#### THE PHOTOELECTRIC EFFECT

OBJECT:

To study the emission of electrons from a metal surface which is irradiated with light. To experimentally determine the value of Planck's constant "h" by making use of the spectral dependency of the photoelectric effect.

APPARATUS:

A Mercury Vapor Light Source, a special h/e apparatus with a photodiode tube, a digital voltmeter (DVM), a digital oscilloscope, green and yellow filters, and a New Focus variable transmission filter wheel.

BACKGROUND:

In 1901 a German physicist Max Planck published his law of radiation. Planck went on to state that the energy lost or gained by an oscillator is emitted or absorbed as a quantum of radiant energy, the magnitude of which is expressed by the equation:

E = hf

where E equals the radiant energy, f is the frequency of radiation, and h is a fundamental constant, now known as Planck's constant. Albert Einstein applied Planck's theory and explained the photoelectric effect in terms of the quantum model using his famous equation for which he received the Nobel Prize in 1921:

E = hf = KEmax + (phi)

where KEmax is the maximum kinetic energy of the emitted photoelectrons, and (phi) is the energy needed to remove them from the surface of the material (the work function). Here E is the energy supplied by the quantum of light known as a photon.

In the h/e experiment, light photons with energy hn are incident upon the cathode of a vacuum tube. The electrons in the cathode use a minimum (phi) of their energy to escape, leaving the surface with a maximum energy of KEmax. Normally the emitted electrons reach the anode of the tube, and can be measured as the photoelectric current. However, by applying a reverse potential V between the anode and cathode, the photoelectric current can be stopped. KEmax can then be determined by measuring the minimum reverse potential needed to bring the photoelectric current to zero. Thus, Einstein's relation becomes:

hf = Ve + (phi)

When solved for V, the equation becomes:

V = (h/e)f - [(phi)/e]

Thus, a plot of V versus f for different frequencies of light will yield a linear plot with a slope (h/e) and a V intercept of [-(phi)/e].

Setup Procedure:

1. Connect a digital voltmeter (DVM) to the output terminals of the h/e apparatus. Select the 2V range on the meter.
2. Direct a beam of light from the Mercury Vapor source toward the h/e apparatus and focus the light onto the white reflective mask about the entrance slit.  Make sure that the light passes from the source through the center of the diffraction grating/lens.  NOTE: The Mercury source emits UV light - Please wear eye protection!
3. Roll the cylindrical light shield, just behind the slit, out of the way to reveal the white photodiode mask inside the Apparatus. Move the h/e Apparatus until the light passes through the entrance slit and produces an image centered on the dark window in the photodiode mask. Focus the light until you achieve the sharpest possible image on the photodiode window.  Be sure that the photodiode assembly is secure on its post and will not rotate (the screw on the postholder should be tight).  Then rotate the cylindrical light shield back into position.
4. Turn the power switch ON. Move the apparatus to select one of the colored maximums to pass directly into the h/e Apparatus through the slot in the white reflective mask and onto the window of the photodiode mask.
5. Press the red zero button on the side panel of the Apparatus and hold for a second to discharge any accumulated charge in the unit's electronics. Release the button and wait for the reading on the digital voltmeter to settle. This is a direct measurement of the stopping potential for the photoelectrons.
6. You may observe the charging time of the vacuum photodiode tube by connecting a digital oscilloscope to the output terminals. Make sure that the ground connection is correct.  Put the scope on auto-trigger with DC coupling, the time base at 250 ms per division, and the vertical scale on ~500mV per division.  Depress the zero button for a second or two and release it.  Observe the waveform on the oscilloscope.  Note the zero voltage time when the button was depressed, the fast increase in voltage when the button was released, and the ~ exponential settling of the charge.  Note that you can use the oscilloscope cursors to measure voltage and time.
7.

Experiment 1: Wave Model versus Quantum Model

According to the photon theory of light, KEmax for photoelectrons depends only on the frequency of the incident light, and is independent of intensity. Thus the higher the frequency, the greater its energy.

In contrast, the classical wave model of light predicted that KEmax would depend on light intensity. In other words, the brighter the light, the greater the energy.

This lab investigates these assertions. The experiment selects two spectral lines from a mercury line source and investigates KEmax versus intensity. The different spectral lines show if KEmax changes with different light frequencies.

Procedure:

1. Adjust the h/e apparatus so that only green light passes through the entrance slot and falls on the opening of the mask of the photodiode. Place the green colored filter over the entrance aperture.
2. Now place the New Focus filter wheel holder right in front of the entrance aperture so that the light passes through both filters at normal incidence just before it reaches the photodiode.  The filters must be as close as possible to the detector to minimize the impact of stray room light.  BE CAREFUL NOT TO TOUCH THE OPTICAL SURFACES OF THE FILTERS.  Rotate both filter wheels to the 0.04 transmission setting.  Press the instrument discharge button, release it, and observe on the oscilloscope the time required to recharge the instrument to the maximum voltage.  When you have a good, complete trace on the oscilloscope, save the waveform data on the computer (open OpenChoice Desktop, select the GPIB instrument and the Waveform Data Capture tab, then Get and Save the data) and record the final steady-state DVM voltage reading.
3. Rotate both filter wheels to the 0.5 transmission setting.  Note that if x and y are the wheel settings, the transmission is reduced by the factor 10(x+y) so the light is reduced by a factor of 10 in this case. Observe the recharging time on the oscilloscope for this intensity, save the waveform on the computer, and  record the final DVM reading.  Note that the charging process is very sensitive to how the zero button is released.  For best results when comparing different intensities, you should try to obtain oscilloscope traces that begin at the same time and have similar initial peak heights.
4. Repeat step (3) for filter wheel settings that reduce the intensity by a factor of 100.
5. Repeat the procedure using the yellow light from the spectrum.  Be sure to use the yellow filter to remove stray light.

Analysis

1. For each color, plot the 3 oscilloscope measurements (with factors of 1, 10, and 100 intensity reduction) together on a single graph of voltage vs. time.  Shift the time axes so that the button release times are approximately coincident and the responses can be compared.  You may also want to remove any initial vertical drop and normalize each of the curves (i.e. divide each voltage by the maximum voltage) to correct for any differences in starting conditions.
2. Describe the effect that passing different amounts of the same color of light through the Variable Transmission Filter Wheel has on the charging time.  Should the stopping potential and thus the maximum energy of the photoelectrons depend on the intensity of the incident light?   If your experimental results are inconsistent with your expectations, explain why your low intensity measurements might be inaccurate.
3. At each intensity, compare the stopping potential for the green and yellow light.   For a given intensity, does the measured energy of the photoelectrons depend on the color of the light?
4. Based on your lab results, discuss whether this experiment supports a wave or a quantum model of light.

Experiment #2: Determining Planck's Constant

In this experiment you will select different spectral lines from mercury and investigate the maximum energy of electrons as a function of the wavelength and frequency of the light.

Procedure:

1. Adjust the h/e apparatus so that only one color of light falls on the opening mask of the photodiode and that the light coming through the slit strikes the center of the photodiode.
2. Record the DVM voltage reading (stopping potential) in the table below.
3. Repeat the process for each color in the spectrum. Be sure to use the yellow or green filter when measuring for the yellow or green spectral line, respectively.  Do not use a filter for the blue and uv lines.
4. Repeat the process for the same colors in the second order.

 Color Stopping Potential First Order Stopping Potential Second Order Yellow Green Blue Violet Ultraviolet

Analysis:

1. Put this data on a spreadsheet. Add columns to indicate the wavelength and the frequency of each spectral line. Plot a graph of the stopping potential vs. frequency.
2. Perform a regression on the data to determine the slope and y-intercept. Interpret the results in terms of the h/e ratio and the [(phi)/e] ratio. Then, calculate h and (phi). Compare your experimental h to the accepted value. To what wavelength does your value of (phi) correspond?
3. In your conclusions, discuss your results in the context of the wave and quantum models of light.

 COLOR WAVELENGTH Yellow 579.0 nm (average) Green 546.1 nm Blue 435.8 nm Violet 404.7 nm Ultraviolet 365.5 nm