion”
A “d” subshell is more stable when it is…
EXACTLY 1/2 FULL (5 electrons), or…
EXACTLY FULL! (10 electrons)!
The same is true for “f ” subshells!
(7 or 14 electrons)
When a “d” is ONE electron short of 1/2 full or
full…
It PROMOTES one electron from the nearest “s”
subshell!
Configuration notation

With configuration notation, the concept of orbital notation
is still used…BUT


The orbitals are no longer represented by boxes
The energy level # and the sublevel are still used (1s, 2s
2p and so on)…BUT


(aka REGULAR NOTATION)
The arrows representing the electrons are not used
The number of electrons is still important AND

The number of electrons are written as superscripts above the
sublevel designation
Example: Sodium, Na (11 electrons)
 1s2 2s2 2p6 3s1
Short hand notation





With shorthand notation, the same technique as
configuration notation is used.
The difference is …
all of the electrons to the previous row NOBLE GAS
are accounted for
the configuration continues from the end of the noble gas
row and picks up at the beginning of the next energy level
the technique is to put the noble gas element symbol in
brackets Ex. [Ar 18]
the configuration notation picks up and continues until all
the electrons are accounted for
Ex. Cu29  [Ar18] 4s2 3d9
“d” and “f ” Subshells Fill LATE
•“d” subshells fill 1 shell behind!
•3d fills after 4s
•4d fills after 5s
• “f” subshells fill 2 shells behind! MORE complex!
• The first “f” subshell is in the 4th shell (4f)…
• 4f fills after 6s! (then comes 5d, and then 6p)
• 5f fills after 7s, (then comes 6d, and then 7p)
Just follow the elements in order!!
Electron “Promotion”
Example: Silver (Ag) 1s2, 2s2, 2p6, 3s2, 3p6, 4s2, 3d10, 4p6, 5s2, 4d9
21
5s
10
9
4d
4d
9 – 1 short of full!
4d
6
2
6
2
10
6
Silver (Ag) 1s2, 2s2, 2p , 3s , 3p , 4s , 3d , 4p , 5s1, 4d10
Silver is now more stable with a full
4d subshell! (4d10)
Electron “Promotion”
Remember! One “s” electron will “promote”
to the nearest “d” or “f ” subshell if…
…that “d” or “f ” is one electron short of
being full or 1/2 full!
Watch for d 4, d 9, f
6
or f
13!
Practice quantum #’s
 Consider the following sets of quantum
numbers … a) 3, 1, 0, +1/2 b) 1, 1, 0, -1/2 c) 2, 0, 0, +1/2 d) 4, 3, 2, +1/2
 which
ones are valid
 If valid, identify the orbital involved
VALENCE ELECTRONS
 The
electrons in the outermost energy level
are called valence electrons.
 Valence electrons are the ones that cause
chemical properties and reactions
 Look for the highest “n” (principle energy
level), such as 3s, or 4p, etc.
 Valence electrons will ALWAYS be in “s”
or “p” subshells!
Lewis Dot Structures
This is EASY!
The dots placed around the symbol of an element
represent ONLY THE OUTSIDE ELECTRONS!
These outside electrons are called the…
“valence electrons”!
Remember, ONLY “s” AND “p” SUBSHELLS ARE ON
THE OUTSIDE!!!
This means that the total number of dots around a
symbol can NEVER exceed 8!! (“s” = 2, “p” =6)
This is called the “OCTET RULE”!
Lewis Dot Diagrams
• A Lewis dot diagram illustrates valence
electrons as dots around the chemical symbol
of an element.
Lewis Dot Diagrams
• Each dot represents one valence electron.
• In the dot diagram, the element’s symbol
represents the core of the atom—the nucleus
plus all the inner electrons.
Lewis Dot Diagrams Represent Valence Electrons
The dots are written around an imaginary
box surrounding the element symbol, up to a
maximum of eight!: (no pairs before 5!)
(the dots may start on any side)
One valence electron:
Sy
Three valence electrons:
Two valence electrons:
Sy
Four valence electrons:
Five valence electrons:
Sy
Sy
Six valence electrons:
Sy
Sy
OK…
WHY does 4s fill before 3d?
Higher energy
Farther out than
2nd shell, but all 3
an equal distance
from the nucleus.
Farther out than
1st shell, but both
an equal distance
from the nucleus.
Closest to
the nucleus
“3d” subshell
“3p” subshell
“3s” subshell
3rd shell
“2p” subshell
“2s” subshell
2nd shell
“1s” subshell
1st shell
Higher energy
Note that, even though the 4th shell
is farther out than the 3rd shell,
the energy of 4s is LESS than 3d!
4th shell
Farther out than
3rd shell, but all 4
an equal distance
from the nucleus.
3rd shell
Farther out than
2nd shell, but all 3
an equal distance
from the nucleus.
“4f” subshell
“4d” subshell
“4p” subshell
“3d” subshell
“4s” subshell
“3p” subshell
“3s” subshell
Higher energy
7s
6s
5s
4s
3s
2s
1s
7f
7d
6f
7p
6d 5f
6p 5d
5p 4f
4d
4p
3d
3p
2p