certain convergence frequency v in the spectrum of the gas by a similar equation,

Now, in view of the results in the X-ray region, we should reasonably expect a certain interchangeability in the effects of electron collision and radiation. We may perhaps expect a gas to be ionized whether it is struck by an electron moving with the critical velocity (corresponding to V1) or illuminated by radiation of the corresponding wave-length, for the same quantum of energy is involved in both cases.1 Thus, in mercury vapor, we know that direct ionization is produced by electrons of velocity Vi = 10.4 volts, which corresponds to X 1188, and we should also expect that radiation of this wave-length would be effective also. This is too far in the ultraviolet to allow of easy verification.

No direct ionization of a primary character, of mercury vapor, has been definitely proved for electrons of velocity 4.9 volts, the radiating potential corresponding to the strong line 2536 (though effects associated with "low voltage arcs," to be discussed later, show that a strong ionization of a secondary character can be obtained even here). In line with this is the fact that when mercury vapor is illuminated by light of wave-length A 2536, as in R. W. Wood's' experiments, no ionization is observed, although the illuminated gas re-emits the radiation strongly. Similarly, with the alkali metals, we find that no ionization is produced by electrons with velocities above the radiating potential but below the ionizing potential, and we should, therefore, expect that no ionization should be produced by light whose frequency is less than that of the convergence frequency, or limit, of the principal series. This result seems to be borne out by Kunz and Williams' recent experiment. The ionizing potential and radiating potential for caesium are 3.9 volts and 1.5 volts, respectively, which correspond to the limit (λ 3191) and the first line doublet (x 8946 and λ 8523), of the principal series of doublets in the spectrum of Cs. Kunz and Williams showed that caesium vapor only began to be ionized by light whose wave-length is not far from X 3191. Should

1 It should, however, be pointed out that ultraviolet light of frequency, say λ 2536, incident upon most metals produces a copious flow of electrons. Electrons having the same quantum of energy-4.9 volts-falling on the metal instead of the radiation, do not, as far as we know, produce any analogous effect, so that some caution perhaps is to be observed in carrying ideas from the X-ray region to the ultraviolet light region. 2 P. M., 23, 689 (1912).

this view be correct, it is difficult to account for Steubing's' result that mercury vapor can be ionized by light from a mercury lamp, i. e., by light whose wave-length is longer than λ 1800, and, therefore, far longer than the limit X 1188 for mercury. It is certainly worth while investigating carefully where ionization of mercury vapor by ultraviolet light sets in, as Steubing's criterion for distinguishing between surface effects and true ionization of the vapor is far from conclusive.

Indirect evidence that there is no ionization by light of wavelength of the frequency corresponding to the radiating potential, is obtained from the fact that when mercury vapor, or any monatomic gas, is subjected to bombardment by electrons of energy just sufficient to call out the radiation, no ionization can be detected, although molecules are being illuminated by radiation from their neighbors. (However, one should bear in mind some recent work of Compton on helium, which indicates that a gas under the influence of its own radiation, when sufficiently intense, is more readily ionized by electron impact than in its normal state.) Hughes's results on air indicated that air is ionized by light of wave-lengths shorter than X 1350, corresponding to about 9 volts. Now 9 volts is not far from the values 7.5 volts for nitrogen and 9.5 volts for oxygen, the values formerly associated with the ionizing potentials. Later results have shown that 7.5 volts for nitrogen, however, is a radiating potential rather than the ionizing potential, which is about 18 volts. A similar test has not been made for oxygen, but the analogy of some recent experiments on metallic vapors and on hydrogen and helium would imply that the 9.5 volts for oxygen was the radiating potential and not the ionizing potential.3 Ionization of air by light of wave-length A 1350 apparently then contradicts the result tentatively arrived at, that the wave-length which ionizes air corresponds to the ionizing potential and not the radiating potential. It is just possible 1 P. Z., 10, 787 (1909).

2 P. M., 40, 553 (1920).

3 Mohler and Foote (Jour. Opt. Soc. Amer., 4, 49 (1920)) in some recent experiments found that the radiating and ionizing potentials for N2 are 8.18 and 16.9 volts, for O2 7.91 and 15.5 volts and for H2 10.4 and 13.3 volts, thus apparently following the rule observed for monatomic gases that the lower critical potential is always a radiating potential. However, Franck, Knipping and Kruger, and Compton find that the lower critical potential for H, is definitely an ionizing potential. In view of this, one may perhaps require further proof that the lower critical potential for diatomic gases is always a radiating potential as appears to be the case for monatomic gases.

that when a molecule is already in an abnormal state due to the absorption of radiant energy of wave-length correponding to the radiating potential, further radiant energy of the same wave-length may cause it to be ionized. (This speculation, and it must be recognized merely as such, implies, in other words, that intense. radiation may produce ionization when feeble radiation would not.) The recent work of Compton, just referred to, is suggestive in this connection.

It is recognized, of course, that the effect of radiation impinging on an atom is not exactly analogous to the effect of a collision with an electron, for the absorption of radiation is probably a continuous process, while the absorption of energy through an electron collision is essentially discontinuous. Again, from the experiments of McLennan and others, there is only strong absorption at the isolated wave-lengths of the principal series, whereas electrons moving with any velocity between the radiating potential and the ionizing potential give rise to radiation.

The whole subject is full of obscurities and suffers from lack of experimental data. A systematic investigation, with improved methods, of the ionization of gases and vapors by light, should repay investigation. It is of considerable interest to ascertain definitely whether the wave-length of the light which ionizes a gas is related to the ionizing potential by the quantum relation.

CHAPTER III

THE ENERGY OF PHOTO-ELECTRONS

Exact measurements of the velocities of photo-electrons are of the utmost importance in furnishing evidence for testing the theories of the photo-electric effect. The photo-electric effect was among the first effects to which the quantum theory was applied. In 1905, Einstein proposed a law governing the relation between the maximum emission energy of the photo-electron and the frequency of the light causing its emission. Each advance in experimental accuracy has given a more accurate verification of its correctness. According to Einstein, the energy of a photo-electron ejected from a substance by light of frequency is equal to the energy associated with a quantum of light of that frequency, viz., hv, less the loss of energy in getting out of the substance. The relation The relation may be

where Ve is the energy of the electron after leaving the surface (V being the voltage necessary to stop it), and Voe is the energy lost in getting out of the substance.

Some implications of this equation are as follows:

(1) The energy of a photo-electron is a linear functon of the frequency of the light.

(2) The slope of the line connecting the energy and the frequency is the well-known quantum constant “h."

(3) The long wave-length limit of the photo-electric effect, or the "photo-electric threshold" (to introduce a convenient term), is that for which the electron escapes with zero energy. Hence, the frequency vo of the photo-electric threshold is given by

so that, once we know the threshold for any substance, we know the work necessary to pull a photo-electron out of the substance.

Up to the date at which this report begins, these implications had been confirmed through the work of Richardson and Compton

Light

Case

Earth

FIG. 1.

and of Hughes. In view of the importance of testing the implications to as high a degree of accuracy as possible, further work was necessary as the researches referred to yielded a value of "h" from 10 per cent to 20 per cent smaller than the accepted value, and the limited range of wave-lengths naturally restricted the precision with which the other relations could be tested. (When these results were obtained, there was a certain amount of speculation as to whether one could expect complete agreement between the

photo-electric value and the theoretical value of "h," as it was conceivable that the slope of the line connecting energy of photoelectrons and frequency might in some way be slightly affected by the nature of the substance or by other conditions.)

METHOD OF MEASUREMENT OF VELOCITIES

The most common way of measuring the velocities of photoelectrons is to measure the photo-electric current with various Current

retarding fields. Consider a small illuminated surface surrounded by a considerably larger conductor, which we may call the "case," as in fig. 1. The photo-electric currents from the illuminated electrode to the "case," as functions of the applied accelerating or retarding potential, take the form shown in fig. 2a (where the saturation currents are adjusted to the same value for each wavelength). In general, the curves imply that while some electrons require a retarding field to stop them, the part of the curves between the ordinates at O and A apparently indicates that some photo