Today
The Photo Electric Effect
(Part 2)
Summary from last class
The photoelectric effect:
Light shines on metal.
 Electrons are emitted.
Is it just a heating effect?
http://phet.colorado.edu
We found an interesting current vs. voltage curve
What’s happening here?
Each electron that pops out is accelerated and
hits the plate on the right side.
Here,
electrons BUT: # of electrons = constant
sec
are
So current is constant!
repelled
by neg.
electrode
Current
Last class: We found that electrons come out
of the metal plate when we shine light on it.
not I = V / R !!
0
reverse V,
no electrons
flow.
Battery Voltage
Similar V-I curve as a
vacuum tube diode!
Measure the current!
What do you think does actually happen?
Optical power P
- frequency f
Voltage U
Now: Take out a piece
of paper and draw
the following graphs
with what you expect
will happen.)
Let's do the ‘experiment’!
Play with color and
intensity. Measure
current I. (I ~ #e-/s)
http://phet.colorado.edu
Current I
1. Current vs. Voltage with the lamp on (fixed color,
say UV light, and fixed intensity.)
2. Current vs. Frequency (color) at a fixed intensity
and voltage (right plate is on positive potential)
3. Current vs. Intensity for fixed color (right plate is at
fixed, positive voltage)
photoelectric_en.jar
photoelectric online
Measure the current!
1
Which graph best represents low and high intensity
curves for a fixed color of the light?
That's what happened:
0
Intensity
Initial KE
I
Frequency
0
I
I
D
C
or: Initial KE vs. f:
Threshold
0 Batt. V
0 Batt. V
U
2. I vs. f:
0
I
I
0
B
A
high intensity
low intensity
Threshold
I
I
3. I vs. intensity:
1. Current vs. Voltage:
Threshold
0 Batt. V
I
0 Batt. V
E
Frequency
0 Batt. V
B
0
Frequency
0
Frequency
0
D
0
Frequency
Initial KE
Initial KE
C
Initial KE
e’s
I
Predict shape
of the graph
Initial KE
A
Predict what happens to
the initial KE of the
electrons as the frequency
of light changes? (Light
intensity is constant)
Initial KE
photoelectric_en.jar
0
Frequency
Frequency of light
E. something different
Correct answer is D.
Review: PE sim. That's what we found:
3. I vs. intensity:
1. Current vs. Voltage:
Initial KE
Ekin,max=hf - 
Threshold
As the frequency of light increases
(shorter !), the KE of electrons
being popped out increases.
(it is a linear relationship)
2. I vs. f:
I
Threshold
0
0
Frequency of light
What about different metals?
(try sim)
photoelectric_en.jar
high intensity
low intensity
0
e’s
I
I
Frequency
I
U
0
Intensity
or: Initial KE vs. f:
Initial KE
There is a minimum frequency
below which the light could not
kick out electrons…
even if we wait a long time
0
Threshold
Frequency
2
What did we observe so far?
Remember definition of 'eV'
• Color does matter! The velocity (and
number) of the electrons seems to increase
with frequency (fUV > fblue > fred)
• Positive voltage does not affect current
(at fixed color and intensity).
• Large negative voltages make current go to
zero; but never observe negative current.
• Frequency and negative voltage show
‘threshold’ behavior. (Need f > fthreshold)
Define electron-volt (eV):
1eV = kinetic energy gained (or lost) by an electron when
accelerated (decelerated) through 1 volt of potential
difference
Questions?
0V
F
path
E
-U
-
 The lowest negative voltage required to stop the current
multiplied by the electron charge qe corresponds to the initial
kinetic energy of the fastest electrons! This lowest voltage is
called the stopping potential.
photoelectric_en.jar
photoelectric_en.jar
HIGH intensity
e’s
e’s
photoelectric_en.jar
I
I
Low intensity: fewer electrons pop
out off metal  Current decreases.
Current proportional to light intensity.
I
I
Voltage to turn around
most energetic electron:
“stopping potential”
Same initial kinetic
energy.  same
“stopping potential”.
0
Battery Voltage
Summary of PE experiment results
1.
Current linearly proportional to intensity.
2. Current
3.
appears with no delay.
Electrons only emitted if frequency of light
exceeds a threshold.
4. Maximum
kinetic energy with which electrons
come out increases linearly with frequency
but does not depend on intensity.
5.
LOW intensity
Threshold frequency depends on type of
metal.
how do these compare with classical wave predictions?
0
Battery Voltage
Classical wave predictions vs. experimental observations
• Increase intensity  current increases.
Experiment matches with classical prediction
• Takes time to heat up ⇒ if thermal effect, current would
initially be low and increase with time.
Experiment: electrons come out immediately, no time
delay to heat up
• Classical: Color of light does not matter, only intensity.
Experiment shows strong dependence on color
• Current vs. voltage: step close to zero Volts, then flat.
Flat part matches to classical pred., but experiment
has 'tail' of energetic electrons  Stopping potential,
which depends on color (not only intensity).
3
The PE effect is inconsistent
with classical E&M theory!!
Is light a stream of particles?
Yes! Also….
PE effect: Discovered 1887 by Hertz, 1905 Explained by
Einstein, using some of Plank's ideas. Nobel prize: 1921
E = hf
Einstein proposed:
"…the energy in a beam of light is not distributed
continuously through space, but consists of a finite
number of energy quanta, which are localized at points,
which cannot be subdivided, and which are absorbed
“…”
and emitted only as whole units." He took the energy of
these single units to be hf, as proposed earlier by Planck.
What could it be?
Ekin,max=hf - 
“Work function” (I’ll explain later)
Doesn’t look like a wave to me… Seems more like a particle!!
Properties of photons
The energy of a photon is
The wavelength of a photon is
The momentum of a photon is
The mass of a photon is
E = hf
λ = c/f = hc/E
p = E/c = hf/c
m=0
h ≈ 6.626 ·10-34 J·s: Plank constant
It sometimes is useful to define h = h/(2π)
The energy of a photon is then: E = hf = hω
Photons
The frequency of a beam of light is decreased but
the light’s intensity remains unchanged. Which of
the following is true?
A. There are more photons per second but each
photon has less energy.
B. There are more photons per second and each
photon has more energy.
C. There are fewer photons per second and each
photon has less energy.
D. There are fewer photons per second but each
photon has more energy.
E. Nothing happens to the photon number because
light is a wave.
What happens in the metal? Kicker analogy:
What actually happens in the metal
when a photon strikes?
Photon is like a kicker in a pit…
Puts in energy. All concentrated
on one ball/electron.
Blue kicker has a fixed strength.
Red kicker (photon) kicks less
than blue one. Nothing gets out.
Why do the emitted electrons have
different velocities/kinetic energies?
What determines the work function ‘Φ’?
‘Photon’
‘Electron’
Ball emerges with:
KE = kick energy - mgh
mgh = energy needed to
make it up hill and out.
mgh for highest electron
analogous to work function.
For electrons:
KE = hf - Φ
Φ
h
Fixed kick energy:
Top ones get out…
…bottom ones don’t.
electrons
metal
4
Different metals  different ‘pit depths’
PE effect: Apply Conservation of Energy
Energy in = Energy out
Energy of photon = energy needed to kick
KE of electron
+
electron out of metal
as it exits the metal
Φ
sodium- easy to kick out
small work function  shallow pit
platinum, hard to kick out
large work function  deep pit
Loosely stuck electron, takes least energy to kick out
Electron Potential
Energy
Φ
Outside the metal
Φ
work function () = energy needed to kick
highest electron out of metal
“Fermi” level (weakest bound electron)
Inside
metal
Tightly stuck, needs more
energy to escape
5