Experiment A1

THE FRANCK-HERTZ EXPERIMENT

References Weidner and Sells, Elementary Physics, p. 256. Harnwell and Livengood, Experimental Atomic Physics, pp. 314-323. Eisberg, Fundamentals of Modern Physics, pp. 124-128 The Taylor Manual, pp. 410-415.

Object: To observe energy level quantization in mercury atoms. The method uses a measurement of the energy loss in inelastic collisions between electrons and atomic mercury in a gaseous state through which they pass. This classic experiment was important when the quantum theory was still under challenge. It showed that the same energy level difference observed when the atom lost energy through photon emission can account for the energy lost by electrons in the beam when the atom absorbed energy.

Background: The first excited state of a mercury atom is about 5 volts above the ground state. When an electron collides with one of these atoms, but has less than 5 eV of kinetic energy, the only option available is an elastic collision. Because there is an enormous difference between the rest mass of the electron and the rest mass of the mercury atom, very little kinetic energy will be transferred from the electron to the mercury atom. Once the electron has a kinetic energy greater than 5 eV, it is possible for the electron to undergo an inelastic collision. In this case the electron will loose the energy of excitation plus the same small energy transferred as in the elastic collisions. In both the elastic and inelastic collisions momentum must be conserved as well as energy. This explains the small kinetic energy of the mercury atom after the collision in both cases.

The main part of the apparatus is a tube that has been evacuated and then filled with a few drops of mercury. In addition, there are several electrodes as shown in Fig. 1. When filament current is flowing, the cathode is heated to a dark red glow enabling electrons to be emitted. With a DC voltage applied between the grid and the cathode the field accelerates the electrons toward the grid. The grid is a wire mesh, so many electrons pass through the grid and head toward the anode. A retarding potential of 1.5 volts is applied Figure 1 between the grid, also called the 'counter-electrode', and the anode. As the accelerating voltage increases, all of the electrons that pass through the grid with have a sufficient energy to overcome the retarding potential will reach

1 the anode and be recorded by the current meter. This means that the accelerating voltage must be at least 1.5 volts to get any current at all. When the accelerating voltage and, therefore, the electron kinetic energy is high enough for an inelastic scattering to occur, the electron will loose so much energy that it is no longer able to reach the anode and the current will fall. If the accelerating voltage is raised higher by another 1.5 volts, the electrons can undergo an inelastic collision yet pickup enough additional energy to reach the anode once more. The current will continue to flow until a second inelastic collision occurs and the current drops again. This can be repeated until the accelerating voltage is high enough for as many as a dozen inelastic collisions to occur before the electrons reach the anode.

The variation in the current as the accelerating voltage is increased is shown in Figure 2 Fig.2. The dashed line shows the idealized curve if the process described in the last paragraph were followed precisely. There are three major factors that result in the curve which is actually observed: 1) The electrons don't necessarily encounter a mercury atom immediately upon reaching the kinetic energy where an inelastic collision can occur. Further, there can be a slight energy loss through accumulated elastic collisions and these are random events that will produce a small amount of smoothing. 2) As the accelerating voltage increases more electrons are drawn off the cathode. 3) There is a horizontal displacement as the result of differences in the work functions of the materials used for electrodes. (This is also said to be the effect of contact potential.) The result is the curve shown by the solid line in Fig. 2. In spite of these influences, the spacing between the peaks, or alternatively the spacing between the valleys, should accurately reflect the energy lost in an inelastic collision.

Raising the temperature in the tube causes more of the mercury to vaporize, increasing the density of mercury and decreasing the mean free path between collisions for the electrons. Until the temperature reaches about 140 C the mean free path is too long and the electrons may pickup enough kinetic energy to excite the mercury atom to an energy level above the first excited state. As a result the dips in the curve disappear. If the temperature is too high, about 170 C, the mean free path becomes so short that the accumulated effect of elastic collisions can become considerable. According to this analysis, within this temperature range the separation between peaks should be independent of temperature.

Procedure: Wire up the apparatus as shown in Fig. 1. The cathode heater current is taken from a Bud Box that contains a 110:6.3 Volt transformer. The potentiometer shown in the figure is contained inside the box as well. It can be adjusted to vary the filament current. The electron current, in the nanoampere range, requires a sensitive ammeter. The Keithley Electrometer is a voltage measuring device, but in its current mode a resistance is introduced into the circuit and the electrometer measures the voltage developed across this resistance. The accelerating voltage can be more easily varied by raising the power supply voltage to about 50 volts and then using a ten-turn, wire-wound potentiometer as a voltage divider to slowly vary the voltage between the cathode and anode.

2 Although it is not shown in Fig. 1, a signal (proportional to the current measured) is taken from the back of the electrometer and presented to the Y-input of an XY recorder. The accelerating voltage is presented to the X-input of the recorder. The experiment is performed by using the potentiometer to slowly vary the DC voltage over the range of interest. The plotter will plot of the current as a function of the voltage between plate and cathode as the accelerating voltage is varied. This gives a very useful record, but better precision is obtained by using a multimeter to actually read the voltages of the inflection points as you trace out the curve. As an alternative to the X-Y plotter, data may be transferred from the electrometer to one of the lab Mac's using LabView and a simple interface. This gives data in a digital format immediately available for plotting and statistical analysis.

Note that the connector to the electrometer determines the ground potential for the apparatus. You need to be careful that no wiring mistake is made introducing a ground somewhere else and shorting out part of the circuit. If you find that there is a problem with Electrostatic pickup as you move about, you can reduce it by putting a grounded aluminum foil (but otherwise insulated from the components) around the apparatus. Be careful you don't short anything out.

Runs should be performed at temperatures between 140 and 170 C. The temperature can be set using a thermostat on the box. However, we have found that this regulation is poor. You can do better by using this to set the upper temperature limit and actually controlling the temperature by varying the heater current using a Variac. You should be able to use any equivalent points on the curves (maxima, minima, or halfway points) for the voltage determinations. Then use the computer to find the best linear fit the data, voltage increase per peak, in order to determine the voltage increase (delta V) for each peak. Do you see a temperature dependence in any aspects of the data? Can you account for it?

Compare your results (and your experimental undertainty) with the photon energy given off as mercury goes from the first excited state to the ground state, and discuss reasons why your results agree or disagree. (Wavelength tables for mercury can be found in any one of several handbooks.) The energy of the photon is given by

E = hc/λ = e ∆V

Notes provided by KLINGER: The tube construction is similar to the original tube used by Franck and Hertz. Rigid mounting and stable position of the electrodes assures dependable results. The tube is housed in a thermostatically controlled metal over.

The Tube: 1. The tube has a planoparallel system of electrodes to avoid deformation of the electric field. The distance between the anode and in comparison to the average free path of electrons whereas the distance between the cathode and perforated anode is large in comparison to the free path of electrons to assure the highest probability of collisions.

2. A platinum ribbon with small barium-oxide spot serves as a direct heated cathode. An electrode

3 with a hole, connected to the cathode, limits the current and eliminates secondary and reflected electrons, thus making the electric field more uniform.

3. To avoid current leakage along the hot glass wall of the tube a protective ceramic ring is fused into the glass containing the electrical feed-through to the electrodes.

4. The tube is highly evacuated and coated inside with a getter that absorbs traces of air during the manufacturing process and acts as an absorbent during the lifetime of the tube and prevents any changes in performance.

The Oven: 1. The oven contains a heating element that uniformly heats the tube and all connecting leads. Its consumption is 300 watt.

2. The temperature in the cabinet is kept constant by a thermostat that can be regulated from the outside. A hole in the top of the cabinet is provided for the thermometer.

4