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Experiment 2 Millikan Oil Drop
Experiment 3 Photoelectric Effect
Experiment 1 Young's Double Slit Experiment
Diffraction and Interference of Light
Young’s Double Slit Experiment
Apparatus:
Optics Bench
Diode Laser
Single and Double Slit
Blank White Paper
Meter stick
Small Ruler
Objectives: The purpose of this lab is to observe and study the diffraction pattern from a single slit and the interference pattern from a double slit. We will use these patterns to measure the width of the slit, and the distance between two slits.
Experiment 1: Diffraction from a Single Slit
Theory:
When diffraction of light occurs as it passes through a slit, the angle q to the mth minima in the diffraction pattern is given by
a sin q = m l (m = 1, 2, 3…) (Equation 1)
Where a is the slit width, q is the angle from the center of the pattern to the mth minimum, l is the wavelength of light and m is the order (1 for the first minimum, 2 for the second…counting from the center out). See figure 1.
Figure 1, single slit diffraction, experimental set-up. D is the distance from the slit to the screen, m is the order number, a is the width of the single slit, and y is the distance from the center of the diffraction pattern to the mth dark fringe.
Since the angles are usually small, it can be assumed that sin q is roughly equal to tan q or sin q is roughly equal to q. Therefore, we see that
tan q = y/D, (Equation 2)
and thus combining equations 1 and 2 yeilds…
(Equation 3)
Procedure:
1. Set up the laser at one end of the optics bench and place the single-slit disk about 3 cm in front of the laser.
2. Place a piece of paper a good distance from the slit/laser. It is best to use a wall for this.
3. Select the 0.04mm slit by rotating the slit disk until the 0.04mm slit is centered in the slit holder. Adjust the position of the laser beam (using the two knobs on the back of the laser housing) until the beam is centered on the slit and the diffraction pattern is clear and symmetric on the paper. Notice, the laser has two knobs, one for horizontal and one for vertical adjustments. Take the time to optimize the diffraction pattern on the screen for best results.
4. Measure the parameters necessary to determine the slit width using equation 3. Use as many side orders as you can to determine numerous values for the width. Take the average value of your measurements as the final experimental value. Be sure to include uncertainty in all your measurements and propagate them through your calculation to determine the uncertainty in the experimental value for the width.
5. Repeat the experiment using a different width of slit.
5. Determine the percent discrepancy between your experimental results and the expected value of the each width (listed on the apparatus).
Experiment 2: Interference from a Double Slit
Theory:
When light passes through two slits, the two light rays emerging from the slits interfere with each other and produce interference fringes. The angle q to the mth maxima (bright fringes) in the interference pattern is given by
(Equation 4)
Where d is the slit separation, q is the angle from the center of the pattern to the mth maximum, l is the wavelength of light, and m is the order number (0 for the central maximum, 1 for the first side maximum, 2 for the second side maximum, etc., counting from the center out).
Since the angels are small, it can be assumed that sin q = tan q = q, and thus…
(Equation 5)
Where y is the distance on the screen from the center of the pattern to the mth interference maximum and D is the distance from the slits to the screen as shown in figure 2.1.
Figure 2.1: Double slit experimental set-up. D is the distance from the slit to the screen, d is the distance between two slits, y is the distance on the screen between the center of the pattern to the mth bright fringe, and m is the order number.
Combining equations 4 and 5 produces the equation for the slit separation
(Equation 6)
While the interference fringes are created by the interference of the light coming from the two slits, there is also a diffraction effect occurring at each slit due to the single-slit diffraction. This causes the envelope as seen in Figure 2.2.
Figure 2.2: Diffraction envelope superimposed on the double slit interference pattern. Note that the third interference fringe is eliminated by the first diffraction minimum.
Procedure:
1. Again, set the laser on one end of the optical bench about 3 cm from the double slit disk.
2. Tape a piece of paper to the wall a good distance from the laser.
3. Select the double slit with 0.04 mm slit width and 0.25 mm slit separation by rotating the slit disk until the desired double slit is centered in the slit holder. Adjust the position of the laser beam to optimize the interference pattern on the paper.
4. Measure the appropriate quantities to use equation 6 to determine the slit separation. Use as many side orders as you can to determine numerous values for the separation. Be sure to include uncertainty in all your measurements and propagate them through your calculation to determine the uncertainty in the experimental value for the width.
5. Repeat the experiment using a different slit separation but the same slit width.
5. Determine the percent discrepancy between your experimental result and the expected value of the each width.
END
Experiment 2.
Millikan's Oil Drop Experiment
Measuring the electric charge of an electron
The Millikan Oil Drop Experiment
Apparatus:
Millikan Oil Drop Experiment apparatus
Latex spheres
Atomizer for latex spheres
Web-cam (and computer to view video)
The purpose of this lab is to demonstrate that the charge on an electron is quantized, i.e. the charge is in discrete units. In addition, we will measure the magnitude of the fundamental charge on an electron.
Background:
The experiment is named for R. A. Millikan, the American physicist who devised it and performed it in 1910. Millikan wanted to determine whether electrical charge occurred in discrete units and, if it did, whether there was such a thing as an elementary charge. In Millikan’s original experiment, oil drops were ionized after passing through a small hole into a region between two charged, horizontal plates. The schematic of his original experiment is shown in Figure 1.
Figure 1: Millikan’s original experimental set-up
When the drops were illuminated from one side, they appeared as bright spots against a dark background. These drops were then subjected to a combination of electrical, gravitational, and viscous forces. Millikan analyzed the motion of the drops to determine the charge on each drop to show that the charge on each drop was an integral multiple of the fundamental charge on an electron, thus demonstrating the quantized nature of charge, and ultimately determining the charge on the electron.
Millikan’s original experiment used drops of oil because they do not tend to evaporate and thus have a constant mass. We will use spheres of latex liquid of known mass and diameter.
Theory:
In the experiment, a small charged ball made of latex moves vertically between two metal plates. This sphere is too small to be seen with the naked eye, and so a microscope and camera are used to enable the experimentalist to see the sphere as a small dot of light (the sphere used is on the order of the wavelength of visible light – what shows up in the microscope is the light scattered from the sphere). When there is no voltage applied to the plates, the sphere falls slowly and steadily under the influence of gravity. Because of air resistance the sphere quickly reaches a terminal velocity rather than accelerating continuously. When a voltage is applied to the plates, the terminal velocity of the sphere is affected not only by the force of gravity but also by the electric force acting on the sphere.
Consider a
latex sphere of mass m and charge q, falling under gravity between
two horizontal plates. In falling, the sphere is subjected to the force of
gravity, and an opposing force due to air resistance. The speed of the sphere
quickly increases until a constant terminal speed is reached, at which time the
weight of the sphere, mg, is exactly equal to the air resistance force.
The value of the air resistance force on a sphere was first derived by Sir
George Stokes and is given by F =
where
is the coefficient of viscosity of air, r is the
radius of the sphere and s is its terminal speed.
The free body diagram and the equation of motion of the sphere is (at terminal velocity, acceleration = 0):
where Fd is the viscous drag force given by Stoke’s law.
Now suppose
the metal plates are connected to a source of constant potential difference
(voltage) such that an electric field of intensity E is established between the
plates and a latex sphere of charge q experiences a net force upwards.
The resultant upward force on the charge is
and this force causes the sphere to move upwards with a
constant terminal speed s+. The free body diagram and
equation of motion is:
If now the polarity of the electric field is reversed, the sphere will move downwards under the combined force of gravity and the electrostatic force. This free body diagram and equation of motion is:
Notice that the drag force still applies and that the terminal speed is achieved in the opposite direction than in the previous case.
The effects of gravity can now be eliminated by adding the equations of motion yielding:
If the terminal speeds are changed to velocities by incorporating the proper sign convention of upwards (+) and downwards (-), the following equation results:
or 
(Equation 1)
Both
and r are known quantities for the latex spheres in
air, which will allow the calculation of the charge q if the
electrostatic field E and the difference in terminal velocities are
measured.
END
The apparatus is designed so that all necessary components are contained in one unit. The apparatus is mounted on a metal base, which supplies all necessary power inputs when it is connected to a 110 VAC, 50/60 Hz outlet. It consists of the following parts:
· A storage bottle and spray bulb pump for producing spheres of latex liquid
· A 30X scale microscope, which has a resolution of 0.2 mm between the small divisions and 1 mm between the large divisions.
· An electrode assembly;
· Appropriate controls, including a polarity-reversing switch, a potentiometer for fine control of plate voltages, and a voltmeter indicating the plate voltage applied.
(1) Electrode Housing
(2) Illuminator
(3) Voltmeter
(4) Potentiometer
(5) Power Cord
(6) On-Off Switch
(7) Microscope Adjustment Knob
(8) Polarity-Reversing Switch
(9) Metal Base
(10) Box Microscope
(11) Electrode Housing Set Screw
(12) Spray Bulb
(13) Latex Storage Bottle
(14) High Voltage Electrode Leads
Fig. 2: illustration of the apparatus with a key listing the parts.
Begin by setting the apparatus on a level surface. (Use a spirit level to be sure the apparatus is level). Make sure all power to the unit is turned off whenever you are making any adjustments to it.
Make sure the electrode housing is set as in Fig. 2. This requires unscrewing the electrode housing setscrews and removing the upper electrode housing plate. Then insert the atomizer ring between the upper and lower electrode housings and retighten the setscrews. Notice the small aperture to allow the light into the space between the parallel plates; this should be aligned with the light. Exercise extreme caution, as the ring is fragile.
To use the latex spray, first loosen the setscrews of the electrode housing to permit air to escape. Then inject latex spheres into the chamber by using the spray bulb pump. To feed the latex spheres in, cover the air hole of the spray bulb pump with a finger and squeeze the bulb. Note that the latex spheres will not be injected unless the air hole is covered.
Spraying is usually difficult the first few times. We recommend that you begin your measurements after making several test sprays.
After using the apparatus, clean the spray tubing with water. If the spray is not cleaned after each use, the residue of latex in the spray tubing will harden, preventing smooth operation of the spray.
1. Ensure that the D.C. volt leads are plugged into their respective color terminal lugs.
2. Position the 3-way polarity switch in its mid position, establishing a “no-charge” condition. Turn the “on/off” switch to “on.” The illuminating lamp should light.
3. Adjust the microscope by rotating the focus-adjusting knob until an approximate mid position is established. The eyepiece divisions should be distinguishable from the background.
4. Adjust the electrode voltage of 300 volts using the voltage-adjusting knob, but keep the polarity switch in its mid position. (You may need to adjust the voltage once you see the spheres.)
5. Spray latex into the apparatus and carefully look for the “dots of light” in the microscope. If after several pumps on the atomizer bulb, the latex spheres are still not visible, adjust the microscope carefully to attempt to focus in on the spheres.
Obtaining a suitable drop may require patience as drops continue to enter the region between the plates for several seconds after spraying has stopped. Select a small drop which takes about 30 seconds to move between two large divisions in the eyepiece. When you are ready to collect data, simply begin recording a video on the webcam. Note that you need to take data for the same drop rising and descending, so continue to record the drop for upward motion, and also reverse the polarity of the voltage across the plates and record the same drop as it moves downward. With careful planning, you may be able to record several drops in one video recording. Continue to take similar data on as many different spheres as possible.
Record the rise time t+ and the fall time t- of the latex sphere between two large divisions in the eyepiece. Calculate the corresponding velocities v+ and v- , which are merely the distance between the two large divisions divided by the time the sphere took to travel that distance
When the experiment is completed, clean the electrode housing. Turn off and unplug the unit. Remove the pipe from the latex container. Loosen the setscrew of the electrode housing and remove the housing. Wipe off any water and latex with a soft cloth. Clean the latex spray tube by flushing is thoroughly with clean water. Reassemble the housing and set it in the designated position.
Analysis:
Plot the
difference in upward and downward velocities
on a graph similar to Fig. 4. The data points should
fall into groups, each group representing spheres with the same charge.
Since the
difference in terminal velocities is directly proportional to the charge q, the fact
that the data points are grouped in distinct steps indicates the charge on the
spheres occurs in distinct amounts.
Drop number
Fig 4
Calculate the actual charge on each sphere, beginning with Eq. 1
Recall that q = ne where n is the number of electrons providing charge q and e is the charge on a single electron.
The electric field E between two plates is given by the voltage across the plates (V) divided by the distance between the plates (d) .
So 
(equation 2)
Or 
For the latex spheres in air:
(coefficient of dynamic viscosity)
Latex sphere radius
Plate Voltage = V (measured)
Velocity difference = (v+ - v-) (measured)
Distance between plates: d = 5 x 10-3 m (you should verify this by measuring)
The charge on an electron (e) has the value of 1.602 x 10-19 coulomb.
Calculate the actual charge on each sphere using equation 2. Make a plot similar to Fig 3 but with charge q on the y-axis. From this plot, determine which data represent spheres with a single excess electron, which represents spheres with two excess electrons, etc. Then, divide each charge q by n (the number of electrons) to determine the charge on the electron e = q/n. Your final experimental value will be the average of all your values of e. Compare your result with the accepted value of the fundamental charge e.
END
Experiment 3. The Photoelectric Effect
Purpose:
The purpose of this lab is to investigate the nature of light and determine whether the classical wave model or the quantum theory of light best explains the phenomenon observed in the Photoelectric effect. Specifically, we will investigate the wave model of light vs. the quantum model, and the relationship between energy, wavelength and frequency of light.
Theory:
By the late 1800’s, many physicists thought they had explained all the main principles of the universe and discovered all the natural laws. But in several areas, inconsistencies that couldn’t be explained continued to plague the scientific community. One such area was the absorption and emission of light. Unable to explain the spectral distribution of light based on the classical wave model, Max Planck formulated a new model for light emission, called the quantum model. His model postulated that light is absorbed or emitted by atoms in discreet quantities called quanta. A consequence of this model is that an atom has a discrete set of possible energy levels: energies between these values never occur. The emission and absorption of light quanta is associated with transitions between two energy levels of an atom. The energy lost or gained by the atom is emitted or absorbed as a quantum of radiant energy, the magnitude of which is expressed by the equation,
E = h n
where E is the radiant energy, n is the frequency of the radiation, and h is a fundamental constant of nature, known as Plank’s constant.
When light is incident on certain metallic surfaces, electrons are emitted from the surface. This phenomenon is called the photoelectric effect, and the emitted electrons are called photoelectrons. Figure 1 shows a schematic diagram of the apparatus in which the photoelectric effect can occur. This experimental apparatus consists of an evacuated glass tube containing a cathode (the emitter) and an anode (the collector) connected to a circuit. Incident light falling on the cathode causes the ejection electrons. (Think about how this can happen…light is causing electrons to be freed from the electrons in the atoms of the metal!). The electrons travel toward the anode when a positive (accelerating) voltage is applied. The current (I) in the circuit arises from the flow of photoelectrons from the emitter to the collector, and is measured in the ammeter. (Would current flow in this circuit if there were no electrons in the evacuated vacuum tube?)
Figure 1: When light strikes the emitter, electrons are ejected from the metal. Electrons are attracted to the collector by means of a potential difference between the emitter and the collector. These electrons constitute a current in the circuit, An ammeter measures this photoelectric current.
Considering light as an electromagnetic wave, we may imagine that light incident on the electrons in a metal confers energy to the electrons, allowing them to escape the metal. The classical wave model of light predicts that as the intensity of incident light is increased, the amplitude and thus the energy of the light wave will increase. In this model, the photoelectric effect will occur, regardless of the frequency of light, provided the light intensity (amplitude) is high enough. Increased intensity will cause more energetic photoelectrons (i.e. electrons with higher kinetic energy) to be emitted. In addition, classical wave theory would predict that the electrons would require some time to absorb sufficient radiation before acquiring enough energy to escape from the metal.
The new quantum model assumes quantization of electromagnetic radiation, whereby light is not distributed evenly over the classical wave front, but is concentrated in discrete ‘bundles’ called quanta or photons. Light of frequency n can be considered a stream of photons and each photon has an energy given by E = hn. The photoelectric effect arises as a photon gives all of its energy to a single electron in the metal. Electrons emitted from the surface, then, have a maximum kinetic energy
KE = hn - f ,
where f is the work function of the metal. (Or, in other words, photons have a total energy E = hn = KE + f ). The work function represent the minimum energy with which the electron is bound to the metal. The incident radiation must have photon energy sufficient to overcome the work function and impart kinetic energy to the electron. According to this model, no electrons are emitted if the incident light frequency falls below some cutoff frequency, nc , which is characteristic of the material being illuminated. If the light frequency exceeds the cutoff frequency, a photocurrent is observed. In this model, the number of photoelectrons (i.e. the amount of current) emitted is proportional to the light intensity. However, the maximum kinetic energy of the photoelectrons is independent of the light intensity and depends only on the frequency of the incident light. In addition, this theory would predict that electrons are emitted from the surface instantaneously even at low light intensities.
The amount of current in the circuit is a direct measure of the number of electrons accelerated between the cathode and the anode, and thus we can determine the relative number of electrons emitted by measuring the current. The kinetic energy of the photoelectrons can be measured by reversing the voltage across the cathode and anode, so that the emitter is now positive and the collector is negative. This creates retarding voltage conditions in which the electrons are now repelled from the collector rather than being attracted. As the retarding voltage is made more negative, only the electrons with an initial kinetic energy greater than eV (the charge on the electron, e times the voltage, V) can make it to the negative collector and be recorded as part of the photocurrent by the ammeter. At some value of the retarding voltage, the photocurrent becomes zero. This voltage is called the stopping potential or V0. Hence, the kinetic energy of the photoelectrons is related to the stopping potential by,
KE = eV0 .
To summarize, according to the quantum theory of light, the kinetic energy, KE, of photoelectrons depends only on the frequency of the incident light, and is independent of the intensity. Thus the higher the frequency of the light, the greater is the energy of emitted photoelectrons. In contrast, the classical wave model of light predicts that the kinetic energy of the ejected photoelectrons would depend on light intensity. In other words, the brighter the light the greater the photoelectron energy.
Experiment:
This lab provides the opportunity to investigate the quantum theory vs. the classical wave theory of light for describing the photoelectric effect. In experiment 1, part A you will select two spectral lines from a mercury light source and investigate the maximum energy of the photoelectrons as a function of intensity. In part B, you will utilize 5 different spectral lines and investigate the maximum energy of light as a function of frequency, or color, of the light. In experiment 2, you will examine the relationship between light frequency and kinetic energy and from this will determine the value of Planck’s constant, h, and the work function, f, of the metal in the h/e apparatus. The anode and cathode in this apparatus function like a small capacitor which becomes charged by the photoelectron current. What the potential on this capacitor reaches the stopping potential (Vo) the current decreases to zero and the anode and cathode voltage stabilizes. The final voltage between the anode and cathode is therefore the stopping potential of the photoelectrons. This potential is then measured by connecting a digital voltmeter across the output terminals on the hack of the h/e apparatus. A discharge knob, also on the back of the apparatus, discharges the capacitor and enables subsequent measurements. (The anode and cathode and associated electronics are not visible in this apparatus)
Photoelectric effect apparatus.
Figure 2: The photoelectric effect apparatus.
Figure 3a and 3b show a schematic of the photoelectric effect apparatus with salient features labeled.
Figure 3a Figure 3b
Photoelectric effect apparatus, back Photoelectric effect apparatus, front
Mercury Light Source
Figure 4: Mercury vapor light source and power supply
When electrically excited, the mercury atoms within the light source emit radiation at 5 discreet frequencies or colors. The spectrum characteristic of mercury includes yellow, green, blue and two violet spectral lines. Table 1 lists the color, frequency, and approximate wavelength of each spectral line.
Color Frequency Approx. wavelength
Yellow 5.19 x1014 Hz 578 nm
Green 5.49 x1014 Hz 546 nm
Blue 6.88 x1014 Hz 436 nm
Violet #1 7.41 x1014 Hz 405 nm
Violet #2 8.22 x1014 Hz 365 nm
Table 1. Color, Frequency, and approximate wavelength of
spectral lines in the mercury spectrum.
Filters.
Three filters are included with this experiment, yellow, green and variable transmission filter. Because the yellow and green spectral lines are not completely monochromatic, experimenting with yellow and green spectral lines requires the use of the yellow or green filter, respectively. These filters also limit higher frequency light such as that in the ambient room light, from entering the h/e apparatus and interfering with the lower energy yellow and green light and thus skewing the true results. The variable transmission filter consists of computer generated patterns of dots and lines that vary the intensity (but not the frequency) of the incident light, The relative transmission percentages are 100%, 80%, 60%, 40%, and 20%.
In addition, a voltmeter will be utilized to measure the voltage corresponding to the stopping potential.
Set up the equipment as follows.
1) Couple the mercury light source to the h/e apparatus by connecting the base pin and hole assembly.
2) Turn on the light and observe the 5 spectral lines of mercury (yellow, green, blue, violet1 and violet2) emitted from the light source and diffracted by the lens.
3) Turn on the h/e apparatus (on-off switch on the back of the apparatus)
4) Adjust the h/e apparatus so that a spectral line falls upon the opening of the white reflective mask of the photodiode. Tilt the light shield of the apparatus out of the way to reveal the white photodiode mask inside the apparatus. Adjust the h/e apparatus until you achieve the sharpest image of the aperture centered on the hole in the photodiode mask, then replace the light shield.
5) If you are using the green or yellow spectral line, place the corresponding colored filter over the white reflective mask on the h/e apparatus. (The filter has a magnet for attaching to the white reflective surface).
6) Use the multi-meter to check the voltage across each battery (there is a terminal on the back of the h/e apparatus). If the battery voltage is less than + 6, replace the batteries.
7) Connect leads from the digital voltmeter (DVM) to the OUTPUT terminals on the back of the h/e apparatus, making sure that the polarity is the same on each end.
Experiment 1.
Part A
1. Select a spectral line to use in this experiment and adjust the apparatus as described above.
2. Place the variable transmission filter in front of the white reflective mask (and over the colored filter if one is used) so that light passes through the section marked 100% and reaches the photodiode. Record the voltage reading from the digital mult-meter.
3. Press the discharge button (on the back of the h/e apparatus) and observe the approximate time required to charge the h/e instrument to the maximum voltage. Record this time measurement. (Remember to also record which % transmission is being measured). Be sure to take at least 5 or 6 measurements and average them.
4. Move the variable transmission filter so that the next section (80%) is directly in front of the incoming light. Record the new voltage reading, and the approximate time to recharge the apparatus after pressing the discharge button.
4. Repeat step 2 until you have tested all five sections of the variable transmission filter.
7. Repeat the entire procedure using a second color from the mercury spectrum.
8. Tabulate your data, your table should include the headings; % transmission, Stopping potential, Approx charge time, and should include data for each of two different spectral lines. Make sure and also note what color of spectral lines you measured.
Part B
1. Remove the variable transmission filter from the white reflective mask on the h/e apparatus.
2. Beginning with the yellow spectral line, adjust the h/e apparatus so that this line falls directly on the opening of the mask of the photodiode (as before).
3. Place the yellow filter on the white reflective mask on the h/e apparatus
4. Record the voltage reading.
5. Repeat the process for each color in the spectrum, using the green filter when measuring the green spectral line. No filters are used to measure the blue and violet lines.
6. Tabulate your data, your table should include the headings, ‘light color’ and ‘stopping potential’.
Experiment 2
We can use the data collected in experiment 1B for this section of the lab. Determine the wavelength and frequency of each spectral line and record these values in a table that includes the headings, light color, stopping potential, frequency and wavelength.
Analysis:
Experiment 1
Describe (qualitatively) the effect that passing various intensities of light (through the variable transmission filter) has on the stopping potential and thus the maximum kinetic energy of the photoelectrons. Also comment on the charging time after pressing the discharge button.
Describe (qualitatively) the effect that different colors (i.e. frequencies) of light had on the stopping potential and thus the maximum kinetic energy of the photoelectrons.
Plot stopping potential (voltage) vs. percent transmission. (make a separate graph for each of the two colors used).
Plot the stopping potential (voltage) vs. frequency (Hz) of light.
Make sure that all three graphs (two of V vs. % transmission and one of V vs. frequency) have the same scale for their Y axes (voltage). You must have the same axes in order to compare these data.
Defend whether this experiment supports a wave or a quantum model of light based on your results.
Experiment 2
Using your plot of stopping potential vs. frequency, fit the data with a best fit line and determine the slope and intercept of the line.
Using the equations:
E = hn = KE + f
KE = V0 e
derive a linear equation for the graph V vs. n.
Interpret the results in terms of h/e ratio and f/e ratio. Calculate h and f.
In your lab write up, report your values for h and f (compare your value of h with the accepted value) and discuss your results based on a quantum model for light.