Download Photoelectric Effect: The Quantization of Energy and Light

Photoelectric Effect: The Quantization of Energy and Light
OBJECTIVE: To observe, analyze and understand the quantum phenomenon known as
the Photoelectric Effect. To calculate the values of Planck's constand and the work
function.
EQUIPMENT: Photoelectric Effect box, DC power supply, multimeters (2), cables
INTRODUCTION:
Here are two reasons to study the Photoelectric Effect: one, it is the basis on which
many of today's optoelectronic devices work and two, it can give you insight into how
this experiment, together with Blackbody Radiation, Compton, and Atomic Spectra
experiments, led to the mathematical description of how matter and energy behave on a
very small scale, Quantum Mechanics.
Digital cameras, automatic garage door openers, notebook computer displays and lightemitting diodes (LEDs) all operate on the Photoelectric Effect - the ejection of negative
particles from a metal upon which light is incident. Ironically, Heinrich Hertz
discovered the phenomenon in 1887 during an experiment in which he produced and
detected electromagnetic waves, simultaneously confirming Maxwell's theory while
leading to the particle description of light. Philip Lenard identified the particles
experimentally as electrons in 1900, but it took the genius of Einstein to explain the
phenomenon in a 1905 paper for which he was awarded the Nobel Prize, and which
helped usher in the era known as "Modern Physics'.
The Apparatus
In the schematic on the left, light enters a
vacuum tube and strikes a metal surface E
(cathode). Electrons are then emitted from the
metal and strike collector plate C (anode).
The stream of electrons coming off E
constitutes a current in the circuit, which can
be detected and measured by the ammeter A.
The potential between E and C can also be
varied by connecting a variable power supply
between them. Voltmeter V monitors this
potential difference. If plate C can be kept at
either a higher or lower potential than plate E,
which can decrease or increase the current.
The flow of electrons is enhanced or retarded
by the force experienced from the electric
field created between E and C. By adjusting
the potential between them, you can vary the
number of electrons that reach C and hence
control the current of the circuit. At high
enough voltages, all the electrons reach C and
maximum current is achieved.
Increasing the light intensity also increases the maximum current. In fact, they are
proportional. This jibes well with classical physics since doubling the energy on E
doubles the number of ejected electrons. Now, if C is kept at a lower potential than E,
electrons are repelled from C. Remember from the E&M Forces lab that an electron
gains kinetic energy eV when accelerated through a potential difference V - only
electrons with kinetic energies greater than e|V| (energy can't be negative) can reach C.
Look at the graph above, in which photoelectric current vs. potential difference is
plotted for three different intensities of light (by varying the lamp-metal distance).
Notice that for all light intensities there is no photoelectric current when the voltage is
greater than V0=0.8. V0 is called the stopping potential. Since the initial electron's
kinetic energy is lost in overcoming the stopping potential, we can relate the maximum
kinetic energy of the electron:
1
 mv 2  =eV 0
2
max
Now, what does all this have to do with Quantum Mechanics? Look once again at the
graph above – V0 does not depend on the light intensity. If we increase the rate of
energy falling on the metal, we don't increase the kinetic energy of the electrons
ejected! Einstein theorized that light energy, rather than being spread out like a wave,
was quantized into discrete amounts (quanta) of energy hf , where h is Planck's
Constant (4.136 x 10-15 eV-sec or 6.626 x 10-34 J-sec) and f is the frequency of the light.
When one of these quanta, also known as a photon, enters the metal, all of its energy is
given to an electron. This would explain why intensifying the light results in higher
numbers of electrons rather than higher electron energies.
There are other energy losses to bear in mind other than the energy required to traverse
the cathode-collector potential – the electron loses energy going through the metal
before hitting its particular electron, and the electron has to overcome the binding
energy of the metal, denoted by  . (You can think of  as being similar to
gravitational or electrical potential – the energy required to move a charge or mass from
where it is to someplace very far away.) Keeping these in mind, the maximum energy
of the electron (others will lose more energy it traveling through the metal) is hf −
and Einstein's equation for the photoelectric effect is:
hf = eV 0 
(photon energy) -> (K.E needed to just break stopping pot.)+ (energy needed to leave metal)
We can rewrite Einstein's equation in y=mxb form as;
h
V 0 =  f − 
e
e
h
does
e
not depend on  ; it is independent of the material ejecting the electron. Note also that
we can determine the work function, since the Y-intercept is  . See graph below:
e
If we plot V0 as a function of f , a graph will yield a straight line whose slope
Stopping
Potential,
V
Frequency, Hz
Labeled in the above graph is f t , the threshold frequency. Photons which have
frequencies lower than this do not have enough energy to eject an electron from the
metal. The relationship between f t and  can be obtained by setting V0=0 in
the photoelectric equation:
Φ=hf t =
hc
λt
The value hc is usually expressed in eV-Å or eV-nm, since wavelengths are typically
expressed in Anstroms or nanometers:
hc=1240 eV-nm = 12,400 eV- Å
Visible light ranges from 400-800 nm (4000-8000 Å), so most work functions are on
the order of a few electron volts:
Metal (atomic symbol)
 (eV)
Na
2.46
Al
4.08
Cu
4.7
Zn
4.31
Ag
4.73
Metal (atomic symbol)
 (eV)
Pt
6.35
Pb
4.14
Fe
4.5
PROCEDURE
Look at the photo labeled “The Apparatus”. The box houses the photoelectric tube and
circuit picture in the schematic on page 2. The cables are pre-wired; please don't
change any connections. However, here are the connections in case they have been
tampered with - on the metal box (housing the photoelectric tube), the labeled jacks are
connected to:
Vcurr --> red jack on Voltmeter
Vr--> red jack on other Voltmeters
Gnd--> ground on Power Supply, ground on Voltmeter
-12--> -12 on Power Supply
+12--> +12 on Power Supply
(the remaining Voltmeter ground should be connected to the remaining Power Supply
ground)
Two multimeters, connected to the two green jacks, monitor the photoelectric voltage
Vcurr and potential difference VR. The photoelectric current is too small for your
multimeter to measure directly – instead, an operational amplifier in the box outputs
Vcurr, which is proportional to the current. You can obtain the current from the equation
I=Vcurr/6.6 x 107Ω or I=Vcurr/2.0 x 108Ω (see top of box for conversion factor).
The blue knob varies VR. This will range from roughly 0 to 3.2 V. At the top of a box
is a dial on which seven filters are mounted (yes, that is a Gerber baby food lid –
physicists do recycle). Each filter will transmit light of a specific wavelength that will
strike the photoelectric tube; the wavelengths are marked on the dial. Do not assume
that a filter lined up with the dial mark on the box perfectly aligns it wth the hole
in the box – "fine tune" the dial until you get maximum Vcurr with each reading.
Position the desk lamp a few inches above the dial (don't turn it on yet) and turn the
power supply and voltmeters on.
Qualitative Observations & Predictions
Turn the blue knob fully counterclockwise (zero stopping potential). Turn the dial to the
500 nm filter. You will be asked to make a series of predictions, which are written in
the hand-in sheet at the end of this write-up. Your instructor will not penalize you
for incorrect predictions, and will just check to see that you attempted a
prediction.
Quantitative Observations
(WARNING – THE DESK LAMP CAN GET QUITE HOT TO THE TOUCH)
I vs. V
You will vary VR (using blue knob) and see how Vcurr changes, for two different light
intensities. Select the 500 nm filter on the dial. Keep the light a few inches above the
box. Vary VR in 0.1 Volt intervals, from 0 to about 1.4V, each time recording the Vcurr.
Make sure you do not change the orientation of lamp or box during this time, as
you may may render your results useless.
Repeat the above, after raising the lamp to approximately twice the original distance
above the box (several inches). You should then generate two plots on one graph, one
for each light intensity.
V0 vs. f
You will now vary f (using filter dial) and see how V0 changes. Starting at the highest
wavelength (which corresponds to the lowest frequency), vary V to obtain zero Vcurr.
Once you have obtained zero Vcurr, note your Vr at that point – that will be your
stopping potential V0. Repeat for the other filters and generate your plot. Again, make
sure you move neither box nor lamp during the measurements.
A simple application of the Photoelectric
Effect: A garage door sensor consists of a
sending unit (infrared light beam) and a
receiving unit (phototube), which produce
a photoelectric current in the receiving
unit. Interrupting the beam disrupts the
current, causing a circuit to activate the
motor, pulling the door open.
A more sophisticated application of the
Photoelectric effect: Charge-coupled devices, or
CCDs, are arrays of insulating silicon dioxide,
sandwiched between semiconducting silicon and
electrodes. CCDs are used in digital cameras and
most of the research telescopes around the world.
Shown here is one picture element (pixel), many
of which constitute the picture grid. Photons
incident on the silicon generate electrons, which
are trapped in the pixel due to the positive voltage
of electrodes under the insulating layer. The
number of electrons that accumulate is
proportional to the number of incident photons.
Filters (red, green, blue) are used to separate the
light colors. One row of pixels serves as the shift
register, into which the contents of the adjacent
row are shifted. The transfer of electrons by rows
is done by changing electrode voltage, conveying
the row-by-row picture information into an analog
signal processor. The processor senses the
varying number of electrons in each pixel as an
analog wave. This is sent to an analog-to-digital
converter to produce binary digits that computers
can recognize.