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Lab Experiments  Syllabus

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Experiment 1 Double Slit

Experiment 2 Millikan Oil Drop

Experiment 3 Photoelectric Effect

Experiment 4 Mirror Lens Experiments

Experiment 1 Young's Double Slit Experiment

Experiment 1

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 m^th 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 m^th 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 m^th 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 m^th 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 m^th 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 m^th 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 m^th 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

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Experiment 2.

Millikan's Oil Drop Experiment

Measuring the electric charge of an electron

The Millikan Oil Drop Experiment

Apparatus:

Millikan Oil Drop Experiment apparatusxperiment 2

Latex spheres

Atomizer for latex spheres

Web-cam (and computer to view video)

Purpose:

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.

In Figure 1, vf is the velocity of fall, k is the coefficient of friction between the air and the drop, m is the mass of the drop, and g is the acceleration of gravity. Since the forces are equal and

opposite:

                                    mg = kv_s     = F_d                         ( 1 )

George Gabriel Stokes in the year 1851 derived an expression now known as Stokes Law for the frictional force exerted on spherical objects with very small Reynolds number (e.g., very small diameter),

where:  Fd is the frictional force acting on the interface between the fluid and the particle (in N), μ is the dynamic viscosity (N s/m2), R is the radius of the spherical object (in m), and v_s is the particle's settling velocity (in m/s).

If the spherical particles are falling in the viscous fluid by their own weight due to gravity, then a terminal velocity, also known as the settling velocity, is reached when this frictional force combined with the buoyant force exactly balance the gravitational force. The resulting settling velocity (or terminal velocity) is given by:

 where: v_s  is the particles' settling velocity (m/s) (vertically downwards if ρ_p > ρ_f, upwards if ρ_p < ρ_f ),g is the gravitational acceleration (m/s2), ρ_p is the mass density of the particles (kg/m3), and ρ_f is the mass density of the fluid (kg/m3). The student should derive this equation using the force diagram and known relationship between sphere volume and sphere radius.  Note that the presence of the term g would allow us to experiment on the moon or any other celestial body where gravitation is known, and where a known atmosphere (r_f) exists.

In our experiments, for the oil droplets of unknown diameter, we will substitute latex spheres of 1.07microns (1.07_-6 m) diameter and 1050 kgm/m³ density. We will read local barometric pressure from the mercury barometer located on the wall in the back corner of our laboratory. For purposes of preliminary calculations, the barometric pressure is taken to be 609 mm Hg  (60.9cm Hg)(standard atmosphere at 6250 ft above sea level) and laboratory temperature is assumed to be 25C. The temperature dependent viscosity of air is obtained from the chart in the back of this procedure, to be               ~ 1.8465_-5Nsm^-2  (1.8465_-4dyne s/cm²=poise).  For particles falling less than 1 mm/s, the viscosity needs to be corrected for Brownian motion.  The correction factor is given by 

            m_eff = m/(1+b/pR)   where b = 6.17_-6 cm of Hg m and p= barometric pressure in cm Hg

 Assuming 60.9 cm Hg  barometric pressure, and particle radius of 0.535_-6m, the corrected viscosity becomes m=1.8465_-5Nsm^-2  /[1+6.17_-6/(60.9*0.535_-6)]  = 1.5525_-5 Nsm^-2

Under expected laboratory conditions of 60.9cmHg pressure (0.801 atmospheres) and 25C (298K) temperature, the density of air would be

            r_f= pMw/RT = 0.801atm*.0286kg/mol/(8.205746₋₅ m³/atmmolK*298K)=0.937kg/m³

The latex spheres have a specific gravity of approximately 1.05, corresponding to a density of 1050 kg/m³. Buoyant forces on the latex spheres are therefore virtually negligible. Computed settling velocity for the spheres, in the absence of any Coulomb forces is 

                                    =2*(1050-0.937)kg/m³*9.8m/s² * (0.535_-6m)²/(9*1.5525_-5 Nsm^-2)

                                    = 4.21_-5 m/s = 0.042 mm/s

This is the settling velocity which we should observe for uncharged particles, or particles in the absence of an electrical field. About 24 seconds to settle one millimeter. If we observe values significantly different from this with the field grounded to zero, perhaps there are two or more particle stuck together, perhaps we have made and experimental error, or perhaps we should re-visit the analyses.

When the particles are charged and subjected to an electrical field, they will settle faster or slower or reverse, depending upon the charge magnitude and the field direction. In general, if the electrical field and electrical charges are high enough, the particle will rise rather than settle, so we term the velocity v_r for rise velocity.  The force balance tells us

                                    Eq = mg + kvr                             (2)

Employing (2) and also equation (1), we find that the charge is given by

                                    q =mg (vf + vr)/Evf                   (3)

for an electric field strength of say 500V/0.767cm = 650 V/cm = 65,000 V/m, a particle mass of 1050 kg/m³*p* (1.07_-6m)³ /6 = 6.55_-16kg  and a charge of n= 1,2,3 and 5 electrons (q = n e = n 1.6_-19C)we would expect to see rise velocities of

                        v_r  = -v_f + n e E v_f  / mg 

                        = - 4.21_-5 +n*1.6_-19*65,000*4.21_-5/(6.55_-16 *9.8) = (-4.21_-5 +n* 6.82_-5) m/s 

Clearly, the electric field influences  particle settling velocity. Since we can direct the electrical field in the opposite direction by simply throwing a switch, during our experiment we can make the second term either positive or negative in the result above. We will measure the rise velocity and compute the charge for as many particles as we can during the laboratory session.  

From our results we will hopefully see the computed charge to always be a multiple of the basic electron charge. If we did not already know the value of e, we should be able to infer the value from our data.  For each particle, measure rise and fall rates for various field strengths and field directions, and compute from the measurements a value for n. Tabulate the n data, and give your best measure of the basic electrical charge e.  

For these experiments, we have the benefit of knowing the (vendor’s opinion of) particle size and density. Millikan, in his laboratory did not have this benefit. He had to produce droplets from a spray of oil.  The droplet diameters were essentially determined from fall velocity in the absence of a field. The Pasco manual for our apparatus (link given at the beginning of this analysis section) details the somewhat more complex approach to determination of e using droplets of unknown diameters. Read that approach and be happy that we have those known particles.  The following is the procedure we will take during our experiments, except, we will utilize the web cam attached to the computer back in the lab corner where the barometer is located. rather than the microscope, and we will use the new Millikan apparatus described in the Pasco link (thus, you need to read and understand both procedures)

Old Equipment

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.

Procedure   

Detailed procedure for setup of the current apparatus is given in the Pasco manual. That procedure is based upon use of oil droplets which are charged with a nuclear source (built into the apparatus).  Our particles are supplied in a liquid carrier, and the particles are dispersed by spritzing extremely small amounts of the carrier into the apparatus in much the same manner as oil is introduced in the manual procedure.  We expect our particles to become charged naturally during this process so we hopefully will not have to employ the radiation source. We will be using the Web Cam to record our results on video/audio during the actual experiments. 

 The following is extracted from the Pasco manual. With some additional information, you can compute Avogadro’s number.  Your computation of the number will only be as accurate as your determination of e.

 The measurement of the charge of the electron also permits the calculation of Avogadro’s number. The amount of current required to electrodeposit one gram equivalent of an element on an electrode (the faraday) is equal to the charge of the electron multiplied by the number of molecules in a mole. Through electrolysis experiments, the faraday has been found to be 2.895 x l014 electrostatic units per gram equivalent weight (more commonly expressed in the mks system as 9.625 x l07 coulombs per kilogram equivalent weight). Dividing the faraday by the charge of the electron, 2.895 x l014 e.s.u./gm equivalent weight 4.803 x l0-l0 e.s.u.,

yields 6.025 x l023 molecules per gram equivalent weight,or Avogadro’s number.

Original Operation

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 (v⁺ - v^-) 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 (v⁺ - v^-) 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           

   q =mg (vf + vr)/Evf        

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) E=DV/d        

so,                                        q =mg (vf + vr)d/ DV vf         (equation 2)

For the latex spheres in air:       

 (coefficient of dynamic viscosity)

m=1.8465_-5Nsm^-2  /[1+6.17_-6/(60.9*0.535_-6)]  = 1.5525_-5 Nsm^-2

Latex sphere radius R= 0.535 microns  (0.535 x 10 ^-6 m) verify this

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

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Experiment 3.  The Photoelectric Effect

Experiment 3

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:  

Background:

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.

The Photoelectric Effect:

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.

Classical Wave Theory vs. Quantum Theory:

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, n_c , 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 (V_o) 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)

Equipment

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.

Experimental Set Up

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.

Procedure

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.

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EXPERIMENT 4 LENSES AND MIRRORS