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1 Umeå University Department of Physics Leif Hassmyr 2012-02-05 FRANCK-HERTZ EXPERIMENT 2 The Franck–Hertz Experiment Background of the Experiment In 1912 Niels Bohr developed his model of the atom, in which electrons are allowed only certain discrete orbits. Transitions between these orbits may take place only when the atom absorbs or emits quantized packets of energy E = hc . This explains the spectral lines given off by an excited element, such as described by Rydberg’s formula for the series of spectral lines for hydrogen. In 1914 James Franck (American (German-born) physicist, 1882-1964) and Gustav Hertz (German physicist, 1887-1975, nephew of Heinrich Hertz, who discovered radio waves) reported an energy loss occurring in distinct “steps” for electrons passing through mercury vapour, and a corresponding emission of the ultraviolet line (λ=254 nm) of mercury. A few months later, Niels Bohr recognized this as evidence confirming his model of the atom. The Franck-Hertz experiment is thus a classic experiment confirming quantum theory and earning them the 1925 Nobel Prize in Physics. Task: To perform Franck-Hertz experiment and from it determine excitation energy of mercury (Hg) and neon (Ne). Theory The experiment is performed by electrons emitted thermally from a cathode filament (K). Then they are accelerated between the cathode (K) and anode grid (A) using an applied voltage, UB. Between the anode grid and the collector plate (M) is a low reverse voltage, UM=1.5 V, to stop electrons whose kinetic energy is below a certain value. The substance to be examined, in our case, mercury / neon, is contained in the tube in gaseous form,. Current, IM from the collector plate (M) is studied as a function of the applied acceleration voltage, UB. The curve thus obtained exhibits a series maxima and minima, which must be explained. 3 Fig. 1 Circuit diagram for the Franck-Hertz experiment If the kinetic energy of the electrons is too small to excite the atoms in the vapour, the electrons collide elastically and lose almost no energy, as required by the conservation of energy and momentum, and a large current is detected at plate M. If, on the other hand, the electrons gain just enough kinetic energy to equal the energy level transition of the atoms, some will collide inelastically and transfer energy to the atoms. These electrons will not have enough energy to overcome the retarding potential at plate M, and a smaller current will be detected. As the voltage is increased further, some electrons will transfer their energy to the vapour early enough to be accelerated again to an energy eV0, and the current detected at M will again increase until the next excitation energy threshold is reacted. This occurs at either the energy of a different transition or twice the energy of the ground state transition. Measurement of the differences in the accelerating voltage between the minima in the detected electron current can be used to determine the first excitation level of mercury atoms. As soon as the acceleration voltage increases above the brake voltage a current is flowing from the final electrode This current will increase with increasing accelerating voltage. The collisions that constantly take place between electrons and gas atoms are elastic and exert very little energy loss for the electrons. At a certain critical value of a few volts however the first excitation energy for the gas is reached. The electrons taking part in inelastic collisions will not have sufficient remaining to reach the anode leading to a rapid decrease in current. By further increasing the acceleration voltage, the electrons can again reach the anode and the current is growing again. When the acceleration voltage gives the electrons a kinetic energy equal to twice the excitation energy electrons can undergo two successive inelastic collisions leading again to a current which is rapidly declining. Further increase of accelerating voltage means that the electrons of the two energy losses are accelerated so much that they can reach the anode. The current increases again. This process is then repeated for acceleration voltages, resulting in three-and quadruple excitation energies. 4 The kinetic energy of an electron that goes through the potential difference V is eV and we get an excitation when : eV = En-E0 Where En is the energy of the excited state and E0 is the energy of the ground state. This equation can be compared with the Bohr equation: hν = En-Em where En and Em denotes two energy states. Then Em =E0 apply: eV = hν The atom remains in its excited state a very short time and then emits most energy in the form of a light quantum with frequency ν. Task l: Determine the excitation energy of mercury. Apparatus Franck–Hertz tube with connector panel (NEVA didactic ) Oven, capable of heating (200°C) (Warning, outside of the oven is hot!) Franck–Hertz power supply, (NEVA Betriebsgerät) (swept 0–70 V UB and reverse voltage UG , with amplifier to boost the current detected at the collector plate M) 1 BNC/BNC-cable and 4 banana plug cables to run from the power supply to Franck–Hertz tube. 2 dual banana plugs to BNC adapters to run from the power supply to the Oscilloscope Oscilloscope (Agilent Technologies DSO6012A) Thermometer (200°C) Connect them according to the following wiring diagram (Fig. 2). Fig. 2 Circuit diagram for the Franck-Hertz experiment on Mercury (Hg). 5 Fig. 3 Picture of equipment to determine the excitation energy of mercury, Hg The experiment is then carried out as follows: 1. 2. 3. 4. 5. 6. Turn on the oven and set the temperature to 170 - 180 °C. It takes about 15 minutes to heat up the oven. Keep an eye on the thermometer. Do not let the temperature exceed 205 °C. (Warning, outside of the oven is hot!) Turn on the power supply and set the acceleration voltage UB to 0 V. Switch "UB" in setting ). Set “Heizung”(heating of cathode filament, K) roughly in the middle. Set the gain in the middle. Set the reverse voltage on minimum. Start the oscilloscope and press the “menu”-button to put the oscilloscope in x/ymode.(Fig. 4) 6 Menu button Gain x- & y- Fig. 4 7. 8. Set gain for x-channel (ch1) to 0,5V/cm and y-channel (ch2) to 2V/cm. (Fig.4) Slowly increase the acceleration voltage, UB. On the oscilloscope, you will hopefully get a curve of the electrode current as a function of UB/10. 9. To get the best curve as possible, you can now fine tune the settings: 1. Varying the temperature of the gas. 2. Varying the temperature of the cathode filament (“Heizung”). 10. When you are satisfied with the result, you can press the "Cursors" button and place (x1) and (x2) with the knob to the left of the "Cursors" button to measure the difference in the accelerating voltage between two successive reductions of the current. (Fig. 5) Cursors button Knob Fig. 5 7 11. You can save the curve to USB stick as a .csn-file or a .bmp-picture for the laboratory report: 1. Place the USB stick in USB connector and press the “Save/Recall” button. (Fig. 6) Save/Recall button USB connector Fig. 6 2. Press “Save” button. (Fig. 7) 3. Change format with “knob”. Choose BMP file (24 bit) image file for picture or CSV datafile for x/y-file. Knob Save button Fig. 7 8 4. Press “Save to”. (Fig. 8) 5. Press “File Name”. Change File Name with “knob”. Knob Save to button Fig.8 6. Press “Press to save”. (Fig. 9) Press to save button Fig. 9 7. Picture or data file of screen is saved on the USB stick with the chosen File Name. 9 Question 1. Question 2. Question 3. Question 4. How do these changes in temperature alter the shape of the curve? Explain why? Determine the excitation energy of mercury from the curve! Which transition corresponds to this energy? See energy level diagram for mercury, Fig. 13. Explain the origin of the curves. Can you determine some more excitation levels? Why not? At sufficiently high accelerating voltage a new phenomenon arises. What is it and how was it discovered? In the gas tube the cathode-anode distance much is longer than the free middle path length, while the anode-electrode distance is much shorter. Why is this geometry chosen? 10 Task 2: Determine the excitation energy of neon. Apparatus Replace the metal box from the previous experiment to the black cylinder containing neon gas. (Warning, outside of the oven is hot!) Make the connection in the same way as before but also connect a control grid (Steuergitter) located between the cathode and anode. It controls the acceleration just after the cathode. (Fig. 10). Control grid A KH ,UG ,UB ͦ Collector plate, Control grid (Steuergitter) A=Anode grid, K=Cathode, H=Cathode heating, M= Fig. 10 Circuit diagram for the Franck-Hertz experiment on Neon (Ne). 11 Fig. 11 Picture of equipment to determine the excitation energy of Neon, Ne. Fig. 12 Power Supply 12 1. 2. 3. 4. 5. Turn on the power source. Set UB to 0V. Set “Heizung” (heating of cathode filament, K) on minimum. It takes about 1,5 minutes to warm the filament. Set the gain (Verstärkung) on maximum. Set the reverse voltage (Gegenspannung) (UG) 6-10V. Switch "UB" in setting ).Slowly increase the acceleration voltage, UB. On the oscilloscope, you will hopefully get a curve of the electrode current as a function of UB/10. If the curve “goes out of range”, reduce the power gain. 6 To get the best curve as possible, you can now fine tune the settings: 1. Varying the reverse voltage (Gegenspannung) between 6-10 V. 2. Varying the temperature of the cathode filament (“Heizung”). 7. To save the curve you do the same procedure as in task 1. (10-11) Question 5. Question 6. Question 7. Determine now from the curve the excitation energy of neon! Which transition corresponds to this energy? (See energy level diagram for Neon, Fig. 14) Why can´t the excitation energy be determined solely on the basis of the first minimum? Study neon gas during the study. Is there any other method to determine the excitation energy based on the same tests? Fig. 13 Energy level diagram for Mercury (Hg) 13 Fig. 14 Energy level diagram for Neon (Ne) Good Luck! 14 Umeå University Department of Physics FRANCK-HERTZ EXPERIMENT Name: ………………………………….. Course:…………………………………. Supervisor:……………………………... Approved ................................................. .. CONTENTS: Mercury: Chart: The current as a function of UB/10 Estimated value of excitation energy p. … p. … Neon: Chart: The current as a function of UB/10 Estimated value of excitation energy p. … p. … Answers to questions 1-7 p….