On the Confirmation of Bohr’s Theory of the Atom by Studying Collisions of Electrons and Gas Molecules

(J. Franck and G. Hertz, Die Bestätigung der Bohr’schen Atomtheorie im optischen Spektrum durch Untersuchungen der unelastischen Zusammenstösse langsamer Elektronen mit Gasmolekülen. Phys. ZS, 20, p. 132—1919).

The authors, in a series of works (1914), showed that if slow electrons undergo collision with molecules of noble gases or metallic vapors, then they are reflected from the molecules according to the laws of elastic impact, preserving their velocity. At the same time, if the velocity of the electrons reaches a certain limit, then upon collision the electrons lose their velocity. In helium, neon, and mercury vapors it can be found that this threshold energy is identical with the energy needed to produce ionization of the gas, and the authors concluded that the energy lost by the electrons is expended on ionizing the gas.

The quantitative confirmation of this view lies in the circumstance that the minimum threshold energy \(q\), determined by a voltage of 4.9 volts in mercury, if its transformation into radiant energy is allowed, must give radiation determined by the relation \(q = h\nu\), where \(h\) is Planck’s constant and \(\nu\) is the frequency of oscillations of light. In mercury we do in fact encounter a line satisfying this relation, namely

\(\lambda = 2536\) Å. As was shown by Åkeson, if the electrons have a high velocity, then \(h\nu\) of their energy is absorbed, while the remaining energy stays with the moving electron. If Bohr’s theory of the atom is applied to the explanation of this phenomenon, the following data are obtained.

If gases are ionized, then, according to Bohr, this must mean that the electron is removed from an outer orbit by the action of the ionizer to infinity, and in doing so energy \(Q\) must be expended. If, conversely, an electron transfers from infinity to the orbit determining the dimensions of the atom of the substance, then radiation must be produced, determined by the relation \(Q = h\nu_\infty\), where \(\nu_\infty\) is the number of oscillations of the light emitted when the electron passes from infinity to the outer orbit. If electrons pass not from infinity, but from nearer possible orbits to the outer orbit, then radiation must result for which \(\nu < \nu_\infty\), since \(Q'\), corresponding to this radiation, is less than \(Q\). Consequently the radiation corresponding to \(\nu_\infty\) must be the extreme radiation, lying in the violet part of the spectrum. Meanwhile, calculations for the mercury line 2536 show that it is, on the contrary, the first member of the series, lying nearer to the red part of the spectrum, and consequently that this line can arise when the electron jumps to the outer orbit of the atom from the nearest and, in my opinion, more distant orbit. The absorption line 2536 can thus exist in a gas in which there has been an action of the field (in the excited atom) forcing the electron to make a transition to more distant orbits than is observed in the atom without the action of the field. For the extreme line, lying toward the violet end of the spectrum, there should be obtained the line 1187.98 Å, belonging to the same series as 2536, and it should correspond to an energy of 10.4 volts. The authors in fact obtain 4.9 volts.

The authors try to explain the contradiction arising between Bohr’s theory and experiment by comparing the results obtained by them with those of other authors, chiefly American physicists. Reviewing in their survey the works on metallic vapors, noble gases, and polyatomic gases (hydrogen, oxygen, nitrogen, and a number of other complex gases), the authors correct their previous conclusions and arrive at the following views.

1) Every jump of an electron from one orbit to another, accompanied by absorption or radiation, may be caused by the impact of a free electron, in which its energy is diminished by \(h\nu\).

2) The jumps occurring in a gas depend on the state of the atom.

3) In a normal, unexcited atom the possible jumps give an absorption series of lines of the unexcited atom.

4) The extreme ultraviolet frequencies of oscillation of a series, multiplied by \(h\), give the work of ionization of the atom; moreover, the work of ionization for an unexcited atom is calculated from the limiting frequency of the absorption series of the unexcited atom.

5) The study of internal collisions and of the radiations connected with them gives a new means for arranging lines into series and establishing the relations between them. The boundaries of the series are accessible to observation.

6) The analogy of optical absorption and of the loss of energy in collisions of electrons with atoms in the form of quanta speaks in favor of Planck’s first hypothesis concerning the absorption of light by quanta.

P. Lazarev.