The Franck–Hertz Experiment

The image of German physicist and Nobel laurea...Image via Wikipedia The Franck–Hertz experiments provided early evidence of the quantization of atomic energy levels. They demonstrated that the amount of energy that could be stored in an atom was not arbitrary. Rather, these energies come in discrete increments. Moreover, the increments were different for different atoms. For their work, first reported in 1914, James Franck and Gustav Ludwig Hertz shared the 1925

Fig. 1.2 (a) Schematic diagram of the apparatus used in the Franck–Hertz experiment. The cathode, grid and anode are labeled C, G, and A, respectively. (b) Simulated data
Nobel Prize in Physics. The citation for the 1925 prize reads: “for their discovery of the laws governing the impact of an electron upon an atom.” Notice that this is the same Hertz who discovered the photoelectric effect and whose student, Lenard, won the Nobel Prize for elucidating it.
    Figure 1.2a shows a schematic diagram of the apparatus used for this experiment. It consists of a cathode C from which electrons are emitted by heating with a high current (not shown in the diagram), an anode A to collect the electrons, and a grid G between the cathode and anode. The entire apparatus is contained within a

glass envelope from which the air has been evacuated and atoms of a given species introduced. In the original experiments, mercury atoms were used, but any atom will suffice. Electrons emitted from the cathode are accelerated by the grid voltage VG, pass through the grid and are collected at the anode. The anode is kept at a slightly lower potential than the grid to prevent the electrons from acquiring additional kinetic energy. Electrons arriving at the anode are collected and the current i A measured.
    Data are in the form of graphs of VG versus i A. As expected, the current increases as VG increases, but it decreases at regular intervals as shown in the hypothetical data plotted in Fig. 1.2b. These data clearly suggest quantized atomic energy levels. For any setting of the grid voltage the maximum electronic kinetic energy in the
apparatus is eVG. When eVG is lower than energy separation between the lowest atomic level, referred to as the “ground state”, and the next highest level, the “first excited state,” none of the electronic kinetic energy can be converted to atomic internal energy. This is because there simply isn’t any level to excite between the ground state and the first excited state. The only thing that can occur is elastic scattering between the electrons and the atoms.When, however, eVG reaches the energy separation between the ground state and the first excited state some of the atoms “become excited.” In these inelastic collisions the exciting electrons lose kinetic energy (by an amount equal to the excitation energy) and are thus not collected at the anode. The result is that the current decreases. As VG is further increased, the electrons that have already excited the atom once can be reaccelerated and collected. The current thus increases again. When these electrons are accelerated to a kinetic energy sufficient to excite the atom again, the anode current again decreases. (For simplicity we are assuming that only the ground and first excited states are important in this experiment.) Thus, the peaks in the curve of VG versus i A will be equally spaced. From the hypothetical data we would conclude that the energy separation between the ground state and the first excited state is e V . This experiment clearly demonstrates that the atomic energy levels are quantized, for if they weren’t the current would simply rise continuously and then level off (saturate) when all the electrons were collected.
    While energies in the SI system are measured in joules, this is a rather large unit for measurement and discussion of atomic energies. It is frequently more convenient to use the electron-volt, abbreviated eV. One electron-volt is the kinetic energy acquired by a particle of charge e when it is accelerated through a potential difference of one volt. Thus,
                                             1eV = (1.602 × 10−19C) (1V)
                                                    = 1.602 × 10−19J (1.6)
It is often convenient to write Planck’s constant in terms of eV rather than J in which case (h bar) = 6.58×10−16 eV· s. In the original Franck-Hertz experiment the separation between peaks along the abscissa was roughly 4.9 V.

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reference : C.E. Burkhardt, J.J. Leventhal, Foundations of Quantum Physics, 1
DOI: 10.1007/978-0-387-77652-1 1, C Springer Science+Business Media, LLC 2008

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