Question

In what ways does the Franck-Hertz experiment disagree with the Bohr model?

Answer 1

While Franck and Hertz were unaware of it when they published their experiments in 1914,[16] in 1913 Niels Bohr had published a model for atoms that was very successful in accounting for the optical properties of atomic hydrogen. These were usually observed in gas discharges, which emitted light at a series of wavelengths. Ordinary light sources like incandescent light bulbs emit light at all wavelengths. Bohr had calculated the wavelengths emitted by hydrogen very accurately.[17]

The fundamental assumption of the Bohr model concerns the possible binding energies of an electron to the nucleus of an atom. The atom can be ionized if a collision with another particle supplies at least this binding energy. This frees the electron from the atom, and leaves a positively charged ion behind. There is an analogy with satellites orbiting the earth. Every satellite has its own orbit, and practically any orbital distance, and any satellite binding energy, is possible. Since an electron is attracted to the positive charge of the atomic nucleus by a similar force, so-called "classical" calculations suggest that any binding energy should also be possible for electrons. However, Bohr assumed that only a specific series of binding energies occur, which correspond to the "quantum energy levels" for the electron. An electron is normally found in the lowest energy level, with the largest binding energy. Additional levels lie higher, with smaller binding energies. Intermediate binding energies lying between these levels are not permitted. This was a revolutionary assumption.[6]

Franck and Hertz had proposed that the 4.9 V characteristic of their experiments was due to ionization of mercury atoms by collisions with the flying electrons emitted at the cathode. In 1915 Bohr published a paper noting that the measurements of Franck and Hertz were more consistent with the assumption of quantum levels in his own model for atoms.[18] In the Bohr model, the collision excited an internal electron within the atom from its lowest level to the first quantum level above it. The Bohr model also predicted that light would be emitted as the internal electron returned from its excited quantum level to the lowest one; its wavelength corresponded to the energy difference of the atom's internal levels, which has been called the Bohr relation.[4] Franck and Hertz's observation of emission from their tube at 254 nm was also consistent with Bohr's perspective. Writing following the end of World War I in 1918, Franck and Hertz had largely adopted the Bohr perspective for interpreting their experiment, which has become one of the experimental pillars of quantum mechanics.[1][3] As Abraham Pais described it, "Now the beauty of Franck and Hertz's work lies not only in the measurement of the energy loss E2-E1 of the impinging electron, but they also observed that, when the energy of that electron exceeds 4.9 eV, mercury begins to emit ultraviolet light of a definite frequency ν as defined in the above formula. Thereby they gave (unwittingly at first) the first direct experimental proof of the Bohr relation!"[4] Franck himself emphasized the importance of the ultraviolet emission experiment in an epilogue to the 1960 Physical Science Study Committee (PSSC) film about the Franck–Hertz experiment.[16]

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