Laboratory #12: Franck-Hertz Experiment: Electron Spectroscopy

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1 INDIANA UNIVERSITY, DEPARTMENT OF PHYSICS, P309 LABORATORY Laboratory #12: Franck-Hertz Experiment: Electron Spectroscopy Goal: Verify Bohr's hypothesis that atomic excitation energies are quantized by repeating an experiment which was first carried out by J.Franck and G.Hertz (Verband Deutscher Physikalischer Gesellschaften, 16 (1914) 457), 12 years before quantum mechanics was developed. Equipment: Franck-Hertz tube, oven, thermostat (NEVA), power supply -50V DC, 6.3V AC (NEVA mains rect.), electrometer (Keithley 414A), variable 15Ω resistor, variable battery supply, 100:1 voltage divider, 2 instrumentation amps (Vernier), LabPro Box (Vernier). (A) The physics V o ΔV Figure 1 Electrons are ejected from a heated cathode and accelerated toward a grid that is at a positive potential V o relative to the cathode. Some electrons pass through the grid and reach the plate, which is kept at a slightly lower potential V p =V o ΔV. The current due to the electrons which reach the plate is measured by a picoammeter. The tube is filled with mercury vapor. The Hg density depends on the tube temperature. The density can be calculated from the pressure p that is given by the law of Clausius-Clapeyron: log p = A/ T + B + C log T (1) Here, the vapor pressure p is in Torr, the temperature in K, the logarithm is to base 10, and the values of the constants are A=3332.7, B= , and C= An electron traveling from the cathode to the grid collides with Hg atoms. The mean free path λ between collisions is 2 λ = 1/( 2 π n ) (2) R 0 where R o = m is the radius of the mercury atom and n is the number of atoms per unit volume. At the end of one mean free path, the electron has gained a kinetic energy K from the electric field E, where K = e E λ (3) where e is the electron charge and E is the electric field established by the accelerating voltage V o.

2 The loss of energy of an electron when it collides elastically with a Hg atom is greatest for a head-on collision. One can show that this is still very small (see question below). If, however, the accelerating voltage is large enough, some of the electrons may excite Hg atoms from the ground state to any of the 3 P excited states (see the Hg energy level diagram in fig.2). An electron that makes such a collision has to give up the corresponding amount of energy, it then does not have sufficient energy to overcome the opposing potential ΔV, and thus, it cannot reach the plate. Initially, as the accelerating potential V o is increased, the plate current rises until some of the electrons can excite Hg atoms. At this point the plate current starts to decrease. After a minimum is reached, further increase of V o gives again a current rise until electrons can initiate an excitation twice. Then, a similar drop in current occurs. With increasing V o, this repeats many times. The maxima are spaced by the 3 P o excitation energy, E 1 of Hg. The first maximum is not at E 1 because of the additional work required to extract electrons from the cathode surface. Excitation of states other than the first is in principle possible, and you should look for them when you do the experiment. Questions: - Calculate the Hg density for 180 o C (453K) and 220 o C (493K). - For the two temperatures, calculate the electron mean free path and the energy at the end of the mean free path. - Calculate the fractional loss of kinetic energy in a head-on collision with a Hg atom. (B) Experiment: Plug in the oven box heater. It takes about 20 min for the temperature of the tube to reach the operating point of 170 o C to 190 o C. The thermostat adjustment is on the right side of the box. Also turn on the picoammeter; it takes time to warm up, too. Check, sketch, and understand the wiring of the setup; refer to figures 3 and 4. Add meters to measure V o and ΔV. Set the retarding potential ΔV to 1.4V. Set the accelerating voltage V o to the maximum of about 70V and adjust the AC filament current with the 15Ω variable resistor such that the plate current reaches about na. Start the Vernier Logger Pro software and configure CH1 and CH2 as Instrumentation Amplifiers. Setup the plot to display potential 1 (V o ) on the X axis and potential 2 (plate current) on the Y axis. Configure the LabPro software for a time-based measurement for 100 seconds and 10 samples/sec. Return the accelerating voltage to 0 and start the data collection. Measure the plate current as a function of the acceleration V o by slowly and smoothly turning the voltage adjustment knob on the Mains Rectifier from the lowest to the highest setting; this should take about 30 seconds. Stop the data collection and save your data. Repeat for a different temperature. How does the measurement depend on the bias ΔV? From your measurement deduce the excitation energy and its uncertainty. Does your experiment really measure the energy of the 3 P o state in Hg, or is there a contribution from the other two 3 P states? (C) [EDM83] [Wikipedia] References: D.S. Edmonds, Cioffiari's Experiments in College Physics, Heath and Co., Lexington, 1983, p

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4 Fig 3 B L A C K R E D V a r i a b l e B a t t e r y V o l t a g e M a i n s R e c t i f i e r > K 6. 3 V A C H C A S E A o h m M e - K H H e a t e r T h e r m o m e t e r C O A X K e i t h l e y A P i c o A m m e t e r O U T + I N G N D O U T : 1 D i v i d e r B L A C K _ I N B L A C K _ O U T 1 0 K o h m B L U E _ O U T 1 M o h m B L U E _ I N R E D 2 I n s t r u m e n t a t i o n A m p 0 - > 1 V B L A C K 2 R E D 1 I n s t r u m e n t a t i o n A m p 0 - > 1 V B L A C K 1 B o x 2 1 U S B C o m p u t e r

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