Photoelectric Effect

RIT alum

October 6, 2011

AbstractThe emission of electrons from matter upon which electromagnetic waves are incident

is called the photoelectric effect. This phenomenon of emitted electrons occurs only abovea threshold frequency of light. The frequency of the incident photons, and thus theirenergy, affect the kinetic energy of the emitted photoelectrons. With this experiment,the ratio of Planck’s constant to the charge of an electron, h/e, has been experimentallycalculated. Also investigated was the independence of the stopping potential on theintensity of the incident light.

Introduction

The particle-like properties and behavior oflight can be seen using the photoelectric ef-fect. It can be determined from the rangeof wavelengths of light used in the experi-ment, that the energy of a photon is inde-pendent of the intensity of the light—onlythe frequency of the light matters. From thedata collected during this experiment the ra-tio h/e, Planck’s constant to the charge onan electron, was found.

Theory

Electrons can be emitted from the surface ofa material (in this case, metal) when theyare bombarded with energy that is greaterthan the work function φ for the metal. Suchelectrons are called photoelectrons. The ki-netic energy of the photoelectron can then

Figure 1: The photoelectric effect experi-ment vacuum and simple circuitry.

be found knowing that it is equal to thework function subracted from the photon’senergy.

K = Ep − φ (1)

Figure 1 shows the apparatus used in this ex-periment. The photoelectrons are producedwhen light is incident upon the cathode

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metal surface located within the tube.

The electrons are emitted from the metalwith some kinetic energy K. When the elec-trons travel to the anode, a current is mea-sured with the ammeter. If the voltage isincreased to be large enough, the flow ofelectrons is halted, and thus no current isproduced. This voltage is called the stop-ping potential, Vs, and is related to the ki-netic energy by the charge of the electron:K = eVs.

As proposed by Max Planck, the energy oflight of a frequency ν is hν, where h is hisconstant. Now knowing that the kinetic en-ergy of the electron is equivalent to the stop-ping potential, Equation 1 gives:

eVs = hν − φ (2)

Since the intensity of the light does not af-fect the kinetic energy of the photoelectrons,the stopping potential remains constant fordifferent intensities of light. And becausethe stopping potential depends only on thewavelength of the light, or frequency, thenthe quantum theory claim is confirmed thatphoton energy is equivalent to hν. Aftermeasurements are recorded, the plot of Vsas a function of ν should show a straightline with slope h/e and an intercept of−φ/e.

Vs = (h/e)ν − φ/e (3)

From this plot alone, both the work func-tion φ and the ratio of Planck’s constant toelectron charge h/e can be found.

Procedure

In this experiment, a mercury vapor lampwas chosen for a light source since thespectral emission lines of mercury are wellknown. The light entered the monochroma-tor which has an adjustable grating to allowa specific wavelength to continue throughto the output slit, as can be seen in Fig-ure 2. At this output slit was mounted anevacuated photocell, a Leybold Heraeus part55877.

Before the experiment was started, the UVfilter was checked and double-checked to bein place. The mercury lamp produces ul-traviolet light which was blocked with plex-iglass.

First, the mercury vapor lamp was lined upwith the input slot. Then the grating anglewas adjusted until the green line was alignedwith the exit slit via an index card, visually.This was confirmed and optimized by ad-justing the grating angle slightly to find themaximum photocurrent around that pointwith the ammeter.

A direct current power supply was set to 4V and connected to a voltage divider boxto allow for precise adjustment between 0and 4 V; this is the voltage supply shown inFigure 1. Reversing the leads gave a negativesupplied voltage. All voltage measurementswere taken with a Fluke DVM.

Starting at 4 volts, the Keithley electrome-ter was set up for current measurement inamps. The electrometer was quite fussy,and measurements were taken as far awayas possible with minimum movement. Pho-tocurrent versus applied voltage values were

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recorded in an Excel spreadsheet from 4 V to−4 V with smaller steps between 2 and −2V. These measurements for the green linewere repeated for the yellow, blue, violet,and both ultraviolet lines.

Next, the blue line was set with themonochromator and data was taken as be-fore. After this run without a filter, theprocedure was repeated using a filter of op-tical density 0.3 placed between the lightsource and the entrance to the monochro-mator. This procedure was repeated oncemore, but with a filter of optical density 0.5.

Analysis

For each wavelength of light, a plot wasmade of the photocurrent as a function ofvoltage. From these plots, the stopping volt-age can be determined. The stopping poten-tial Vs is the kink in the plot. Although Vscan be visually determined from the plots, itis more accurate to use the method of inter-secting tangents. A tangent was fit to thedata both above and below the kink (seeFigure 3), and the intersection of the tan-gents was taken to be the stopping potential.This method of analysis was then repeatedfor the yellow, blue, violet, first ultraviolet,and second ultraviolet data, and the inter-section of the fit line tangents was found foreach.

For the intensity dependence, photocurrentwas plotted versus accelerating voltage andthen the method of intersecting tangent lineswas used again to determine the stoppingvoltage.

Results

To determine the value of h/e, Equation 3is used. Plotting Vs versus the frequency ν,the slope was then found with uncertainty,as seen in Table 1. The stopping voltagesfound were plotted in Figure 4.

Theoretically the value of h/e was calculatedto be 4.14 × 10−15V s. Experimentally, thevalue found was (3.9 ± 0.3) × 10−15V s bythe linear fit of the line on the graph donein gnuplot. The value calculated experimen-tally agrees with the theoretical value of h/ewithin the uncertainty.

For the intensity dependence, Vs was foundfor the blue line by way of insecting tangentlines as plotted in Figure ??. This was donefor the light with with no filter, a 0.3 filter,and a 0.5 filter. The stopping voltages arelisted in Table 2 with uncertainties.

The photocurrent data for the filters werethen normalized by the largest value for eachfilter. Each new set of data points wasthen plotted on one graph, Figure 5. All ofthe normalized data collapsed onto a singlecurve. This is conclusive proof that chang-ing the intensity of the light changes onlythe magnitude of the photocurrent in direct

ν (1014Hz) Vs (V)

Yellow 5.18 0.35Green 5.49 0.41Blue 6.88 0.89

Violet 7.41 1.071st UV 8.21 1.392nd UV 9.58 2.08

Table 1: Here are the results of the Photo-electric Stopping Voltage versus Frequency.

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proportion, and the energy of the emittedphotoelectrons is unchanged. The intensitydetermines the number of ejected electrons,not their energy.

References

L. Barton, Photoelectric Effect, March2007.

http://www.phy.davidson.edu/

ModernPhysicsLabs/hovere.html

http://galileo.phys.virginia.edu/

classes/252/photoelectric_effect.

html

Vs (V) ∆Vs (V)

No filter 0.90 0.040.3 filter 0.91 0.130.5 filter 0.92 0.08

Table 2: Stopping potentials for the bluemercury line with intensity variance.

Figure 2: This is the monochromator for theexperiment. The dotted line traces the pathof the light. A crank allows for the gratingangle to be changed, which in turn changesthe wavelength of the light arriving at theexit slit.

Figure 3: Photocurrent versus voltage forgreen line.

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Figure 4: Plot of the stopping potential asa function of the frequency of the incidentlight. The slope of the linear fit was takento be the constant h/e.

Figure 5: Normalized photocurrent of filterdata as a function of accelerating voltage.

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