(If you thought
Special Relativity
was strange…)
Actually, we need not speak of particles at all. For many experiments it is more convenient to speak of
matter waves . . . The two pictures are of course mutually exclusive, because a certain thing cannot at
the same time be a particle . . . and a wave . . . but the two complement each other. By playing with both
pictures, by going from the one picture to the other and back again, we finally get the right impression of
the strange kind of reality behind our quantum experiments.”
~ Werner Heisenberg
I read Chapter 15 before coming
to class
y.
t..
.
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so
m
lit
e,
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on
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ly
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0% 0% 0% 0%
...
.
th
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g
4.
e,
e
3.
op
2.
Yes, the whole
thing.
Nope, essentially
none.
Well some, more
than ½.
A little only.
N
1.
10
Light is
250
97%
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y
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..
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at
t
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av
a
3.
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st
2.
Just a wave that
transports energy
through space.
Just a stream of
particles that carries
energy with it.
A unique entity that
exhibits both wave and
particle properties.
Ju
1.
10
In the Bohr model of the atom,
electrons
in
to
..
d
dd
e
e
ar
an
ve
ha
n
ca
em
be
y
sp
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ec
...
if.
.
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at
0
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250
25%
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y
3.
73%
to
2.
orbit only at specific
distances from the
nucleus.
can have any sized orbit
just like planets orbiting the
sun.
are embedded into a
positively charged
“pudding” like substance.
or
bi
1.
10
Laser diffraction demo vs.
photo electric effect
How does the photoelectric effect
imply that light is made up of
particles?
 How does a diffraction experiment tell
us light is a wave?

Matter Models continued…

Two puzzles remain at this point:


The wave-particle duality of light.
The physical basis for the Bohr model.

In 1923 a struggling graduate student
named Louis deBroglie proposed that
moving matter also has a wave-particle
duality defined from
wavelength = h/(mass×speed)
where h = Plank’s constant = 6 x 10-34
Examples
Wavelength = 10-38m
(nonsense?)
60 mph
Wavelength = 10-34m
(again nonsense?)
100 mph
2,000 mps
Wavelength = 10-10m which
is the diameter of an atom.
Now we are getting
somewhere…
But are electrons really
waves?



See if they diffract. We need slits about
the size of the electron wavelength (10-10m)
to witness it.
How do you make a slit that
small? You don’t. You use the
space between atoms in a
crystal.
Fire an electron beam at a
crystal and we DO get
diffraction rings! Electrons ARE
waves?!?!
Double slits again…



OK. The Millikan oil drop
experiment says that
electrons are particles. Or
at least they are picked up
in discrete chunks by oil
drops.
But electrons clearly diffract
like waves.
Let’s turn to our old friend,
the double slit experiment,
and see if electrons
interfere!
particles
waves
Davisson-Germer
Experiment
Do a “double slit”
experiment using
the spaces between
atoms in a crystal.
 An interference
pattern is clearly
seen. Electrons
ARE waves!

Harnessing the Wavelength of
Electrons

Diffraction is bad if you want to see things clearly.
Sharp
image
Large
hole
See this
Small
hole
Fuzzy
image
Electron Microscopes



Microscopic things
diffract light and
limit how clearly
we can see small
items using light.
Electron
wavelengths are
1/1000th the size of
optical
wavelengths.
Using electron
beams we can see
1000 times smaller
with the same
clarity.
Electron
Microscope
Images
Ragweed Pollen
Velcro
Flea
Fruit Fly Eye
Mosquito Antenna
Wave-Particle Duality
 Experiments
done with neutrons
and even whole atoms show that
they, too, have a wave nature.
 But experiments also show that
all atomic matter clearly has a
particle aspect to it. How can we
reconcile this into a single model?
What is Waving?
 For
starters, having a “wave nature”
does NOT mean that electrons move up
and down or back and forth as they
move through space like the waves of
chapter 10.
 The “wave” is interpreted as being the
probability of locating the particle.
 Let’s ask someone really smart…
Huh?
“Electrons or photons arrive in
lumps, like particles, but the
probability of arrival of these lumps
is determined as the intensity of
waves would be. It is in this sense
that the electron behaves
sometimes like a particle and
sometimes like a wave.”
Richard Feynman
Nobel Prize, 1965
Probability


Laws of probability
predict the overall
distribution of many
results.
These laws do not
predict what any
specific result will be
before it is tabulated,
just the range in which it
will fall.
Moving Electrons
Look at a single
electron moving though
space. Its position is
given by a probability
distribution.
 We know the range of
positions it may have
and the most likely
position it may have but
not the exact position is
has.

Reconciling Wave and
Particle
When we detect it , it
does have a specific
position but not
necessarily the middle
of the probability
distribution.
 Repeat the experiment
a million times and the
entire curve will be
filled.

Electron Double-Slit
Diffraction


The electrons
arrive as particles.
They arrive in
locations
determined by the
interference pattern
of a wave with
wavelength equal
to h/(mass×speed)
Heisenberg Uncertainty
Principle



The wave nature makes it impossible to know with
infinite precision how atomic matter moves.
Specifically: To know a particle’s motion we must know
its position and velocity at the same time.
But how do you locate the position of a wave/particle
electron?
Pure sine wave  no position
but clear wave properties.
Sharp pulse  clear position
but unclear wave properties.
Heisenberg Uncertainty
Principle

Electrons: fuzzy position and fuzzy
wave properties. How fuzzy?..

..The uncertainty in position times the
uncertainty in momentum (mass x
velocity) is greater than Planck’s
constant. Or ∆x ∆(mv) > h
This is the Heisenberg Uncertainty Principle
Consequences

The more we know about where an
electron is, the less we know about where
it is going.

Measuring position more accurately makes
uncertainty in momentum larger. This is an
alternative explanation for electron diffraction.
In other words…

We can predict this interaction perfectly using
Newton’s Laws of motion.
8

We cannot predict the results of an interaction
between electrons perfectly. We can only say what
will probably happen.
?
?
?
?
Important Tie-in to atoms!
An electron orbiting a nucleus has its
position determined to within the
diameter of the atom.
 But its momentum is therefore made
so uncertain we CANNOT know how it
orbits!
 More in chapter 16…

Philosophy
Is probability all there is to electron
motions? Does God really “play at
dice” with the universe?
 Do we determine reality by our
interactions with it? Or does it just
seem that way?
 Bear in mind that these effects are
only noticeable for sizes on the
order of an atomic diameter.
