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

(J. Franck und 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).

In a series of works (1914), the authors showed that if slow electrons collide with molecules of noble gases or metallic vapors, then they are reflected from the molecules according to the laws of elastic impact, retaining 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 vapor it can be found that this limiting energy is identical with the energy required to produce ionization of the gas, and the authors concluded that the energy transferred by the electrons is expended on ionization of the gas.

A quantitative confirmation of this view is found in the circumstance that the smallest limiting energy \(q\), determined by a voltage of 4.9 volts in mercury, if it is allowed to be transformed into radiant energy, should give radiation determined by the relation \(q = h\nu\), where \(h\) is Planck’s constant and \(\nu\) is the frequency of the light. In mercury we do indeed encounter a line satisfying this relation, namely

\(\lambda = 2536\ \text{Å}\). As was shown by Åkeson, if the electrons have a high velocity, then \(h\nu\) is absorbed from their energy, 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 the gases are ionized, then according to Bohr this must mean that the electron, from the outer orbit, must, under the action of the ionizer, be removed to infinity, and in this process energy \(Q\) must be expended. If, conversely, an electron passes from infinity to an orbit determining the dimensions of an atom of the substance, then radiation must be obtained, determined by the relation \(Q = h\nu_{\infty}\), where \(\nu_{\infty}\) is the frequency of the emitted light when the electron passes from infinity to the outer orbit. If the electrons pass not from infinity, but from nearer possible orbits to the outer orbit, then radiation must be obtained 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 limiting radiation lying toward the violet part of the spectrum. Meanwhile calculations for the mercury line 2536 show that, on the contrary, it is the first, lying nearer to the red part of the spectrum, member of the series, and consequently this line can be obtained when an electron jumps to the outer orbit of the atom from the nearest, more distant orbit. The absorption line 2536 can thus exist in a gas in which the action of a field has been produced (in an excited atom), forcing the electron to make a transition to more distant orbits than is observed in an atom without the action of a field. For the limiting line, lying toward the violet end of the spectrum, one should obtain the line \(1187.98\ \text{Å}\), 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 contradictions arising between Bohr’s theory and experiment by comparing results obtained by them or by other authors, chiefly American physicists. Reviewing in their survey work on metallic vapors, the noble gases, and the diatomic gases (hydrogen, oxygen, nitrogen, and a number of other complex gases), the authors correct their earlier conclusions and arrive at the following views.

1) Every transfer of an electron from one orbit to another that is accompanied by absorption or emission can be caused by the impact of a free electron, in which its energy changes by \(h\nu\).

2) The jumps encountered in gases depend on the state of the atom.

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

4) The limiting ultraviolet frequencies of the vibrations of a series, multiplied by \(h\), give the ionization work of the atom; moreover, the ionization work 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 the lines in a series and establishing the connections between them. The boundaries of the series are accessible to observation.

6) The analogy between optical absorption and the giving up of energy in the collision of electrons with atoms in the form of quanta supports Planck’s first hypothesis on the absorption of light in quanta.

P. Lazarev.