Phys 233
Mon. 9/12
Tues. 9/13
Wed. 9/14
Thurs 9/15
Mon. 9/19
Tues 9/20
Wed. 9/21
Thurs 9/22
Day 3, Q3: Wave Optics
Q3 particles, S.2, S.3
L2: Rolling ball 2 & std dev, LC2, LR 3.4, 6, 7 & 7b (prop unc.exe)
Q4 Wave Matter, E-gun demo S3, S5
Q5 QM Facts, S3, S4
L3: Standing Wav & graphs, LC3, LR 2, 3.2.2; (Q1) (linreg.exe)
Sci Center Poster Session tonight in Hedco
Q6 Wavefunctions B5, S9 (Spins.exe)
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HW1: Q1: S.6, S.7, R.2; Q2: S.2, S.9, R.1
RE-Q3; Lab Notebook
PL2; Quiz 1: Q1, Q2
RE-Q4
HW2: Q3: S.3, S.5, R.1; Q4: S.5, S.9, R.2
RE-Q5; Lab Notebook & Procedure section
PL3; Quiz 2: Q3, Q4
RE-Q6
Equipment
o PhET‟s Photoelectric Effect, http://phet.colorado.edu/en/simulation/photoelectric
o Load simulation on machines around room
o Ppt.
o My schedule for office hours
Collect lab notebooks
Q3: Particle Nature of Light
Q 3.1 Photoelectric Effect
Q 3.2 Idealized Photoelectric Experiments
Q 3.3 Predictions of the Wave Model
Q 3.4 Confronting the Facts
Q 3.5 The Photon Model of Light
Questions?
1st – Rayleigh Criterion clean up
Q 3.1 Photoelectric Effect
Significance
o Q: In the context of understanding light and developing a Quantum Mechanical
picture of the world, what was the significance of the Photoelectric effect?
 Observe that matter adsorbs energy from light in discrete units, one at a
time, and those units are related to the light‟s frequency / wavelength
hc
hf .
through E
h = 4.136 ×10-15 eV/s is called Plank‟s constant.
 Together with Plank‟s previously developed explanation of blackbody
radiation (which no one really took at face value), this prompted Einstein‟s
tentative proposal of the Photon model – initially, that light‟s energy is
transferred in discrete packets, but eventually expanded to be that light is
itself quantized.
 This was the first time a fundamental physical entity was recognized to
display both wave and particle behavior.
The Basic Observation. Short a capacitor (two metallic plates) through an ammeter and
shine light on one of the plates. Under the right conditions you‟ll register a current
flowing through the shorting wire, indicating that electrons are coming off the
Phys 233
Day 3, Q3: Wave Optics
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illuminated plate, landing on the dark plate, and flowing back through the wire to
rebalance charge in the two plates.
Q 3.2 Idealized Photoelectric Experiments
Experimental Questions
o At what rate are electrons ejected (i.e., what‟s the current)?
o How does the rate depend on the light‟s wavelength / frequency (color)?
o How does the rate depend on the light‟s intensity (rate with which light delivers
energy per area)?
Experiment 1 – zero voltage
o Illustrated above; shine light on plate, monitor the current of electrons that get
ejected from the plate and happen to land on the other plate and thus run back
through the wire to the first plate.
o Allows you to see how rate of electron ejection varies with
 light‟s color
 light‟s intensity
Experiment 2 – zero current
o Shine the light and vary the battery‟s voltage until the current stops
Q3T.1 - In the experiment shown in figure Q3.1b, the final voltage difference between the plates
is proportional to
A. The rate at which electrons are ejected from the cathode
B. The average kinetic energy of the ejected electrons
C. The maximum kinetic energy of the ejected electrons
D. Both A and C
Phys 233
Day 3, Q3: Wave Optics
o Allows you to see how much excess kinetic energy the electrons had when they
left the illuminated plate since
K .E. U 0
0 K .E.initial q Vgap 0

K .E.initial e Vgap 0
K .E.initial
e Vgap
For when the voltage is just enough to stop the current and so the
electrons come to a stop just before striking the second plate.
Q 3.3 Predictions of the Wave Model
Distinguishing Feature of Wave Model
o The truly distinguishing feature of the wave model is that the energy is
uniformly distributed throughout the wave and can be varied smoothly. So
cEo2
 I
4 k
o is the uniform and continuous intensity of the wave (rate of energy passing
through unit area)
Q3T.3 - If the experiment shown in figure Q3.1a (and above), which of the following possible
results (if seen) about the rate of electron ejection would probably not be consistent with the
wave model of light?
A. The rate is zero for some time after the light starts shining.
B. The rate increases as the light‟s intensity increases.
C. The rate varies as the light‟s wavelength changes.
D. The rate is zero if the light‟s wavelength is above a certain value.
Results of a wave model
1. At low intensities, there would be a time delay between illumination and the first
emission of electrons as more and more energy is delivered
i. Note: He ignores energy transfer from the target atom to other atoms in
the material. Considering this, it could even be that the material is good
enough at dissipating the energy from the surface that this delay is
essentially infinite as you never get enough energy accumulated in the
surface.
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Day 3, Q3: Wave Optics
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2. At high enough intensities, the flow of electrons from the surface would scale
with the intensity.
3. The rate of electron ejection could depend in a complicated (resonance) way on
the frequency of light.
4. The amount of energy transferred to an electron will likely scale with intensity
and thus maximum kinetic energy (voltage to stop electron current) would too.
Q 3.4 Confronting the Facts
Exerxise. On the machines around the room, see which of these „facts‟ you can
observe Note: at least in my edition, the book actually writes one of them incorrectly,
so test each and see which is wrong.
1. Number of electrons ejected is proportional to Intensity (at sufficiently
high intensity and frequency.)
2. Electrons are ejected virtually instantly, no matter the intensity!
3. At constant intensity, the number of electrons ejected decreasing with
increasing frequency (decreasing wavelength).
4. No electrons are ejected if the frequency is too low (the “cutoff frequency”
varies from one metal to another.)
5. The electrons‟ maximum kinetic energy (and thus stopping voltage) is
independent of intensity!
6. The electrons‟ maximum kinetic energy scales with frequency once above
the cutoff.)
Note: number 3 isn’t immediately obvious. Think of it this way,
maintaining constant intensity (rate of energy transfer) while increasing
frequency (energy per photon) would mean decreasing the rate of photons
flowing to the surface, and thus, the rate at which electrons get ejected.
Q 3.5 The Photon Model of Light (as met in Phys 231)
Einstein originally simply proposed that light transferred energy to matter in discrete
packets of
o E hf where h = 4.15×10-15eV s.
Slowly this evolved into the more encompassing picture that light itself comes in
discrete packets with this much energy per packet.
So one way of thinking of the light is not as a smooth and continuous beam but like
rain – discrete droplets, photons, of light.
The book would lead you to believe that everything said about the wave model was
then wrong. The only thing that‟s wrong is that the light and its energy isn‟t
uniformly distributed.
o On average,
cEo2
I

4 k
o still relates the light‟s intensity to the electric field‟s amplitude. But, just as
you could have a rain gage and stop watch tell you what the average intensity
of rain was, yet at any moment there‟s a rain drop hitting here and then there,
and then there,…
o Similarly, individual photon of light can still be thought of as delivering an
oscillation of electric and magnetic fields at frequency f, and thus „rattling‟ the
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Day 3, Q3: Wave Optics
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electron-atom bond at that frequency, but now we have a new relationship for
how strong that rattling is.
In this picture, unless you have insanely high intensity, the delay between the arrival
of one photon at an atom and another photon at the same atom is large enough for the
energy it brought in to be transferred away to the rest of the metal. So the biggest
kick an electron feels is just that of one photon, ph hf .
o Which observations does this explain?
 If the frequency is below the „cutoff‟, it doesn‟t matter how intense
you make the light, you‟ll never deliver a big enough kick to remove
an electron.
Demo in simulation
o If the frequency is above the cutoff, increasing the intensity increases the rate
with which electrons get „rained‟ on by these photons and so get freed, but
doesn‟t increase the amount of energy an individual electron gets or its kinetic
energy (or the stopping voltage).
 Demo in simulation. (electron energy vs. light frequency)

Work Function. As you‟re familiar, for an individual atoms, it takes a certain
amount of energy to liberate an electron and ionize the atom. For example, about
27.8eV for Hydrogen. Now, for a collection of atoms all bound together in a solid,
there‟s a similar minimum amount of energy required to rip off an electron. You can
think of this as the „ionization‟ energy for the chunk, though we usually call it the
“work function” instead. So, if a photon delivers more than enough energy, part of it
goes to simply freeing the electron, and the rest is left over as kinetic energy.
hf W K .E
o
ph
o Thus, the “cutoff” frequency corresponds to
f W /h
 hf W
o And the slope of K.E. vs. f is h and is independent of materials
 Demo: change plates, same slope in energy vs. frequency
Q3S.6 - When iron is illuminated with ultraviolt light with a wavelength of 250 nm, the
maximum potential developed between the plates in the experiment shown in figure Q3.1b is
0.46 V. From these data and the accepted value of hc, find the potential difference between the
plates if the ultraviolet wavelength is changed to 220 nm. Also find W for iron.
Phys 233
Day 3, Q3: Wave Optics
o Q3S.8 - Imagine that you are standing and facing a 60-W incandescent
lightbulb 100 m away. If the diameter of your pupils is about 2mm, about
how many photons enter your eye every second?
Finish working on worksheet
Demo with electroscope (copper/zinc & various light sources) – the appropriate (high
enough frequency) light will knock the excess electrons off the metal
o Consider what we would measure if light behaves as a wave
o Consider what we would measure if light behaves as particles
Begin homework as a group (S8)
Next - Read Q4 and turn in S.3, S.5
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