Download Photoelectric Effect

Lesson Plan: Photoelectric Effect
By Jeff Bourne
Northview High School
The Problem:
To understand how Einstein’s interpretation of the photoelectric effect recreated a
particle-nature theory for light that had been discounted for almost 100 years before that
time.
Abstract:
Students will use an Internet-based simulation of the photoelectric effect to collect
frequency, stopping voltage, and intensity data which will be mathematically analyzed in
order to demonstrate the particle nature of light. Students will understand that wave
properties such as the energy being a function of the intensity do not apply to light. Upon
completion of the virtual experiment, students will analyze results from a device which
utilizes 4 different LED’s as wavelength sources.
Alignment with Standards:
1. National Standards:
AP College Board AP Physics B Standards:
III. Electricity and Magnetism
A. Electrostatics
2. Electric field and electric potential
B. Conductors, capacitors, dielectrics
IV. Waves and Optics
A. Wave motion
1. Traveling Waves: students should understand the description of traveling waves,
so they can
b) apply the relation among wavelength, frequency, and velocity of a wave.
B. Physics Optics
1. Interference and diffraction: students should understand the interference and
diffraction of waves, so they can:
b) apply the principles of interference and diffraction to waves that pass through
a single or double slit or through a diffraction grating, so they can:
(5)describe or identify the interference pattern formed by a diffraction grating
and calculate the location of intensity maxima.
V. Atomic and Nuclear Physics
A. Atomic physics and quantum effects
1. Photons, the photoelectric effect, …
a) Students should know the properties of photons, so they can:
(1) relate the energy of a photon in joules or electron-volts to its wavelength
or frequency.
B) Students should understand the photoelectric effect, so they can:
(1) Describe a typical photoelectric effect experiment, and explain what
experimental observations provide evidence for the photon nature of light.
(2) Describe qualitatively hohw the number of photoelectrons and their maximum
kinetic energy depend on the wavelength and intensity of the light striking the surface,
and account for this dependence in terms of a photon model of light.
(4) Sketch or identify a graph of stopping potential versus frequency for a
photoelectric-effect experiment, determine from such a graph the threshold frequency and
work function, and calculate an approximate value of h/e.
2. State of Georgia Standards: Characteristics of Science
SCSh1. Students will evaluate the importance of curiosity, honesty, openness,
and skepticism in science.
c. Explain the further understanding of scientific problems relies on the design and
execution of new experiments which may reinforce or weaken opposing explanations.
SCSh3. Students will identify and investigate problems scientifically.
b. Develop procedures for solving scientific problems.
c. Collect, organize and record appropriate data.
d. Graphically compare and analyze data points and /or summary statistics
e. Develop reasonable conclusions based on data collected.
f. Evaluate whether conclusions are reasonable by reviewing the process and
checking against other available information.
SCSh4. Students will use tools and instruments for observing, measuring, and
manipulating scientific equipment and materials.
a. Develop and use systematic procedures for recording and organizing
information.
b. Use technology to produce tables and graphs
SCSh6. Students will communicate scientific investigations and information
clearly.
a. Write clear, coherent laboratory reports related to scientific investigations.
3. State of Georgia Standards: Content
SP4. Students will analyze the properties and applications of waves.
a. Explain the processes that results in the production and energy transfer of
electromagnetic waves
SP5. Students will evaluate relationships between electrical and magnetic forces.
a. describe the transformation of mechanical energy into electrical energy and the
transmission of electrical energy.
b. determine the relationship among potential difference, current, and resistance in
a dc circuit.
SP6. The student will describe the corrections to Newtonian physics given by
quantum mechanics and relativity when matter is very small, moving fast compared
to the speed of light, or very large.
a. Explain matter as a particle and wave.
Objectives:
1. The student will understand the importance of Einstein’s interpretation of this famous
experiment.
2. The student will understand how this experiment provided evidence for the “particlelike” nature of light.
3. The student will utilize the scientific method appropriately in the lab design.
4. The student will correctly analyze and interpret graphs that are generated.
Anticipated learner outcomes:
1. The student will be able to define the concept of the work function of a metal.
2. The student will be able to describe the process of metal electron excitation by the
photon, and how that energy is divided into the work function and kinetic energy.
3. The student will be able to discuss the relationship between the intensity of the
photons and the photocurrent.
4. The student will describe the relationship between the electric field created by the
stopping voltage and the photocurrent produced.
5. The student will be able to discuss the significance of Planck’s constant from this
experiment.
Assessment/Rubric
Lab Report : Photoelectric effect
Teacher Name: Mr. bourne
Student Name:
CATEGORY
Experimental Design
________________________________________
4
3
2
1
Group
successfully
designed a lab
with proper
variables and
controls
The group may
have switched
variables or not
controlled all
parameters
The group
No serious effect
included variables at controlling
they shouldn't
variables.
have.
Data
Professional
looking and
accurate
representation of
the data in tables
and/or graphs.
Graphs and tables
are labeled and
titled.
Accurate
representation of
the data in tables
and/or graphs.
Graphs and tables
are labeled and
titled.
Accurate
Data are not
representation of shown OR are
the data in written inaccurate.
form, but no
graphs or tables
are presented.
Scientific Concepts
Report illustrates
an accurate and
thorough
understanding of
scientific concepts
underlying the lab.
Report illustrates
an accurate
understanding of
most scientific
concepts
underlying the lab.
Report illustrates
a limited
understanding of
scientific concepts
underlying the lab.
Report illustrates
inaccurate
understanding of
scientific concepts
underlying the
lab.
Spelling, Punctuation
and Grammar
One or fewer
errors in spelling,
punctuation and
grammar in the
report.
Two or three
errors in spelling,
punctuation and
grammar in the
report.
Four errors in
spelling,
punctuation and
grammar in the
report.
More than 4
errors in spelling,
punctuation and
grammar in the
report.
Components of the
report
All required
All required
elements are
elements are
present and
present.
additional
elements that add
to the report (e.g.,
thoughtful
comments,
graphics) have
been added.
One required
Several required
element is
elements are
missing, but
missing.
additional
elements that add
to the report (e.g.,
thoughtful
comments,
graphics) have
been added.
Calculations
All calculations
are shown and
the results are
correct and
labeled
appropriately.
Some calculations
are shown and
the results are
correct and
labeled
appropriately.
Some calculations
are shown and
the results labeled
appropriately.
No calculations
are shown OR
results are
inaccurate or
mislabeled.
Conclusion
Conclusion
includes whether
the findings
supported the
hypothesis,
possible sources
of error, and what
was learned from
the experiment.
Conclusion
includes whether
the findings
supported the
hypothesis and
what was learned
from the
experiment.
Conclusion
includes what was
learned from the
experiment.
No conclusion
was included in
the report OR
shows little effort
and reflection.
Questions
Correctly
answered 4
questions
Correctly
answered 3
questions
Correctly
answered 2
questions
Correctly
answered 1
question
Appearance/Organization Lab report is
typed and uses
headings and
subheadings to
visually organize
the material.
Lab report is
neatly handwritten
and uses
headings and
subheadings to
visually organize
the material.
Lab report is
neatly written or
typed, but
formatting does
not help visually
organize the
material.
Lab report is
handwritten and
looks sloppy with
cross-outs,
multiple erasures
and/or tears and
creases.
Date Created: June 26, 2007
Background
In 1887, H.R. Hertz worked on testing Maxwell’s theories dealing with
electromagnetism. In this process he noticed that when particular metals were wired to
an electroscope and then irradiated with ultraviolet light waves, the leaves of the
electroscope would move apart. He concluded that when the ultraviolet light struck the
metal plate the electrons on the plate were set free. Hertz, however, did not develop this
idea much further as to explain why.
Several years after Hertz’s nascent research on the photoelectric effect, Max Planck
researched the radiation emitted by a blackbody (an object that is a perfect absorber of
radiation). His interested was sparked by the Ultraviolet Catastrophe, which
demonstrated the inaccuracies of classical calculations and experimental data.
Classically, when incident light (thought of as composed of waves) strikes a surface, the
energy of the emitted electrons should be proportional to the intensity of light. Also,
classical theory predicted that the photoelectric current is not dependent on the frequency
of the light. However, experimental data did not uphold these relationships, especially at
higher frequencies (ultraviolet). Planck created a formula that worked well with the
experimental results, but it only worked if it was assumed that the energy of the excited
particle was quantized.
E=hf
E = Energy
h = Planck’s constant = 6.63 E -34 J-s
f = radiation frequency
Planck was able to create a formula that worked with the experimental results, but the
photoelectric effect itself was not actually explained. In 1905, Albert Einstein made the
radical proposal that the incident light consisted of particles called photons, which carry
energy and have linear momentum. In Einstein’s photoelectric experiment it was shown
that:
1) When light strikes a metal surface, current flows instantaneously, even for
low intensity light.
2) At a fixed frequency, the magnitude of the current is directly proportional to
the intensity of the incident light.
3) The stopping potential (Vo), and therefore the maximum energy of the
liberated electrons, depends only on the frequency of the light and the type
of metal used.
4) Each metal has a characteristic threshold frequency and work function ().
The work function is the minimum amount of energy required for an
electron to escape from a metal.
5) The energy of each photon is proportional to its frequency.
6) Each emitted electron is the result of the absorption of one photon. The
maximum kinetic energy, KE, that any photon can have is given by:
KEmax = hf - 7)
The constant h is found to be the same for all metals and is equal to
Planck’s constant. This constant was shown in two very different
experiments: Blackbody Radiation and the Photoelectric Effect.
8)
The entropy of waves in a box was exactly the same as the entropy of
particles in the box if E = nhf.
Materials and Supplies
1. computers for each lab group
2. Photoelectric Effect apparatus
Plan
This lab activity should take close to 3 lab periods to complete. The first day will be
introduction, data collection, and time permitting, group collaboration. The second day
will be for analysis and demonstrating the photoelectric effect apparatus. The third third
will be spent collecting data from the apparatus. Analysis of that data will be a
homework assignment.
Lab: Photoelectric Effect
Purpose:
1. The student will understand the importance of Einstein’s interpretation of this famous
experiment.
2. The student will understand how this experiment provided evidence for the “particlelike” nature of light.
3. The student will utilize the scientific method appropriately in the lab design.
4. The student will correctly analyze and interpret graphs that are generated.
Background:
Einstein postulated that light contained a certain amount of energy based on its
frequency. He believed that the energy of the light was transferred completely to an
electron on the metal’s surface. The energy of the electron was divided up into two
accounts: the energy needed to escape the metal’s surface, and the kinetic energy due to
its movement after it escaped. Mathematically, this can be expressed as:
Ephoton = Ekinetic + Eescape
The kinetic energy can be measured indirectly by using what is known as the stopping
voltage. As the electrons escape, they find themselves moving through an electric field
that wants to stop them before they complete their journey to the other electrode. If the
field is too great, they turn around and go back to the metal’s surface. If the field is too
low, then all the electrons go to the other electrode, creating a large current. At just the
right amount of voltage, only the electrons that had the greatest kinetic energy will reach
the other electrode. (It the same idea that a ball thrown upward with the greatest KE will
go the farthest against the gravity field.) Since the work done on the electron is equal to
qV, the charge of the electron times the stopping voltage gives you the kinetic energy of
the escaping electron. Rearranging the equation above gives this formula:
KE = Ephoton – Eescape
Max Planck had determined that the energy of the photon was equal to its frequency
times a constant. Planck had no idea what the constant was, only that he needed it to
make his calculations work. Therefore
Ephoton = hf
Where f is the frequency in hertz. This means the important formula for the photoelectric
effect is:
KE = hf – Eescape
This is a linear formula, with the KE on y-axis, frequency on the x-axis, and the escape
energy (known as the work function) the y-intercept. The slope of the line is Planck’s
constant!
Materials:
1. Computer simulation: http://phet-web.colorado.edu/web-pages/simulations-base.html
Choose Photoelectric effect
Lab Design:
This simulation allows you to “see” the photons bombarding the metal plate as well as
the electrons that come off it. There are several factors to be studied today: 1. The
wavelength of the photons; 2. The intensity of the photons; and 3. The type of metal
plate being used. This is too much for one group to handle in the period, so we will split
up into smaller groups.
Group
Independent Variable
Dependent
Controls
Variable
A
Wavelength
Stopping Voltage
Intensity; type of
metal
B
Intensity
Stopping Voltage Wavelength; type of
metal
C
Same as Group A except that they will use a different metal
Hints about the simulation and lab
1. You can either use the sliders to change the voltage, intensity, and wavelength, or you
may manually enter the values. Manually will give you better control.
2. Under Options, select “show photons”.
3. Group A: select 5 different wavelengths. Use sodium as the metal. Be sure to include
one UV wavelength. You will need to make the voltage as small as possible (negative) to
create the least current. Make your intensity 100%. Be aware that some wavelengths
will not cause any electron ejection. If that happens, you have to pick a shorter
wavelength.
4. Group B: pick a wavelength in the violet/blue region to start. Use Sodium as the
metal. Start with 100% intensity and find the lowest negative voltage necessary to get a
current.
Repeat at 3 other intensities with the same wavelength. (Make significant changes in the
intensity. 100 90 is NOT significant.)
5. Group C: you will do the same experiment as Group A, except that you should select a
different metal. Try to find 5 different wavelengths that give you results.
Results:
Group A: You need to record wavelengths and stopping voltages. Calculate the
frequencies of each wavelength, and calculate the kinetic energies due to the stopping
voltages. Graph KE vs. frequency and record the slope and y-intercept. Be sure to print
out the graph.
Group B: You need to record the stopping voltage at each intensity. If there appears to be
a trend, you should graph this data.
Group C: You should do the same thing as Group A.
Analysis/Conclusions:
Groups A and C: Use the Internet to find the work function for your metal. Calculate a
percent error. (Note: you will probably find the results in eVolts. If so, to convert to
Joules simply multiply by 1.6E-19.) Was your slope consistent with the actual value of
h?
Group B: What (if any) is the relationship between the intensity of the light and the
stopping voltage?
Questions for further thought: Everybody should do this.
1. In typical mechanic waves such as sound and water, what is the energy of the wave
proportional to? For example, how do you recognize a high energy wave at the beach?
2. How do the results of this experiment seem to demonstrate that light wave energy is
carried a different way?
3. Imagine 2 electrons on a plate of sodium metal. One electron is found right on the
surface of the metal. The other electron is buried several layers below. A. Which
electron needs the least energy to escape? Why? B. Which electron will have the greater
KE when it absorbs the energy from a photon and escapes? Why? C. Which electron is
more likely to overcome the electric field to reach the other metal? Why?
4. For sodium, even at 100% intensity, a green photon with a wavelength of 557 nm will
never eject any electrons., but at 1% intensity, a UV photon at 235 nm always knocks out
an electron. Einstein’s interpretation of this event (or one just like it) earned him a Nobel
prize. It’s your turn. Why does this result clearly indicate particle-like properties of light
(which Einstein referred to photons)?