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Chapter 7.5:
The Quantum Mechanical Model of the Atom
“It is often stated that of all the theories proposed in this
century, the silliest is quantum theory. Some say the only
thing that quantum theory has going for it, in fact, is that it
is unquestionably correct.”
- R. Feynman, Physicist
The Quantum Mechanical Model
•Quantum Mechanics broke
away from the traditional
particulate models and
offered wave mechanics as
the basis of describing
electrons in an atom.
•The Quantum Mechanical
Model is based on high
levels of mathematics and
visualizes the electron as a
standing wave – fixed at
both ends.
• In 1925, Erwin Schrodinger developed the mathematical
formula that forms the basis of quantum mechanics.
• The wave function puts the electron in all possible states
at once, (i.e. "in two places at once"). The act of
observation or measurement changes the outcome.
• The wave function, Ψ:
• A function of the coordinates (x, y, and z) of the
electron’s position in a three-dimensional space.
• A specific wave function (an orbital), is an area of high
probability of finding an electron.
• The
probability of
finding an electron is
portrayed as a ‘cloud’
shape.
• The
denser the cloud,
the greater the
probability of finding
an electron in that
area.
The propeller blade, just like an
electron, has the same probability of
being anywhere in the blurry region.
One cannot predict its location at any
one instant, so it assumes all locations
at once.
• Schrödinger's equation predicts the shapes of the
various orbitals – these are areas of high probability of
finding an electron.
Schrödinger’s Cat
http://www.youtube.com/watch?v=IOYyCHGWJq4
http://www.youtube.com/watch?v=uWMTOrux0LM
Schrödinger’s Cat illustrates
that since we don’t know
where exactly an electron is
at any given moment, it is
actually in all possible states
simultaneously, as long as we
don't look to check. It is the
measurement itself that
causes the object to be
limited to a single possibility.
Section 7.6: Quantum Numbers
•Quantum numbers:
Each of the
orbitals are characterized by a
series of numbers which
describe various properties of
the orbital
•Assigning quantum numbers are
no longer covered on the AP test
so this section is beyond the
scope of this course.
Section 7.7: Orbital Shapes and
Energies
•The quantum
mechanical model only
represents the
probability distribution
of the electron in the
orbital.
•This allows us to picture
the orbitals in terms of
probability distributions
PREVIEW OF INSIDE AN ATOM:
The nucleus is surrounded by a space in which the
electrons orbit the nucleus: The electron cloud
The electron cloud is divided into 7 principal Energy levels
numbered n=1 to n=7 with n=1 closest to the nucleus. n is
called the quantum number.
Each energy level is divided into sublevels, referring to the
cloud shape. (s, p, d, f)
Each sublevel contains atomic orbitals (s=1, p=3, d=5, f=7)
Each orbital can contain 2 electrons. (s=2, p=6, d=10,
f=14). The total number of electrons in all of the orbitals
equals the total number of electrons for that element.
Energy Levels
Energy level is the distance from the nucleus
where the electron is most likely to be
moving.
Energy levels are in designated quantum
numbers (n).
n = 1, 2, 3, 4, 5, 6 or 7...
• A Quantum number is equal to the period
• Higher the quantum number, the greater
average distance from the nucleus
n=4
n=3
n=2
n=1
Nucleus
•Electrons
do not remain
between energy levels.
•To move from one energy level
to another, an electron must
gain or lose just the right
amount of energy... a
“quantum” of energy
•The steps, like the energy
levels, are not equally spaced.
•The higher the step, the more
energy it has, and the farther
away it is from the nucleus
Energy levels are divided into
sub-levels.
Each sub-level corresponds to a specific cloud
shape.
Letters represent the different orbitals :
s – spherical
p – dumb-bell shaped
d – clover-leaf shaped
f – complex shape
P
S
D
F
Note the Principal energy levels and
sublevels . . .
Summary of Energy Levels / Sublevels
Principal
Energy Level
Number of
Sublevels
Sublevels
(Quantum Number)
n=1
1
1s
n=2
2
2s, 2p
n=3
3
3s, 3p, 3d
n=4
4
4s, 4p, 4d, 4f
The principal quantum number always equals the number
of sublevels within that principal energy level.
Review of Sublevels
The max number of electrons that can occupy a given
energy level is 2n2 where n = energy level.
Shape of
Number of Number of Orbital diagram
Orbital
orbitals
electrons
S (Spherical) 1
2 max
P (dumbbell) 3
6 max
D (clover)
5
10 max
F (complex)
7
14 max
• The 2nd energy level has how many sublevels?
Two
• What orbital types are within the sublevel?
2s and 2p
• The 3rd energy level has how many sublevels
and what orbital types are within the sublevel?
3s, 3p, 3d
Three

How many electrons can be in the 3rd energy
level?
2n2, n=3
2(3)2
18 e-
How many orbital types are in the 4th
energy level?

Energy level = # of sublevels
4 orbital types – s, p, d, and f
How many TOTAL orbitals are in the
4th energy level?
Total orbital # = n2
42=16

1 s, 3 p, 5 d, 7 f
Metallic properties increase as you go down a group,
and decrease as you go across a period.
X
Fr is the most metallic!