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Planck.1
THE PHOTOELECTRIC EFFECT In this experiment you will study the emission of electrons from a metal surface that is illuminated with light of various discrete frequencies. You will measure the dependence of the kinetic energy of the emitted electrons on the frequency of the incident light and you will examine the effect of varying the intensity of the incident light. Theory: The Photoelectric Effect Late in the nineteenth century a series of experiments revealed that electrons are emitted from a metal surface when it is illuminated with light of sufficiently high frequency. This phenomenon is known as the photoelectric effect. In 1905, Einstein explained the photoelectric effect by assuming that light propagates as individual packets of energy called quanta or photons. This was an extension of the quantum theory developed by Max Planck. In order to explain the spectrum of radiation emitted by bodies hot enough to be luminous, Planck assumed that the radiation is emitted discontinuously as bursts of energy called quanta. Planck found that the quanta associated with a particular frequency of light all have the same energy, E = h, where h = 6.626 × 10–34 J·s = 4.136 × 10–15 eV·s (Planck’s constant). Although he had to assume that the electromagnetic energy radiated by a hot object emerges intermittently, Planck did not doubt that it propagated continuously through space as electromagnetic waves. Einstein, in his explanation of the photoelectric effect, proposed that light not only is emitted a quantum at a time, but also propagates as individual quanta. Einstein’s explanation of the photoelectric effect is that it is a result of collisions between photons (light quanta) of the incident light beam and electrons in the metal surface. In the collision, the photon energy h is absorbed by the electron. Some of this energy is then used to overcome the binding energy of the electron to the metal, and the remainder appears as kinetic energy of the freed electron. This quantum theory of light is totally contrary to the wave theory, which predicts that light energy is distributed continuously throughout the wave pattern, and which provides the sole means of explaining many optical effects such as diffraction and interference. This wave-particle duality cannot be avoided; both theories are required to account for the observed behaviour of electromagnetic radiation. The ‘true’ nature of light cannot be described in terms of everyday experience, and both wave and quantum theories must be accepted, contradictions included, as being closest to a complete description of light. Apparatus: The equipment consists of a source of photons (high-intensity mercury vapour light source), a monochromator (a diffraction grating and a set of interference filters), an intensity filter, a phototube, an electrometer (essentially a very sensitive ammeter), a DC voltage source in combination with a rheostat used as a voltage divider, and an interface device which allows phototube current and retarding potential to be processed by a computer. The diffraction grating and interference filters enable separation of the light from the mercury source into prominent spectral lines of discrete wavelength (and hence frequency), the phototube
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Planck.2
contains the metal surface to be illuminated, and the rest of the equipment is used to measure the current due to the emitted photoelectrons as a function of retarding potential. The phototube consists of two electrodes enclosed in an evacuated tube. One electrode (the cathode) has a large photosensitive surface and is called the emitter. The other electrode (the anode) is a wire and is called the collector. When the emitter is exposed to light, electrons are ejected from its surface. Some of the emitted electrons strike the anode, causing a current to flow. This current is measured by the electrometer. To measure the maximum kinetic energy, KEmax, of these emitted electrons, a retarding potential is applied across the cathode and anode. The anode is made progressively more negative than the cathode, resulting in fewer and fewer electrons having sufficient kinetic energy to overcome this retarding potential difference. When the anode potential becomes sufficiently large (equalling Vo, the stopping potential), subsequent photoelectrons have insufficient kinetic energy to overcome the potential difference, so no more electrons reach the anode and the phototube current reaches zero. This occurs when KEmax = eVo. A value of Vo is determined by analysing the plot of phototube current versus retarding potential obtained from the computer. Determining Vo for various known discrete frequencies of light allows analysis of the relationship between KEmax and The intensity filter is used to determine if Vo (and hence KEmax) depend on the intensity of the incident light. Procedure and Experiment: NOTE:
For best results, this experiment should be done with the room lights off. Also, avoid bumping the equipment as proper alignment is crucial.
Turn on the mercury light source, the electrometer, the DC voltage source, the digital voltmeter, and the computer interface. Ask the instructor to explain the operation of the equipment and DataStudio software. The spectral lines to be measured are: violet violet blue green yellow
365.0 nm 404.7 nm 435.8 nm 546.1 nm 578.0 nm (ave. of 577.0 nm and 579.1 nm)
Filters are available for all but the 365.0 nm line. Using the provided holder the desired filter should be positioned as close as possible to the aperture of the mercury light source. For each of the first order spectral lines, acquire phototube current versus retarding potential data.
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Planck.3
For the first order green line, acquire phototube current versus retarding potential data for each of the intensities provided by the intensity filter. Analysis: Use the DataStudio software to determine the stopping potential for each of your sets of data of phototube current versus retarding potential. Determine the stopping potential as accurately as possible and be sure to record a reasonable uncertainty in your values. Plot maximum photoelectron energy (KEmax = eVo) versus light frequency, . Remember to calculate and include error bars for the energy values. Applying conservation of energy to the photon-electron interaction described by Einstein yields: Ephoton = Eelectron Ephoton = KEelectron + BEelectron where KEelectron is the kinetic energy of the emitted electron and BEelectron is the energy required to overcome the binding energy of the electron to the metal. The work function,, is the minimum energy required to remove an electron from the metal surface being illuminated. Electrons that have this minimum binding energy will therefore have the maximum kinetic energy upon release. Thus and since
Ephoton = KEmax + Ephoton = h , hKEmax +
which can be written as
KEmax = h –
Does your graph of maximum photoelectron energy versus light frequency agree with this equation (Einstein’s equation of the photoelectric effect)? Draw the best-fit line and the maximum-fit line through your data. Assuming the Einstein equation is correct, determine values for h, Planck's constant, and, the work function, from your graph. Compare your value of h (and its error range) with the accepted value of 6.626 × 10–34 J·s or 4.136 × 10–15 eV·s. Based on your data acquired using the intensity filters, does KEmax depend on the intensity of the incident light? Does any parameter of the photoelectric effect depend on the intensity of the incident light? Interpret your answers to these questions in terms of Einstein’s explanation of the photoelectric effect.
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Planck.4
Detailed Description of Equipment and Procedure Light Source The source of light is a mercury discharge lamp. Light from the lamp is passed through an interference filter to select the desired wavelength. The light is then passed through a diffraction grating to further ensure that only the desired wavelength is illuminating the phototube. A neutral density filter is available to vary the intensity of the incident light without affecting the wavelength. mercury discharge lamp diffraction grating
interference filter
Phototube The phototube is housed in a light-tight container with an entrance port for the incident light. A mask on the entrance port reduces the exposure of the collector to the incident light. (Light incident on the collector causes a “reverse” current of opposite polarity to the current due to the photoelectrons that are being studied.) Electrical connections to the phototube allow the application of a voltage across the emitter and collector and allow measurement of the electric current flowing between the emitter and collector.
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Planck.5
entrance port
entrance mask
electrical connections for measuring current and voltage
Power Supply and Voltage Divider The Electro Industries Power Supply is set for the 0-15 V range, with the current control set at maximum. The output of the power supply is connected across an 85 rheostat which is being used as a voltage divider. The slider of the rheostat is set so that the voltage available across the rheostat slider and ground connections varies from 0 to 3 volts as the power supply voltage is varied from 0 to 15 volts. The rheostat slider and ground connections are used to apply the retarding potential to the phototube and are also connected to the Channel A Analog input of the Science Workshop 750 Interface. rheostat used as voltage divider
voltmeter to monitor retarding potential
power supply for retarding potential
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Planck.6
Keithley 616 Digital Electrometer The lead from the phototube that allows measurement of the emitter-collector current is connected to the input of the electrometer. The electrometer is set for “FAST” response, midrange sensitivity, and 10–6 A. The 0-1 V output available at the back of the electrometer is connected to the Channel A Analog input of the Science Workshop 750 Interface.
Science Workshop 750 Interface The Science Workshop interface connects to a PC via a standard USB cable and allows the data to be collected, processed, and saved using the DataStudio software loaded on the PC. The Channel A Analog input of the interface receives the retarding potential data via a CI-6503 voltage sensor. The Channel B Analog input of the interface receives the phototube current data also via a CI-6503 voltage sensor.
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Planck.7
Schematic Diagram of Component Connections
DataStudio Software As mentioned, the DataStudio software enables the experiment to be run via a PC. To prepare the interface: 1. Double-click the DataStudio icon on the PC desktop 2. Click “Create Experiment” 3. Click the CH A port on the display of the Interface, select Voltage Sensor, and click OK. 4. Set Sample Rate to 200 Hz and select Low (1) 5. Click the CH B port on the display, select Voltage Sensor, and click OK. 6. The Sample Rate should show 200 Hz. Select Med (10) The data acquisition system is now ready for use. Detailed Procedure To acquire data: 1. Arrange the light source, diffraction grating, and filter so that the desired spectral line is focussed and centred on the entrance port of the phototube holder. 2. If necessary, switch off the “ZERO CHECK” on the electrometer. 3. Click the “Start” button in the DataStudio software, and slowly and steadily increase the retarding potential by turning the voltage control on the Electro Industries power supply. 4. When the applied retarding potential reaches 3 V click “Stop” in DataStudio.
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Planck.8
Detailed Data Analysis Under “Displays” in the left-hand column of DataStudio double-click Graph, select Run #1 under Voltage CH B as the source, and click OK. The graph shows the electrometer output (proportional to phototube current) as a function of elapsed time. To obtain the desired graph of electrometer output versus retarding potential, in the “Data” section of the left-hand column of DataStudio click Run #1 under Voltage CH A and drag to the x-axis of the graph. The graph of electrometer output versus retarding potential should show a rapid and steady decrease followed by a long tail where the electrometer output is constant (see sample graph below). The stopping potential (the retarding potential required to just stop all of the emitted electrons from reaching the collector electrode) is the voltage at the start of the constant electrometer output tail. Alternatively, starting from high values of retarding potential and looking toward lower values, the stopping potential is the value of retarding potential at which the electrometer output starts to increase from the current value of the tail.
Phototube Current vs. Retarding Potential for Hg Green Line
approximate stopping potential
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Planck.9
Choosing appropriate scales allows accurate determination of the stopping potential:
stopping potential
The data can either be analysed within DataStudio or saved to a file for later analysis using a spreadsheet program such as Microsoft Excel. To analyse the data within DataStudio, note that the graph can be easily manipulated:
clicking and dragging the plot area near either of the axes allows adjustment of the starting values on the graph axes;
clicking and dragging the numbers on each of the axes allows the axes scales to be adjusted independently.
To save the data as a tab-delimited text file, click File, Export Data…, select Run #1 under Voltage CH B vs Voltage CH A, and click OK. Choose an appropriate location for the data file, give it a descriptive filename, and click Save. The data file can be opened in Excel for graphing and analysis at a later time.
