FYSP106/1 PHOTOELECTRIC EFFECT

Transcription

1 FYSP106/1 PHOTOELECTRIC EFFECT In the exercise you ll define the ratio of the Planck s constant to the unit of charge h/e. The light source is a gas-discharge tube in connection of a slit monochromator used to select light with different wave lengths. The monochromatic light ejects electrons from the cathode of a s.c. photocell and they are collected to the anode of the device. The maximum energy of the photo-electrons will be defined by stopping them with an electric field (stopping potential) applied between the cathode and the anode. The stopping potential displayed as a function of the frequency of the light is in principle a straight line with the linear coefficient corresponding to h/e. Subject related to this work has been discussed in: Alonso - Finn: Fundamental University Physics, Vol. III Quantum and Statistical Physics pages Ohanian: Physics, Second edition expanded, pages PHOTOELECTRIC EFFECT Light quanta, photons, bombarding a metallic surface can release charge carriers, free electrons from the metal with following three, observed properties: The number of ejected electrons (photo current) is proportional to the intensity of the light beam (fig. 1a). The maximum kinetic energy of the electrons is directly proportional to the frequency of the light. The sensitivity of a photocell (recording device), photo current obtained, depends on the material of the metallic, cathode exposed to the light, as well, as shown in fig. 1b. for alkaline metals, qualitatively. The maximum kinetic energy of the (non relativistic) ejected electrons can be expressed with 1 mv 2 = E max kin = hν eφ, (1) 2 where h is the Planck s constant, ν frequency of the light and eφ, the work function of the metal (minimum energy needed to release an electron from the surface). Using max equation (1) the ratio h/e can be determined measuring E kin for several light frequencies.

2 - 2 - Sensitivity Figure 1. a) Photoelectric current as a function of potential between anode and cathode for three different light intensities. b) Spectral sensitivity of light cells with alkaline -metal cathodes. The equipment used in this exercise is described in fig. 2, where the monochromatic light illuminates the cathode of the light cell. The cathode is coated with a metal with a known work function of equation (1). The current of the photo electrons arriving to the anode is measured with a sensitive pa-meter. The potential difference V between the cathode and anode is tuneable and slows down the electrons with an energy ev. When the maximum kinetic energy of the ejected electrons is ev no current is observed. In fact the potential field in the equipment is arranged so that a small current of electrons released from anode to cathode is present and that the saturation of this current (fig. 7) is used to define the stopping voltage V. U - A K + V pa Figure 2. Schematic diagram of the equipment. The geometry of anode (A) and cathode (K) depends on the photocell used.

3 - 3 - If V s is the voltage preventing any electron just to leave the cathode, then Eq. (1) reads now max s E kin V e =. (2) e V s = hν eφ. (3) V s displayed as a function of ν is a straight line with the linear coefficient equal to h/e. Position V s = 0 gives the minimal frequency ν = ν 0 = eφ/h needed to remove a single electron from the cathode i.e. minimal energy of a single photon needed to counterbalance the work function (energy of least bound electrons). Introduced by Einstein eq. (1) is valid strictly, only at the absolute zero temperature (T = 0 K), when the thermal motion is non existent. In practise our equipment is not sensitive enough to register the uncertainty (diffuse character of ν 0 ) caused by the thermal motion. Because of the working principle of the photocell used, the work function of the cathode, alone, does not define Vs. In fact the ejected electrons feel the potential difference caused by the work functions of cathode and anode materials, both. Schematically this is shown in fig. 3., where eφ C is the energy needed to release an electron from the cathode and eφ A the energy needed to release a secondary electron (used for observations) from the anode. Figure 3. Definition of the closed loop of electrons between the anode (A) and cathode (C). In fig. 3, V is the tuneable, external potential between the anode and cathode and V the stopping potential felt by the secondary electrons. In practice the potential loss caused by the components (wires, electrodes etc.) is neglected here. Conservation of energy means that the work done to/by an electron during the closed loop in fig. 3 must be zero: e ΦC + ev + eφ A ev ' = 0 V V ' = ( Φ A ΦC ). (4)

4 - 4 - Term Φ A - Φ C is called the contact-potential difference and usually the metals are selected so that Φ C < Φ A. Equation (4) is valid for each frequency, so it must be V = 0, when the photoelectrons have energy enough just to release secondary electrons from the cathode. This condition means that the character of V changes from decelerating to accelerating potential. This corresponds to the saturation of the pa-current measured. Normalising the (pa)-curves measured for various frequencies to a single, common saturation point one finds for the contact-potential difference V' = Φ A - Φ C. Now equations (1) and (3) give stopping potential corrected with the contact-potential difference which is equivalent to Hence ev V ( ) ' = V + Φ Φ, s s A C ' 1 s = mv 2 = hν eφc, 2 V ' h s = ν Φ A. (5) e So, if you plot values of the uncorrected stopping potential V s as a function of frequency ν, you ll obtain a straight line with the linear coefficient equal to h/e. The ordinate at ν= 0 corresponds now to the work function of the anode instead of the one of the cathode (explain why). The contact-potential difference can not be defined (why?), but a rough estimate for the work function of the anode is possible to achieve (explain why and give possible sources of error). 2. EQUIPMENT Figure 4. Experimental arrangement.

5 - 5 - The key element of the monochromator (MP-1018B) is a blaze-type reflection grade (fig. 5). A reflection grade enhances certain multiples of reflected wavelengths and kills other ones based on the principle of interference. Together with diffraction the grade is a mirror for the enhanced rays so the reflected angle equals the entrance one. polychromatic light diffracted light α β d Figure 5. "Blaze"-grade The direction of the grade can be controlled manually or with a stepping motor. The reflected light can be read with an accuracy of one tenth of a nanometer. The widths of the openings for incoming and outgoing light can be tuned with an accuracy of micrometers. The light source is an Hg/10 gas-discharge tube, which has strongest intensities at wavelengths of 313, 365.0, 404.7, 435.8, 546.1, and nm. One can also use the Cd/Hg tube, which gives additional lines. Due to the strong ultraviolet background radiation of the tubes, try to avoid looking directly to the tubes. The power source of the photocell is a battery equipped with a potentiometer to tune the voltage desired. The current of the secondary electrons is measured with sensitive pameter. The stopping voltage can be measured with a general-purpose digital meter. 3. MEASUREMENTS In order to check the calibration of the monochromator locate first the spectral lines of the Hg/10 light source using the given reference spectrum. Using several different wavelengths measure the current of the secondary (photo)electrons as a function of the stopping potential. Work according to following steps: 1. Switch the light source on and let it stabilise for few minutes. 2. Set the width of the opening in the monochromator to about 300 µm.

6 Use the Keithley 485 pa-meter (brown, digital instrument) with Auto scale to measure the current. 4. Optimise the incoming light intensity using one strong line by searching for a maximum current reading. Here the sensitivity should be on 10-9 A scale. With the same method, find out accurate values for the wavelengths of the spectral lines. 5. Using at least seven different lines (from Hg or Cd) measure current vs. stopping voltage curves. Start from zero voltage and continue with 0.1 V increments until reaching and monitoring the linear part of the current. Close to this point use increments of e.g V. intensity Figure 6. Spectrum of a Hg - light source. 4. ANALYSIS OF RESULTS Plot the current as a function of the potential for each wavelength used. An example how to estimate the stopping potential for each frequency is given in fig. 7. Display the stopping potential as a function of the frequency. Calculate a least squares fit to the data points and include the result (with error) into the figure. Give your experimental value of h/e with error and compare it to values in literature. Write a report explaining theory, equipment, measurements and results of the work. In the report, also answer the following questions:

7 - 7-1) With what materials does the photoelectric effect occur? 2) Can the stopping potential be negative? 3) What determines the critical frequency, below which the phenomenon doesn t happen? 4) What can you say about the determination of the work function with the device given, if the anode is made of platinum and the cathode of potassium? Figure 7. Estimation of the stopping potential.