Physical Structure of Matter

Transcription

1 Physics of the Electron Physical Structure of Matter Planck s quantum of action from the photoelectric effect -01/05 What you can learn about External photoelectric effect Work function Absorption Photon energy Anode Cathode Principle: A photo-cell is illuminated with light of different wavelengths. Planck s quantum of action, or Planck s constant (h), is determined from the photoelectric voltages meas ured. Set-up of experiment P with electrometer What you need: Experiment P with electrometer Experiment P with amplifier Photocell, for h detection, with housing Interference filters, set of Interference filters, set of Experiment lamp Spectral lamp Hg 100, pico 9 base Power supply for spectral lamps Universal measuring amplifier Digital multimeter Screened cable, BNC, l = 30 cm Connecting cable, 4 mm plug, 32 A, red, l = 25 cm Connecting cable, 4 mm plug, 32 A, blue, l = 25 cm Electrometer Amplifier Adapter BNC socket/4 mm plug pair Power supply 12V AC/500 ma Complete Equipment Set, Manual on CD-ROM included Planck s quantum of action from the photoelectric effect P /05 Voltage of the photo-cell as a function of the frequency of the irradiated light. Tasks: To determine Planck s quantum of action from the photoelectric voltages measured at different wavelengths. PHYWE Systeme GmbH & Co. KG D Göttingen Laboratory Experiments Physics 221

2 Planck s quantum of action from photoelectric effect LEP -01 Related topics External photoelectric effect, work function, absorption, photon energy, anode, cathode. Principle A potassium photo-cell is illuminated with light of different wavelengths. Planck s quantum of action, or Planck s constant (h), is determined from the photoelectric voltages measured. Equipment Photocell, for h-det., w. housing Interference filters, set of Interference filters, set of Experiment lamp Spectral lamp Hg 100, pico 9 base Power supply for spectral lamps Mounting plate R, 16 cm 21 cm Universal measuring amplifier Digital multimeter Screened cable, BNC, l = 300 mm Connecting cord, l = 250 mm, red Connecting cord, l = 250 mm, blue Tasks To determine Planck s quantum of action from the photoelectric voltages measured at different wavelengths. Set-up and procedure The experimental set-up is as shown in Fig. 1. The interference filters are fitted one after the other to the light entrance of the photo-cell. The measuring amplifier is used in the following way Electrometer R e Amplification: 10 0 Time constant: 0 Voltmeter: DC 2V The high-impendance input of the measuring amplifier is discharged via the zero button between measurements. Theory and evaluation Half of the inside of the high-vacuum photo-cell is a metalcoated cathode. The anular anode is opposite the cathode. Fig. 1: Experimental set-up for determining Planck s quantum of action. PHYWE series of publications Laboratory Experiments Physics PHYWE SYSTEME GMBH & Co. KG D Göttingen P

3 LEP -01 Planck s quantum of action from photoelectric effect If a photon of frequency f strikes the cathode, then an electron can be ejected from the metal (external photoelectric effect) if there is sufficient energy. Fig. 2: Voltage of the photo-cell as a function of the frequency of the irradiated light. Some of the electrons thus ejected reach the (unilluminated) anode so that a voltage is set up between anode and cathode, which reaches the limiting value U after a short (charging) time. The electrons can only run counter to the electric field set up by the voltage U if they have the maximum kinetic energy, determined by the light frequency, hf A m 2 v2 (Einstein equation), where A = work function from the cathode surface, v = electron velocity, m = rest mass of the electron. Electrons will thus only reach the anode as long as their energy in the electric field is equal to the kinetic energy: eu m 2 v2 with e = electron charge = As An additional contact potential f occurs because the surfaces of the anode and cathode are different: eu f m 2 v2 If we assume that A and f are independent of the frequency, then a linear relationship exists between the voltage U (to be measured at high impedance) and the light frequency f: 1A f2 U e h e f If we assume U = a + bf to the values measured in Fig. 2 we obtain: h = (6.7 ± 0.3) Js Literature value: h = Js. 2 P PHYWE series of publications Laboratory Experiments Physics PHYWE SYSTEME GMBH & Co. KG D Göttingen

4 Planck s quantum of action from photoelectric effect with electrometer amplifier LEP -05 Related Topics External photoelectric effect, work function, absorption, photon energy, anode, cathode. Principle A photocell is illuminated with monochromatic light of different wavelengths. Planck s quantum of action, or Planck s constant h, is determined from the photoelectric voltages measured. Equipment Photocell, for h-det., with housing Interference filters, set of Interference filters, set of Experiment lamp Spectral lamp Hg 100, pico 9 base Screened cable, BNC, l = 750 mm Connecting cord, l = 250 mm, red Connecting cord, l = 250 mm, blue Power supply for spectral lamps Digital multimeter Electrometer Amplifier Adapter, BNC socket / 4 mm plug pair Power supply 12 V AC / 500 ma Support rod, 100 mm with axial hole Connecting plug, pack of to bring the electrometer amplifier entrance to ground potential into the support rod with hole and to plug a connecting plug into the socket of the electrometer amplifier entrance. If you hold the rod firmly in your hand, your body is brought to the same potential as the experiment and touching the connecting plug with the rod will discharge the amplifier's entrance properly. Otherwise the electrostatic charge of your body will cause an influence charge on the amplifier's entrance in the moment of unplugging the ground cable from the electrometer. Set the digital multimeter's range to 2 V. Set an interference filter on the entrance of the photocell housing and the lamp right in front of it. Discharge the electrometer amplifier entrance and open the light entrance of the photocell housing. Wait until the voltage reading is steady or if not, discharge again. Note down the measured voltage and the filter's wavelength. Repeat with the other filters. The frequency f of the light is calculated by f = c/l with light speed c = m/s. Tasks Determine Planck's quantum of action from the photoelectric voltages measured at different wavelengths. Set-up and Procedure Set up the equipment as seen in Fig. 1. Connect the electrometer amplifier as seen on Fig. 2. To avoid problems with electrostatic influence, you should plug the end of the cable used Fig. 2: Connection of the electrometer amlpifier Fig. 1: Experimental set-up PHYWE series of publications Laboratory Experiments Physics PHYWE SYSTEME GMBH & Co. KG D Göttingen P

5 LEP -05 Planck s quantum of action from photoelectric effect with electrometer amplifier Theory and evaluation Half of the inside of the high-vacuum photo-cell is a metalcoated cathode. The anular anode is opposite the cathode. If a photon of frequency f strikes the cathode, then an electron can be ejected from the metal (external photoelectric effect) if there is sufficient energy. Some of the electrons thus ejected reach the (unilluminated) anode so that a voltage is set up between anode and cathode, which reaches the limiting value U after a short (charging) time. The electrons can only run counter to the electric field set up by the voltage U if they have the maximum kinetic energy, determined by the light frequency, hf A m 2 v2 (Einstein equation), where A = work function from the cathode surface, v = electron velocity, m = rest mass of the electron. Electrons will thus only reach the anode as long as their energy in the electric field is equal to the kinetic energy: Fig. 3: Voltage of the photo-cell as a function of the frequency of the irradiated light. eu m 2 v2 with e = electron charge = As An additional contact potential f occurs because the surfaces of the anode and cathode are different: eu f m 2 v2 If we assume that A and f are independent of the frequency, then a linear relationship exists between the voltage U (to be measured at high impedance) and the light frequency f: 1A f2 U e h e f If we assume U = a + hf for the values measured in Fig. 3 we obtain: h = (6.7 ± 0.3) Js Literature value: h = Js. The strongest emission lines of mercury in the lamp are (see Fig. 4): 366 nm (6 1 D 2 S 6 3 P 0, 6 3 D 1,2,3 S 6 3 P 0 ) nearly invis. violet 405 nm (7 3 S 1 S 6 3 P 2 ) violet 436 nm (7 3 S 1 S 6 3 P 1 ) turquois 546 nm (7 3 S 1 S 6 3 P 0 ) green 578 nm (6 1 D 2 S 6 1 P 1, 6 3 D 1,2,3 S 6 1 P 1 ) yellow Fig. 4: Atomic spectrum of mercury 2 P PHYWE series of publications Laboratory Experiments Physics PHYWE SYSTEME GMBH & Co. KG D Göttingen