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Experimental Verification of Bohr’s Theory of Radiation
T. S. Landsberg.
Very soon after the publication of Bohr’s new theory of radiation, Kramers and Slater, and Bothe, came forward with a plan for an experiment that made it possible to hope to ascertain whether the Compton effect takes place in accordance with the ideas of Debye–Compton, based on the theory of light quanta, or whether it is governed by the laws of Bohr’s new theory. At the present time a detailed report on this experiment has appeared1.
As is known, what was new in Bohr’s conception consisted in the assumption that the laws of conservation of momentum and energy have only a statistical significance and may fail to be fulfilled in an individual act. In accordance with this, the interpretation of the scattering of X-rays will be as follows: the act of scattering is the result of the action, upon the radiation incident on a given atom, of the radiation of virtual vibrators connected with that atom; thus scattering is regarded as a continuous process; but this process is accompanied by the ejection of weakly bound (free) electrons, occurring from time to time (at random), for which the expenditure of a certain amount of motion and energy is required; this expenditure is statistically made up by the circumstance that the frequency and momentum of the scattered X-ray light turn out to be somewhat different from the corresponding elements of the incident light (the Compton effect). The physical cause of the change in frequency lies in the Doppler effect, since the virtual vibrators of the scattering atom are set in motion2.
Bothe’s idea is based on the fact that, in the indicated interpretation, the individual act of ejection of an electron is not connected in time with the continuously occurring process of scattering. Studying this latter, for example by means of the photoelectric effect, we should observe the action of the scattered light at moments having nothing in common with the moments at which the ejected electrons appear. On the contrary, from the point of view of the interpretation of Compton and Debye, in the act of scattering the secondary quantum of radiation and the recoil electron appear simultaneously. Consequently, the effect of the action of this secondary quantum should coincide in time with the appearance of the Compton electron.
The experiment devised and carried out by Bothe jointly with Geiger amounted to the following. Between two Geiger counters placed opposite one another at a very small distance, hydrogen passes through the atmosphere
EXPERIMENTAL TEST OF BOHR’S THEORY OF RADIATION
an X-ray beam. One of the chambers is open, the other is covered with platinum foil \(0.02\) mm thick. The electrons ejected when X-rays are scattered by hydrogen have low velocity and cannot penetrate through the foil; they enter only the first chamber, by means of which the moments of their appearance can be determined (the \(e\)-counter). Into the second chamber, however, only scattered X-rays can penetrate, which there produce a photoelectric effect. The moment of appearance of these secondary electrons will be recorded by the second chamber, which is thus a \(h\nu\)-counter. Of course, not every electron entering the chamber will be recorded. Still less will every quantum entering the \(h\nu\)-counter produce the recorded effect. For the Bothe and Geiger apparatus, as preliminary experiments established, the \(e\)-counter records on the average 1 out of 15 electrons entering it, while the \(h\nu\)-counter records approximately 1 out of 6000 scattered quanta arising near it (owing to the different sensitivity of the counters, the action of quanta on the \(e\)-counter is equal to zero). Therefore one cannot expect that every reading of the \(h\nu\)-counter will coincide with a reading of the \(e\)-counter. However, if Bohr’s theory is correct, the coincidences between the moments of registration by the two counters must always be accidental, and their number must be grouped around the mathematical expectation of this accidental coincidence, departing from it according to the laws of fluctuation. If, on the other hand, the individual acts of scattering and the appearance of recoil electrons are connected with one another according to the ideas of Debye—Compton, then the number of these coincidences must considerably exceed the indicated mathematical expectation.
The readings of both counters, consisting in the deflections of the threads of two string electrometers connected with the chambers, were recorded photographically on a common tape moving at a speed of 10–15 meters per second, which made it possible to obtain accurate time readings. Time marks were applied in the final experiments every \(\frac{1}{1000}\) sec. The accuracy of the time determination was \(\frac{1}{10000}\) sec. A special modification of the counting chamber (an attachment correcting the inhomogeneity of the field near the point) to a considerable degree freed the apparatus from the very troublesome effect of unequal delay in registration. In the final experiments, indisputable signs of a connection between the two effects were obtained. For this group of experiments one has:
| Mathematical expectation of accidental coincidence | 1.8 |
| Observed number of coincidences | 10 |
The same apparatus, applied to the registration of two entirely independent phenomena (ionization by two independent radioactive preparations), gave a picture fully coinciding with the predictions of probability theory. Conversely, the registration of two phenomena known in advance to be connected (ionization by a common beam of \(\beta\)-rays) led to a picture similar to that observed with the scattering phenomenon. Thus the experiments described speak decisively against Bohr’s interpretation of the Compton effect, and at the same time cast doubt on Bohr’s whole conception.¹ Of course, they cannot be regarded as proving the applicability of the laws of conservation of energy and momentum to the elementary process, but they undoubtedly serve as a certain confirmation of the correctness of the original explanation of Debye and Compton, based on the theory of light quanta.
A known shortcoming in the arrangement of the experiments must be recognized in the circumstance that in them the radiation and recoil electrons contained within a definite solid angle were not separated out, but only the integral effect was studied. This gap
¹ According to private information received from Copenhagen, Bohr at the present time no longer supports these new views.
to a certain extent supplement the experiments about which A. Compton reports in a brief note.1
According to the quantum theory of the Compton effect, the relation
\[ tg^{1/2}\varphi = -\frac{1}{1+\alpha}\cdot \operatorname{cotg}\theta, \tag{1} \]
holds, where \(\varphi\) is the angle made by the primary beam with the secondary one, and \(\theta\) with the recoil electrons. Thus, if the theory of light quanta is applicable, a maximum of coincidences between the effects of the scattered beam and the recoil electrons should be observed when the recording apparatus is oriented at angles determined by relation (1).
Conversely, if Bohr’s assumption is correct, no predominance in direction is to be expected: coincidences are distributed randomly and uniformly in all azimuths. Compton mentions two attempts at an experimental resolution of these questions, undertaken in his laboratory.
Bennett used counting chambers of the Geiger type, one (\(h\nu\)-counter) remaining fixed, while the other (\(e\)-counter) was set at various angles. The readings of the counters were recorded by means of telephones, with the primary current amplified by a trigger. The experiment showed the presence of a maximum of coincidences at an orientation at an angle, within an accuracy of 3–5%, coinciding with that calculated theoretically.
In the experiments of Compton himself and Simon, the observing apparatus was a Wilson chamber. The advantage of this method is the presence of only one chamber, for the photograph at once shows both the track of the recoil electron and the direction of the scattered beam. The study of 350 successful stereophotographs showed that the greatest number of “simultaneously” arising paths do indeed form the angle predicted by quantum theory. Deviations from these directions do not exceed the limits indicated by probability theory. It should be noted that a similar conclusion, albeit a qualitative one, had already been made earlier by Academician A. F. Ioffe on the basis of a study of photographs obtained by Skobeltsyn with the aid of \(\gamma\)-rays (JRFKhO).
The work of Compton’s laboratory is still at a preliminary stage. Its fundamentally weak point must be recognized as the criterion of “simultaneity”: in Bennett’s experiments this is the simultaneous sounding of telephones; in the experiments of Compton and Simon simultaneity is determined by the duration of the expansion process. In general, in persuasiveness and precision they cannot compete with the work of the German authors, where the name of Geiger makes especially reliable the use of the difficult method of counting chambers.