Quantum model of an Atom Chapter 17
I read Chapter 15 before coming to
class
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2.
Yes, the whole
thing.
Nope, essentially
none.
Well some, more
than ½.
A little only.
W
1.
10
The wave nature of moving particles is
interpreted as being
...
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pa
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6%
4%
up
3.
90%
do
w
2.
An up and down path that
the particle travels in as it
moves.
A back and forth path that
the particle travels in as it
moves.
Not a traditional wave at
all but instead is a
function that tells us the
probability of detecting
the particle.
d
1.
an
250
Perspective
fast
slow
Relativity
Newton’s
Laws ok
large
Wave-Particle
Duality
small
Standing waves are created when
0
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ar
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ot
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B
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av
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s
1
an
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w
ra
p
2
ta
ar
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nd
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..
38%
W
3.
62%
re
fle
c
2.
Waves reflect and
bounce back to where
they started from.
Waves wrap around
and come back to
where they started
from.
Both 1 and 2 are ways
standing waves can
be created.
s
1.
av
e
250
10
Standing Waves
2 Dimensions

It is easy to create standing waves
in 2 dimensions as well.
Two waves on a drum head
A single wave on a
drum head
Three waves on a drum head
Wrap standing waves around a point

These are patterns of vibration.
Bohr Model Explained!


Take de Broglie’s
waves and wrap
them in a
standing wave
pattern around
the nucleus.
Put one wave ,
then two waves,
then three waves,
etc and you
exactly predict
the location of the
Bohr radii!
A CRUDE representation!
The Quantum Model of the Atom



Electrons are found in 3-D electron
probability waves.
They do not orbit. Instead they exist
in the locations given by standing
wave clouds.
We call these wave clouds orbitals
to reflect the fact that the electrons
do not orbit like a planet.
Three Dimensional Atomic Orbitals

The shape and energies of the actual
orbitals depend on the number of
standing waves in the pattern. They
are found from solving the Shrödinger
Wave equation:
h2
2
8p m
d2Y(x)
2
dx
Kinetic Energy
+ V(x) Y(x) = EY(x)
+ Potential Energy = Total Energy
Orbital Patterns

One wave:


Electrons will resonate in one
pattern, called an “s”
orbital.
s
Two waves:

Electrons will resonate
in two patterns,
“s” and “p”
orbitals
s
p
Orbital Patterns

Three waves: Electrons will
resonate in “s”, “p” and “d” orbitals.
One orbital
s
p
d
S Orbitals



All numbers of
standing waves
have “s” orbitals.
They are all
round but their
interiors are
different.
Still, in each
case there is just
one orbital.
P Orbital

P orbitals come in sets of 3, whether
there are 2 waves or 3 waves or
more.
D Orbitals

D orbitals come in sets of 5, whether
there are 3 waves or 4 waves or
more.
Orbital Patterns

The pattern continues on as s, p, d, f, g,
h, i, j, etc. Each new orbital set has two
more orbitals than the previous one.
Orbital Type
s
p
d
f
g
h
Orbitals in set
1
3
5
7
9
11 13 15
3
i
Standing Waves
1
2
Orbital Types
s
s,p s,p,d
s,p,d,f
Total Orbitals
1
4
16
9
4
j
The Pauli Exclusion Principle

At most two
electrons can
occupy the same
orbital. If two
electrons are in the
same orbital, they
must have
different spins.
e-
e-
Spin Down
f
7
Spin Up
Orbital Type
Orbitals in set
s
1
p
3
d
5
g
9
h i
j
11 13 15
Electrons
2
6
10 14 18 22 26 30
Understanding Atoms



How do electrons fill the orbitals as
we move along the periodic table?
Electrons fill the lowest energy levels
first. For the lighter atoms, fewer
standing waves and simpler orbitals
usually means lower energies.
From here on I’ll refer
to number of standing
High energy
waves (physics lingo)
Low energy
as energy levels or shells
21
3
(chemistry lingo).
Electrons in an Atom: Energy Wells
Fill the lowest energy orbitals first
free electron
Zero Energy
Level 3
Level 2
3
d
3
p
3s
2p
2s
Energy
Level 1
1s
It is
negative
for a
bound
electron
Hydrogen
free electron
Level 3
Level 2
Level 1
3
d
3
p
3s
2p
2s
1s
Helium
free electron
Level 3
Level 2
Level 1
3
d
3
p
3s
2p
2s
1s
Lithium
free electron
Level 3
Level 2
Level 1
3
d
3
p
3s
2p
2s
1s
Beryllium
free electron
Level 3
Level 2
Level 1
3
d
3
p
3s
2p
2s
1s
Boron
free electron
Level 3
Level 2
Level 1
3
d
3
p
3s
2p
2s
1s
Carbon
free electron
Level 3
Level 2
Level 1
3
d
3
p
3s
2p
2s
1s
Nitrogen
free electron
Level 3
Level 2
Level 1
3
d
3
p
3s
2p
2s
1s
Oxygen
free electron
Level 3
Level 2
Level 1
3
d
3
p
3s
2p
2s
1s
25%
4.
0
25%
1
2
3
6
6
3.
25%
3
2.
25%
2
1.
1
250
What is the maximum number of electrons in
the entire set of p orbitals of any given shell?
How many orbitals all together are in
the third shell by itself?
25%
4.
0
25%
16
3.
9
2.
25%
3
5
9
16
3
1.
25%
5
250
10
How many electrons total are in an
atom that has the first and second
shells completely filled?
25%
4.
0
25%
12
3.
10
2.
25%
4
6
10
12
4
1.
25%
6
250
10
Absorption line spectra revisited

The outer electron of any atom can
jump up to higher orbitals creating
a unique absorption spectrum for
that element
free electron
Level 2
3d
3p
3s
2p
2s
Level 1
1s
Level 3
Emission line spectra revisited

It can then fall down creating the
emission spectrum for that element.
free electron
Level 2
3d
3p
3s
2p
2s
Level 1
1s
Level 3