PHYSICS 320 LABORATORY

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, and associated light filters.

 

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 = h n

where E equals the radiant energy, n 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 = hn = KEmax +f

where KEmax is the maximum kinetic energy of the emitted photoelectrons, and f 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 h n are incident upon the cathode of a vacuum tube. The electrons in the cathode use a minimum f 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:

hn = Ve + +f

When solved for V, the equation becomes:

V = (h/e) n - ( f /e)

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

 

SETUP PROCEDURE:

  1. Connect a digital voltmeter (DVM) to the output terminals of the h/e apparatus. Select the 2V or the 20V range on the meter.

    2.  

  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.

    3.  

  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. Then rotate the cylindrical light shield back into position.

    4.  

  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.  

  5. Press the red zero button on the side panel of the Apparatus to discharge any accumulated charge in the unit=s electronics. Read the voltage on the digital voltmeter. This is a direct measurement of the stopping potential for the photoelectrons.

    6.  

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 results with different light frequencies.

 

Procedure

  1. Adjust the h/e apparatus so that only one of the spectral colors passes through the entrance slot and falls on the opening of the mask of the photodiode. If you select the green or yellow spectral line, place the corresponding colored filter over the entrance aperture.

    2.  

  2. Place the Variable Transmission Filter in front of the entrance aperture (and over the colored filter if one is used) so that the light passes through the section marked 100% before it reaches the photodiode. Record the DVM voltage reading in the table below. Press the instrument discharge button, release it, and observe the approximate time required to recharge the instrument to the maximum voltage.

    3.  

  3. Move the Variable Transmission filter so that the next section is directly in front of the incoming light. Record the DVM reading, and approximate the time to recharge after the discharge button has been pressed and released.

    4.  

  4. Repeat step 3 until you have tested all five sections of the filter.

    5.  

  5. Repeat the procedure using a second color from the spectrum.

 

 

 

 Color #1

(name)

 

 
 %Transmission  Stopping Potential   Approx. Charge Time
 

100

  

 

  

 
 

80

  

 

  

 
 

60

  

 

  

 
 

40

  

 

  

 
 

20

  

 

  

 

 

 

 

 

  

Color #2

(name)

 

 
%Transmission   Stopping Potential   Approx. Charge Time
 

100

  

 

  

 
 

80

  

 

  

 
 

60

  

 

  

 
 

40

  

 

  

 
 

20

  

 

  

 

 

Analysis

  1. Describe the effect that passing different amounts of the same color of light through the Variable Transmission Filter has on the stopping potential and thus the maximum energy of the photoelectrons, as well as the charging time.

    2.  

  2. Describe the effect that different colors of light had on the stopping potential and thus the maximum energy of the photoelectrons.

    3.  

  3. Defend whether this experiment supports a wave or a quantum model of light based on your lab results.

 

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.

    2.  

  2. Record the DVM voltage reading (stopping potential) in the table below.

    3.  

  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.

    4.  

  4. If you are using a grating to separate the colored lines, 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.  

  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 f /e ratio. Then, calculate h and f .

    3.  

  3. In your conclusions, discuss your results with an interpretation based on a quantum model 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