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University of Oulu Student Laboratory in Physics Laboratory Exercises in Physics 2 PHOTOELECTRIC EFFECT 1. Introduction The photoelectric effect is one of the processes through which the light and the matter interact. When a metal surface is illuminated with a suitable electromagnetic radiation, generally with the ultraviolet or the visible light, it emits electrons. The photoelectric effect was first observed in 1887 when Heinrich Hertz discovered that electrodes illuminated with the ultraviolet light create sparks more easily. Numerous other scientists made observations on the photoelectric effect in late 19 th and early 20th centuries, but these observations could not be understood using classical physics. In 1905, Albert Einstein published a paper applying Planck’s idea of light quanta to the photoelectric effect’s experimental data. Einstein explained the observations of the photoelectric effect assuming that the light energy was carried in discrete quantized packets. Study of the photoelectric effect was a remarkable stage in the development of the quantum theory. It helped to understand better the quantum nature of light and electrons. In 1921, Einstein was awarded the Nobel Prize of physics for his discovery of the law of the photoelectric effect. In this laboratory exercise, the theory and the measurements of the photoelectric effect are studied. The photoelectric effect is examined especially as one proof of the waveparticle dualism and the quantum nature of light. By measuring the stopping potential as a function of the frequency the Planck’s constant and the work function of the cathode material used are determined. 2. Studies of the photoelectric effect 2.1 Structure of the measurement apparatus Fig. 1 shows a typical apparatus used to study the photoelectric effect. The apparatus includes the following components: Light source resembles a black body, e.g. it emits radiation in the wide spectral range also in the regions of visible or ultraviolet light, which are important in the case of the photoelectric effect. For example a light bulb can be used. In some experiments the intensity of the light source is adjustable. 1 2 PHOTOELECTRIC EFFECT Monochromator is used to choose the desired wavelength from the continuous spectrum of the light source. The essential device is a rotating grating or a prism, which directs only one wavelength at a time to an output slit. Photo cell is a vacuum tube with quartz windows and two electrodes. Quartz is used as the window material because it is transparent also for the UV light. The cathode (C) is a plate coated with some suitable material which emits electrons when illuminated with the light coming from the monochromator. The emitted electrons are called photoelectrons. The anode (A) can be for instance a platinum spiral. External current circuit including a tunable power source, an ammeter (AM) and a voltmeter (VM) connects the electrodes. With the tunable power source the anode’s potential respect to the cathode can be adjusted in the range (-V, +V). The sensitive ammeter is capable to measure the small currents called photocurrents flowing in the circuit and the voltmeter measures the potential difference between the electrodes. Photo cell A Grating hf C Monochromator AM Adjustable light source VM Tunable power source Figure 1 An apparatus used to study the photoelectric effect. 2.2 The intensity experiment In the intensity experiment the photocurrent Iph is measured as a function of the light source’s intensity I. The wavelength of the light is constant during the measurement. The anode is held at a sufficiently high potential compared to the cathode so that all the electrons emitted from the cathode reach the anode. The observed photocurrent Iph is presented as a function of the intensity I of the light source in Fig. 2. University of Oulu Student Laboratory in Physics Laboratory Exercises in Physics 2 3 Iph I Figure 2 The photocurrent as a function of the intensity of the light source. The result of the intensity experiment is not surprising. If the light causes the cathode material to emit electrons it can be understood that the number of the emitted electrons is directly proportional to the amount of the light, e.g. the intensity. According to the classical theory the photoelectric effect can be explained by assuming that the oscillating electric field of the incident light wave can occasionally knock an electron out of the cathode’s surface. The more intense light means the greater amplitude of the electric field, which can release more electrons than the field with the weaker amplitude. 2.3 The frequency experiment In the second experiment the intensity of the light source as well as the potential difference between the electrodes are held constant. The photocurrent Iph is measured as a function of the light frequency f. The graphs in Fig. 3 represent the results achieved using three different light source’s intensities (I 1 > I 2 > I 3 ) . Iph I1 I2 I3 f f0 Figure 3 The photocurrent as a function of the frequency with different intensities of the light source. According to the classical wave theory, the photoelectric effect should be observed at any frequency of the incident light whose intensity is large enough. The result of the frequency experiment shows surprisingly that there is a threshold frequency f0 characteristic to the cathode material below which the photoelectric effect does not 4 PHOTOELECTRIC EFFECT occur no matter how intense the light. With the greater intensity the current increases more steeply when the frequency is increased, but no current is flowing if the frequency is below f0. Based on the classical theory some kind of frequency dependence of the current can be expected. The electrons inside the matter were thought to move periodically and so the electromagnetic radiation with a frequency similar to the frequency of the electronic motion would release more electrons. However, the observed threshold frequency can’t be explained with this model. 2.4 The potential difference experiment In the third experiment the photocurrent is measured as a function of the potential difference VAC between the electrodes. Fig. 4 shows the resulting photocurrent Iph as a function of the potential difference VAC for a light of constant intensity for three different frequencies ( f1 > f 2 > f 3 > f 0 ) . Fig. 5 shows the photocurrent as a function of the potential difference for a light of constant frequency and three different intensities ( I1 > I 2 > I 3 ). When the potential difference is sufficiently large and positive all the electrons emitted from the cathode are collected to the anode. So, in the figures 4 and 5 the curves level off at large positive values of voltage VAC and the photocurrent obtains a saturation value. Iph f1 1 -V0 f2 f3 2 -V0 3 -V0 VAC Figure 4 The photocurrent for three different light frequencies as a function of the potential difference between the anode and the cathode. If the polarity of the power source is reversed, the cathode is at a higher potential than the anode and the potential difference VAC is negative. Now the electrical force on the electrons is toward the cathode. If the magnitude | VAC | of the potential difference is not too great, a part of the electrons can still reach the anode and the photocurrent is observed. However, when the magnitude of the potential difference is increased, the current decreases. When the potential difference becomes negative enough the current University of Oulu Student Laboratory in Physics Laboratory Exercises in Physics 2 stops. The value V0 of potential difference required to stop all the electrons is called the stopping potential. Iph I3 I2 I1 VAC -V0 Figure 5 The photocurrent for a constant light frequency for three different light intensities as a function of the potential difference between the anode and the cathode. From the curves in the Fig. 4 we see that the stopping potential V0 increases if the frequency of the incident light is increased. When examined more precisely it turns out that the stopping potential is linearly proportional to the frequency. Fig.6 shows the stopping potential as a function of V0 the frequency. Using the classical wave model of the light this dependence between V0 and f could not be understood. From the Fig. 5 it can noticed, that if the intensity of the light is increased while the frequency is kept constant, the current levels off f at a higher current value, showing that f0 Figure 6 The stopping potential as a more electrons are being emitted per function of the light’s frequency. time. But the stopping potential V0 remains the same. This can’t be explained on the basis of classical physics. When the intensity is increased the electrons should gain more energy and so the stopping potential should increase. 2.5 Einstein’s quantum model Einstein assumed that the light consists of small energy packets called light quanta or photons. These photons resemble particles although they don’t have a rest mass. They 5 6 PHOTOELECTRIC EFFECT have a momentum and they can collide like any particles. The energy of a photon is directly proportional to its frequency f so that the proportional constant is Planck’s constant h, e.g. hc E = hf = , (1) l where c is the velocity of light and l is the wavelength. The results of the studies considered above can easily be understood with Einstein’s photon model. A photon arriving to the cathode collides with an electron, which absorbs the energy of the photon. Greater intensity in the intensity experiment means a greater number of photons per second absorbed and thus more electrons are emitted per second and the photocurrent increases. In the frequency experiment the frequency of the light, e.g. the energy of the photons arriving to the cathode was decreased until the threshold frequency, below which no electrons are emitted, was achieved. The electrons at the surface of the cathode are more loosely bonded than the electrons deeper in the cathode material. The minimum amount of energy needed to remove an electron from the cathode is called the work function W . With Einstein’s quantum model the existence of the threshold frequency f 0 is understandable. The photon with the threshold frequency has just enough energy for removing the electron from the cathode, e.g. hf 0 = W . (2) The photons with a frequency lower than f 0 do not have enough energy to remove electrons and no photocurrent is flowing. The work function is characteristic to the cathode material. Some materials, for example cesium and potassium have so small work functions, that the quanta of visible light are capable to release electrons from them. When a photon collides with an electron of the cathode it gives all its energy to the electron. If this energy is greater than the work function the electron escapes from the cathode. Einstein applied the conservation of the energy and stated that the maximum kinetic energy K max of the emitted electron is the energy hf gained from the photon minus the work function W, e.g. K max = hf - W . (3) In the potential difference experiment only the electrons having sufficiently high kinetic energy reach the anode when the polarity of the power source is reversed and the potential difference VAC becomes negative. When the potential difference between the electrodes is set to the value - V0 the most energetic electrons leave the cathode with the kinetic energy K max and arrive to the anode with zero kinetic energy. As the electron moves from the cathode to the anode, the electric field does the work - eV0 University of Oulu Student Laboratory in Physics Laboratory Exercises in Physics 2 on the electron. According to the energy conservation law the work done on the electron is equal to the change in the electron’s kinetic energy and so we get - eV0 = 0 - K max Þ K max = eV0 , (4) where e is the unit charge. By combining the equations (3) and (4) the photoelectric law eV0 = hf - W (5) is obtained. From the photoelectric law it can be seen that the stopping potential is linearly dependent on the frequency according to the equation W h V0 = f - 0 . (6) e e 3. Measurement equipment The actual measurement equipment used in this study is shown in Fig. 7. The light source behind the monochromator is a bulb. The monochromator consists of entrance and output slits as well as of plane and spherical mirrors and two reflecting gratings enclosed in a box. The gratings are placed onto the same axis so that by rotating the axis with a selector either one of the gratings can be chosen. In this study the grating operating in the visible region is used. On the side of the box there is a crank. By turning the crank the chosen grating rotates and only one wavelength at a time is directed to the output slit. The wavelength of the monochromatic light in nanometers can be seen from the scale on the top of the box. The photo cell is placed inside a metallic casing, which has a slit for the light coming from the monochromator. The cell includes a cathode plate coated with potassium and a platinum spiral anode. The measurements of this exercise resemble the potential difference experiment discussed above. The photocurrents are measured as a function of the potential difference between the anode and the cathode. The external current circuit includes a power source connected to a potentiometer for tuning the potential difference between the electrodes, a voltmeter for measuring the potential differences and a very sensitive ammeter for measuring the small photocurrents. In this study the polarity of the power source is reversed compared to that shown in the Fig. 1, e.g. the voltage VAC is negative throughout the measurements. 7 8 PHOTOELECTRIC EFFECT Grating selector Crank Potentiometer Monochromator Ammeter Power source Voltmeter Photo cell Figure 7 The measurement equipment. 4. Exercises Answer the following questions before coming to the laboratory: 1. Explain shortly what is measured in the a) frequency and b) potential difference experiment. What kind of observations in these experiments could not be explained using the classical physics? 2. What kind of explanations to the observations mentioned above gave Einstein’s quantum model? 3. Why must the measurement equipment include the monochromator? How does the monochromator work? 5. Measurements and analysis 5.1 Measurements 1. Preparations: Check the circuit with the tutor. Turn the light bulb on. Prepare the Valokenno monochromator for the measurements with the tutor. First, check that the grating operating at the visible region is chosen. Then choose the first wavelength (around 400 nm) by rotating the grating with the crank to the right position. Check that the potentiometer is set to zero value and turn the power source on. Then turn also the ammeter and the voltmeter on and check on the basis of the current and the voltage readings that the light hits well to the photo cell. Set the potential difference first to the value around -1.5 V. Monokromaattori University of Oulu Student Laboratory in Physics Laboratory Exercises in Physics 2 2. Measuring the photocurrents: Choose five wavelengths in the range 360-520 nm to be used in the measurements and measure the (VAC, Iph)-curves with each wavelength by tuning the potential difference from the starting value to zero in suitable steps and register the corresponding photocurrents. When the photo cell has been used a small amount of potassium has drifted to the anode. During the measurement the light can thus release electrons also from the anode. This causes that with the first, quite large negative values of the potential difference VAC a small photocurrent is flowing from the anode to the cathode. So, the first currents observed are negative. The actual (VAC, Iph)-curves observed in this study thus resemble the curve shown in Fig. 8. Iph From the Fig. 8 it can be seen that = measurement points different tuning steps of the voltage with 30 mV steps should be used in the measurements. = measurement points When the potential difference’s with 100 mV steps magnitude is large and the photocurrent is negative the currents can be register in 100 mV steps. The VAC -V0 most interesting part of the curve is the region where the current is near Figure 8 An example (not to scale) zero. So, in this region a smaller of an observed (VAC, Iph)-curve. tuning step around 30 mV can be used. When the current has changed positive and begins to increase more steeply 100 mV is again a suitable tuning step. Because the photocurrents are very small the measurement equipment is extremely sensitive especially to various electrical perturbations. For example the charges on the clothes can disturb the measurement. Therefore, the clothes made of easily electric synthetic fibres should be avoided. It is also recommended to move as few as possible during the measurements in order to avoid the generation of the static electricity. The amount of the background light should be kept same throughout the measurements. 5.2 Analysis 1. The (V AC , I ph ) -graphs and determining the stopping potentials: Present the observed photocurrents in the (V AC , I ph ) -coordinate system and draw a curve representing the photocurrent as a function of the potential difference after the measured points with every wavelength used. Determine the corresponding stopping potentials from the curves. 9 10 PHOTOELECTRIC EFFECT 2. Determining the Planck’s constant and the work function: Change the used wavelength values to the frequencies and show the determined stopping potentials as a function of the frequency in the ( f ,V0 ) - coordinate system. Fit the straight line represented with the Eq. (6) to these ( f , V0 ) -points by using the least squares method. Determine the slope and the intercept of the line with their error limits and calculate the Planck’s constant (in units Js) and the work function (in units eV) with their absolute and relative error limits. Compare the results with the values given in the literature. 3. Considering the possible influence of the thermionic emission: The electrons on the surface of the cathode create a so called electron gas where electrons can move almost freely in the cathode material. The electrons can escape from the cathode’s surface as a result of the thermionic emission which is caused by heating the material so that the kinetic energies of the electrons increase sufficiently high. Has the thermionic emission any influence to the results of this study? Give also the reasons to your answer. (Hint: The kinetic energies of the electrons are distributed according to Maxwell-Boltzmann distribution.) Remember to attach the answers of the exercises and to the thermionic emission question above as well as the (V AC , I ph ) - and the ( f ,V0 ) - graphs to your report. UNIVERSITY OF OULU Student: ___________________________ STUDENT LABORATORY IN PHYSICS Date of measurements: ____ / ____ 20___ Laboratory Exercises in Physics 2 Tutor: _____________________________ MEASUREMENT FORM PHOTOELECTRIC EFFECT l=nm U [V] I [pA] l=nm U [V] I [pA] l=nm U [V] I [pA] l= nm U [V] I [pA] Tutor’s signature _________________________________ l=nm U [V] I [pA]