Electron Collisions.
The excitation of an atom in the normal state ([cf. p. 157]), by which one of its electrons is removed to an outer stationary orbit, may be caused by a foreign electron which strikes the atom. A study of collisions between atoms and free electrons is therefore of the greatest importance when investigating more closely the conditions by which series spectra are produced.
These investigations can be carried out by giving free electrons definite velocities by letting them pass through an electric field, where the “difference of potential” is known in the path traversed by the electrons. When an electron moves through a region with a difference of potential of one volt (the usual technical unit), the kinetic energy of the electron will be increased by a definite amount (of 1·6 × 10⁻¹² erg). If its initial velocity is zero, its passage through this field will make the velocity 600 km. per second; if the potential difference were 4 volts, 9 volts, etc., the velocity obtained by the electron would be 2, 3, etc., times larger. For the sake of brevity we shall say that the kinetic energy of an electron is, for instance, 15 volts, when we mean that the kinetic energy is as great as would be given by a difference of potential of 15 volts.
In 1913 the German physicist Franck began a series of experiments by methods which made it possible to regulate accurately the velocity of the electrons, and to determine the kinetic energy before and after collisions with atoms. He first applied the methods to mercury vapour, where the conditions are particularly simple, since the mercury molecules consist of only one atom. Franck bombarded mercury vapour with electrons all of which had the same velocity. He then showed that if the kinetic energy of the electrons was less than 4·9 volts the collisions with the atoms were completely “elastic,” i.e., the direction of the electron could be changed by the collision, but not its velocity. If, however, the velocity of the impinging electrons was increased so much that it was somewhat larger than 4·9 volts, there was an abrupt change in the situation, since many of the collisions became completely inelastic, i.e., the colliding electron lost its entire velocity and gave up its entire kinetic energy to the atom. If the initial velocity was even greater, so that the kinetic energy of the colliding electron was 6 volts, for instance, then when the collision took place there would always be lost a kinetic energy of 4·9 volts, since the electrons would either preserve their kinetic energy intact or have it reduced to 1·1 volt ([cf. Fig. 30]).
Fig. 30.—Schematic drawing of Franck’s experiment with electron collisions. G is a glowing metal wire which emits electrons. If between G and the wire net T there is a difference of potential of 6 volts, the electrons will pass through the holes of the net with great velocity out into the space R, where there is mercury vapour. a represents a free electron F and a mercury atom Hg before the collision, while b represents them after the collision; with the collision F loses a kinetic energy corresponding to 4·9 volts; at the same time a bound electron B in the atom goes over to a larger stationary orbit.
This remarkable phenomenon can be understood from the Bohr theory if we assume that to send the most loosely bound electron in the mercury atom out to the nearest outer stationary orbit there is required an energy of 4·9 volts, since in that case, according to the first postulate, an energy of less than this magnitude cannot be absorbed by the atom. The use of the word “understanding” must here be qualified; if the forces which influence the free electron as it comes into the electron system of the mercury atom are no other than the usual repulsion from the electrons and the attraction from the nucleus, the conduct of the colliding electron can in no way be explained by the laws of mechanics. But what happens is in agreement with the characteristic stability of the stationary states, and Bohr had prophesied how it would happen. Curiously enough Franck believed in the beginning that his experiment disagreed with the Bohr theory because he made the mistake of supposing that what happened was merely ionization, i.e., complete disruption of a bound electron from a mercury atom.
Franck’s experiments showed, moreover, that mercury vapour, as soon as the inelastic collisions appeared, began to emit ultra-violet light of a definite wave-length, namely, 253·7 μμ. The product of the frequency ν of this light and Planck’s constant h agrees exactly with the energy quantum possessed by an electron which has passed a potential difference of 4·9 volts; but this also agrees with what might be expected, according to the Bohr theory, from the radiation the removed electron would emit upon returning to the normal state. The energy which is respectively absorbed and emitted in the two transitions must be indeed hν.
Since an electron can not only be driven out to the next stationary orbit, but also to an even more distant one (or entirely ejected) and thence can come in again in one or more jumps, it is evident that a far more complicated situation may arise. The Franck experiment, which now has been extended to many other elements, clearly gives extraordinarily valuable information in such cases. In mercury it has been found that the energy a free electron must have in order to eject an electron from an atom and turn the atom into a positive ion, corresponds to a difference of potential of 10·8 volts, a value which Bohr had predicted. At the same time that Franck’s experiments, in this respect and in others, have strengthened the Bohr theory in the most satisfactory way, they have also advanced its development very much. Indeed it may be said that they have been of the greatest help in atomic research. Even if the spectroscope has greater importance, the investigations on electron collisions make the realities in the Bohr theory accessible to study in a more direct and palpable manner.
Fig. 31.—Stratification of light in a vacuum tube.
The peculiarities in the electron collisions appear most clearly in an old and well-known phenomenon of light, namely, the stratification of the light in a vacuum tube ([Fig. 31]). This stratification, which previously seemed so incomprehensible, agrees exactly with the feature so fundamental in the atomic theory that a free electron cannot give energy under a certain quantum to an atom. We can imagine that, in the non-illuminated central space between the bright strata, the electrons each time under the influence of the outer electric field obtain the amount of kinetic energy which must serve to excite the atoms of the attenuated vapour.
As has been said ([p. 161]), electron collisions may cause the emission of characteristic X-rays; but to produce them very great energy is required. Therefore the electrons which are to produce this effect must have an opportunity to pass freely through a certain region under the influence of a proportionately strong electric field (with potential of from 1000 to 100,000 volts and more). The electrons find such a field in a highly exhausted X-ray tube, where the electrons under strong potential are driven from the cathode against the anticathode, into which they penetrate deeply.