In a lab experiment dealing with the Franck-Hertz Experiment, a scientist found

Question

In a lab experiment dealing with the Franck-Hertz Experiment, a scientist found that the first peak of voltage did not occur at the transition voltage for mercury. He found that the accelerating voltage at the first peak was 28 volts and the transition voltage was 4.9 volts. The difference between these voltages was 23.1 volts. What is the significance of this voltage? (In order words, what is the significance of the magnitude of the difference between the found transition voltage and the accelerating voltage at the first peak?)

Explanation / Answer

Franck And Hertz experiment demonstrated the existence of excited states in mercury atoms. This helps to confirm the quantum theory which explains that electrons occupy only discrete, quantized energy states. Electrons were accelerated by a voltage toward a positively charged grid in a glass envelope filled with mercury vapor. Past the grid was a collection plate held at a small negative voltage with respect to the grid. The values of accelerating voltage where the current dropped gave a measure of the energy necessary to force an electron to an excited state.

When the accelerating voltage reaches 4.9 volts, the current sharply drops, indicating the sharp onset of a new phenomenon which takes enough energy away from the electrons that they cannot reach the collector. This drop is attributed to inelastic collisions between the accelerated electrons and atomic electrons in the mercury atoms. The sudden onset suggests that the mercury electrons cannot accept energy until it reaches the threshold for elevating them to an excited state. This 4.9 volt excited state corresponds to a strong line in the ultraviolet emission spectrum of mercury at 254 nm (a 4.9eV photon). Drops in the collected current occur at multiples of 4.9 volts since an accelerated electron which has 4.9 eV of energy removed in a collision can be re-accelerated to produce other such collisions at multiples of 4.9 volts. This experiment was strong confirmation of the idea of quantized atomic energy levels.

Contact potentials: Consideration of contact potentials is also necessary. In simple terms, this means that the accelerating potential is not completely converted into kinetic energy of the electrons: some of it provides the “work function” of the cathode material, i.e. the amount of energy (measured in electron volts) necessary to free the electrons from the cathode. The cathode is coated with a material with a relatively low work function. The collector plate, since it is used merely as electron collector, has a somewhat higher work function. The contact potential is the difference between the work functions, since they are oppositely directed in the electric field, that is, the electric field has to work against the cathode potential but is helped in the case of the collector plate. Thus we should expect that the voltage to the first peak will be greater than the average peak to peak voltage, due to the contact potential. The contact potential can be calculated as the average peak to peak voltage subtracted from the first peak voltage.

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