Physics 248, Spring 2009 Lab 9: Franck-Hertz Experiment

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1 Name Section Physics 248, Spring 2009 Lab 9: Franck-Hertz Experiment Your TA will use this sheet to score your lab. It is to be turned in at the end of lab. To receive full credit you must use complete sentences and explain your reasoning clearly. The Franck-Hertz experiment, first performed in 1914, demonstrates the quantization of atomic energy levels. In the experiment, accelerated electrons collide with mercury (Hg) atoms. A measurement of the electron current as a function of the accelerating voltage reveals a series of rises and abrupt falls. The abrupt drops in current arise from inelastic collisions in which the Hg atoms make transitions to excited states, lending credence to the Bohr theory of the atom. For this discovery, Franck and Hertz were awarded the Nobel Prize in physics in Introduction. The Franck-Hertz experiment consists of a glass tube that surrounds three electrodes (a cathode that serves as the electron source, grid-form anode, and a plate which serves as the electron collector) and a drop of mercury. A thermostat-controlled oven allows the tube to be heated to temperatures of order 180 C, which vaporizes the mercury. The electrons produced at the cathode are accelerated through a potential difference V that is maintained between the cathode and the anode. The electrons then collide with the Hg atoms as they travel toward the anode. These collisions may be elastic, in which the electrons maintain (almost all of) their kinetic energy, or inelastic, in which the Hg atom is excited to a higher energy state. To distinguish between these two possibilities, a small retarding potential is maintained between the anode and the collector plate, such that electrons with sufficiently low kinetic energies cannot overcome this potential difference and therefore are not collected as current. Hence, by measuring the output current as a function of the accelerating voltage, it is possible to observe the energies at which inelastic collisions occur, and thus deduce the quantization of the Hg energy levels.

2 Procedure. Each lab station (there are only 4 in total) includes a Franck-Hertz oven/tube apparatus, a Franck-Hertz controller, a digital multimeter, and a Hg thermometer. To proceed, follow the instructions in the online lab manual as well as the instructions given below. IMPORTANT: the experimental setup is quite delicate and requires that you carefully follow the safety and equipment precautions described here and in the manual! 1. Follow the instructions regarding handling the glass thermometer. Note that these thermometers are extremely delicate, and if they break the Hg can spill, which is very dangerous. Handle the thermometers with EXTREME care. 2. The oven is controlled by a thermostat and must also be handled carefully. Follow an iterative procedure to raise the temperature to the desired value starting from 4 on the temperature controller on the oven, as described in the lab manual. Note that the temperature fluctuations can be quite extreme, so proceed very slowly and carefully, and in small increments. The desired range for the temperature controller should be somewhere between 6 and 7. Hold off on applying the accelerating voltage until the temperature is (reasonably) stabilized. 3. Be sure to monitor the temperature carefully. As stated in the manual, BE SURE NOT TO LET THE TEMPERATURE EXCEED 195 C, as this can damage the oven as well as the Hg thermometer. You must also take great care not to touch the oven once it is heated, as the outside gets extremely hot. 4. Follow the circuit diagram in the manual to connect the apparatus. The Franck- Hertz oven and controller are labeled to indicate which points should be connected. Note that the M denotes the mesh electrode, the Y is the output current, the A is the anode, and the X is the accelerating voltage. 5. You will use the Pasco interface to record your data. To do so, connect the Pasco box to the Franck-Hertz controller. Ignore the (outdated) Using the PASCO 750 Interface instructions in the lab manual and launch the Franck-Hertz lab icon using DataStudio. (Note: you may need to adjust the DataStudio settings to have your data be displayed properly.) 6. As described in the manual, the accelerating voltage at the recorder output is a fraction (about 5/70) of the actual accelerating potential. To calibrate it, connect the digital multimeter to the monitor leads, which measure the actual potential. 7. Once you have taken data, in lieu of the questions asked in the lab manual, you should follow the steps on the next pages of this sheet. 2

3 Results. Measure the output current as a function of the accelerating voltage. (Use the ramp function on the controller.) Be sure to calibrate the accelerating voltage, as described in #6 above. Obtain several sets of data. Place a representative plot (or plots) of your data in the space provided below. Compute the mean of the voltage difference between the peaks. Convert the voltage to electron volts, and compare your result with the energy of the transition of Hg from the 6s6p 3 P 1 state to the 6s6s 1 S 0 ground state, which is 4.86 ev. Include an error estimate. 3

4 Analysis and Discussion. (i) Summarize below why inelastic collisions of the electrons with the Hg atoms result in a drop in the collected current in this experiment. (ii) What is the physical interpretation of the series of drops in current as the accelerating voltage increases? (iii) What are the sources of error that you can identify in this experiment? Can you identify any further measurements you might make to account for these errors (and if so, please make those measurements and include your results)? 4

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