Download Pattern Wave-based Explanation

Foundations for
quantum mechanics
Photoelectric Effect
Some background
Imagine heating an iron bar
with, say, an induction heater.
For example, here.
Color of heated objects
When you heat an object, it
glows. The color depends
on the temperature.
Hypothesis:
Temperature is a measure of the
random kinetic energy of particles
that make up a substance.
Moving electric charges emit
electromagnetic waves.
 reasonable to expect fastermoving charges emit more
energetic (higher frequency) waves.
Hypothesis tested
Wilhelm Wien investigated
the relationship between
temperature of blackbody
emitter to peak wavelength
(1893)
1
𝑚𝑎𝑥 𝛼
𝑇 (𝐾)
 temperature   peak wavelength
  peak frequency
Oops…
Classical physics
predicted a much more
intense peak than what
was actually observed at
low wavelengths.
This was called the
“ultraviolet catastrophe”.
Quantization of light
In 1901, Max Planck proposed an math
trick as a solution.
Also quantized: matter (atoms),
standing waves on oscillating
string, etc.
Assume light comes in tiny
but discrete packets of
energy, known as ‘quanta’
𝐸 = ℎ𝑓
where
𝐸 = energy of photons
ℎ = proportionality constant,
= 6.63 x 10-34 Js
𝑓 = frequency of light
Implications
Reasons to trust the model
+ describes observed blackbody
spectra perfectly
Reasons to question the model
- Requires light to come in chunks (??)
- How do you explain diffraction?
- How do you explain interference?
- How do you explain polarization?
Photoelectric Effect
Hertz (1887) discovered that when you
shine a light on a metal surface, it can
generate a current (i.e., some electrons
are knocked loose).
If you are clever, you can measure how
much current.
Pro tip:
Put a metal plate and an electrode
in an evacuated glass tube and
measure the current produced
when you shine a light on the plate.
Wilhelm Hallwachs(1888) discovered
that the leaves of a neutrally-charged
electroscope will separate when the
plate to which they are attached is
exposed to ultraviolet light.
Photoelectric Effect
If you are especially clever,
you can measure how
much kinetic energy
those electrons have.
Put a voltage source in the circuit and switch the
direction the current flows.
Adjust the voltage until the current drops to
zero.
KEmax = eV0
Where V0 = amount of energy to
stop electrons (verified
by ammeter), called
‘stopping
potential’
Experiment some…
Use the PHeT simulator
to experiment.
1) Explore the impact of changing the
intensity of the light.
2) Explore the impact of changing the
color of the light.
3) Explore the impact of changing the
type of material.
4) Explore the impact of changing the
voltage of the battery.
Patterns: 1 of 2
Experiment
Results
Analysis
Current vs. intensity
of light
 intensity   current
Stopping potential vs.
frequency of light
 frequency   stopping
potential, -V0
Patterns: 2 of 2
Experiment
Current vs. voltage
difference
Current vs. voltage
difference, with
more intense light
Results
Analysis
 voltage   current,
then levels off
 voltage   current, then
levels off at a
higher level. V0
does not change.
Worth noting: ~0 s lag time between light hitting surface and current flowing
Energy in waves
In waves, the height (more properly, the amplitude)
of the wave determines its energy.
Patterns & Explanations
Pattern
current  intensity
Wave-based Explanation
current levels off
with changing
voltage difference
Electrons require some minimum amount of
energy to be released.
Electrons absorb enough energy from light to
be ejected from metal.
Patterns & Explanations
Pattern
Well-defined
stopping potential,
regardless of
intensity
Wave-based Explanation
Below certain
frequency, no
current at all
High-intensity red light releases no electrons.
Low-intensity blue light does.
More intense = more energy
Should be harder to stop electrons liberated
by more intense light; it is NOT.
Making sense of photoelectric effect
Einstein’s insight:
Planck addressed ultraviolet
catastrophe by hypothesizing that
energy is emitted in discrete quanta.
What if energy is only absorbed
in discrete amounts?
Patterns & Explanations
Pattern
current  intensity
Wave-based
Explanation
Electrons absorb enough
energy from light to be
ejected from metal.
Electrons absorb enough
energy from light to be ejected
from metal.
current levels off
with changing
voltage difference
Electrons require some
minimum amount of
energy to be released.
Electrons require some
minimum amount of energy to
be released.
Particle-based Explanation
Patterns & Explanations
Pattern
Well-defined
stopping potential,
regardless of
intensity
Wave-based
Explanation
Particle-based Explanation
More intense = more
energy
Should be harder to stop
electrons liberated by
more intense light; it is
NOT.
Electrons absorb energy from
individual photons, the quanta
of light.
Below certain
frequency, no
current at all
High-intensity red light
releases no electrons.
Low-intensity blue light
does.
If an individual photon at a
particular wavelength does not
have sufficient energy to
release an electron, neither will
any number of similar photons.
What we learned…
1) Some frequencies of light do not have
enough energy to liberate electrons.
2) Energy is conserved. If light has enough
energy to liberate an electron, excess
energy makes the electron move faster.
3) Increasing frequency of light increases
maximum kinetic energy linearly.
Photoelectric effect
𝐾𝐸𝑚𝑎𝑥 = ℎ𝑓 − 𝜑
for values of hf > 𝜑
Where 𝐾𝐸𝑚𝑎𝑥= peak kinetic energy of released electrons
ℎ
𝑓
𝜑
= Planck’s constant, 6.63 x 10-34 Js
= frequency of light [Hz or s-1]
= work function of metal = the least amount of energy required
to knock an electron off an atom, varies from small to very,
very small
Test
While attempting to
disprove photon hypothesis
in 1913-14, Millikan
confirmed it instead.
Implications
The model describing light as
a wave does not work to
describe photoelectric effect.
The model describing light as
a particle does not work
very well to describe
polarization or diffraction.
Light behaves like a wave and a particle.
Particles and inference?
If you shine a bright light
through double slits, you
expect a familiar interference
pattern to form.
Photons and inference?
What happens if you send a stream of
photons through the double slits one
at a time?
Classically, you would expect the “particle”
to go through one slit or the other.
Sensor after very few photons have passed through double slits
Sensor after ~105 photons have passed through double slits
Sensor after ~109 photons have passed through double slits
Sensor after many photons have passed through double slits
Photons and inference?
What happens if you send a
stream of photons through the
double slits one at a time?
Classically, you would expect the
“particle” to go through one slit or
the other.
Instead, individual
photons interfere with
themselves (?!)
Example