# Atoms' excitation energies as derived from Frank-Hertz experiment data

I'm analyzing the experimental data obtained during Frank-Hertz experiment (conducted with Hg atoms):

Accelerating voltage values were multiplied by 0.1 during measurement (i.e. the mean value of energies differences if not 0.508 eV, but 5.08 eV). The output voltage was measured on resistive load of the anode, therefore it is proportional to anode's current.

The first five minimas in output voltage (top graph) have constant voltage difference - this value is used to calculate the first excitation energy of Hg atom (bottom graph).

The sixth minima, however, can be seen to have larger increase in output voltage(top graph - the first five voltage peaks may be fitted by a linear graph, whereas the sixth is no longer fits to this graph) and a higher voltage offset from the previous minima (bottom graph).

Question 1: Is the sixth minima corresponds to the higher order excitation of Hg, or ionization, or else?

Question 2: The curve is clamped at $V_{out} = 5V$. Is there a physical effect which causes this, or it is just the limit of measurement equipment, or else?

• Your voltage minima are well below the normal Franck-Hertz 4.9V Hg excitation, which shows up at the extreme right of your plot. On the other hand, your vapor temperature is above normal, so I suppose you could be seeing transitions in thermally excited Hg. Questions: 1) What's the anode potential relative to the grid? 2) This experiment typically measures anode current. How is your $Vout$ signal produced? – Art Brown Aug 5 '13 at 23:19
• @ArtBrown, the $x$ axis in the graph should be multiplied by 10 to obtain correct accelerating voltage (therefore the minimas are spaced by 5.08 V). The output voltage is measured across anode's load resistor - it is proportional to anode's current. Regarding retarding voltage - I don't know what was its value during the experiment. – Vasiliy Aug 6 '13 at 6:27

The first five minima look okay (accounting for the rescaling of the axes). I don't know what is happening with the last minimum. How reproducible is it? With the flat part you are seeing clipping of the amplifier and/or DAC, not a physical effect in the tube.

The vapour temperature is fine. 180°C is in the range of temperatures our group tested (it got boring re-running the experiment dozens of times at different temperatures!) and you won't see any interesting thermal excitation effects there. On the other hand, our equipment wasn't able to go beyond an accelerating potential above about 32 V so we didn't see your sixth minimum. It may be physical or may be an error, I don't know.

I've attached my old reading list for the Franck-Hertz experiment. Some of these (particularly the original experiment - it is well worth reading their Nobel lectures!) used proper professional laboratory equipment when they weren't worried about electrocuting students. So one of these papers might have the data you want to compare to.

Fletcher J. (1985). Non-equilibrium in low pressure rare gas discharges. J. Phys. D: App. Phys., 18, 221.

Franck, J. & Hertz, G. (1925). Physics Nobel Lectures 1925. Physics.

Gargioni, E. & Grosswendt, B. (1971). Scattering cross sections for electron transport calculations in matter. Physicalisch-Technischen Bundesanstalt. Google scholar search.

Genolio, R. J. (1973). Average Energy of Electrons in a Franck-Hertz Tube. Am. J. Phys., 41, 288–290.

Hanne, G. F. (1988). What really happens in the Franck-Hertz experiment with mercury? Am. J. Phys., 56 no. 8, 696–700. Retrieved from UMK.

Li, B., White, R. & Robson, R. (2002). Spatially periodic structures in electron swarms: ionization, NDC effects and multi-term analysis. J. Phys. D: App. Phys., 35, 2914.

Liu, F. H. (1987). Franck-Hertz experiment with higher excitation level measurements. Am. J. Phys., 55 no. 4, 366–369.

McMahon, D. R. A. (1983). Elastic electron-atom collision effects in the Franck-Hertz experiment. Am. J. Phys., 51 no. 12, 1086.

Nicoletopoulos, P. & Robson, R. (2008). Periodic Electron Structures in Gases: A Fluid Model of the “Window” Phenomenon. Phys. Rev. Lett., 100 no. 12, 1-4.

Nicoletopoulos, P. (2003). Analytic elastic cross sections for electron-atom scattering from generalized Fano profiles of overlapping low-energy shape resonances. arXiv:physics/0307081 [physics.atom-ph].

Rapior, G., Sengstock, K. & Baev, V. (2006). New features of the Franck-Hertz experiment. Am. J. Phys., 74 no. 5, 423

Robson, R. E., Li, B., & White, R. D. (2000). Spatially periodic structures in electron swarms and the Franck-Hertz experiment. J. Phys. B: At. Mol. Opt. Phys., 33, 507–520.

Sigeneger, F. & Winkler, R. (2003). On the kinetics of electron trapping in the Franck-Hertz experiment. XXVI International Conference on Phenomena in Ionized Gases. Greifswald, Germany, 15-20 July 2003.

Sigeneger, F., Winkler, R. & Robson, R. E. (2003). What really happens with the electron gas in the famous Franck-Hertz experiment? Contrib. Plasm. Phys., 43 no. 3-4, 178-197.