The Generation of Cathode Rays by Illumination

8. The Generation of Cathode Rays by Illumination of Solid Bodies

Lenard’s paper explained how the photoelectric phenomena cannot be explained by the energy of light being continuously distributed over the space through which it propagates.

I believe that the incident light consists of energy quanta of magnitude Rβν/N.

However, one can conceive of the ejection of electrons by light in the following way.

Energy quanta penetrate into the surface layer of the body.

Their energy is transformed into kinetic energy of electrons.

A light quantum delivers its entire energy to a single electron.

The possibility should not be excluded, however, that electrons might receive their energy only in part from the light quantum.

An electron to which kinetic energy has been imparted in the interior of the body will have lost some of this energy by the time it reaches the surface.

Furthermore, we shall assume that in leaving the body each electron must perform an amount of work P characteristic of the substance.

The ejected electrons leaving the body with the largest normal velocity will be those that were directly at the surface. The kinetic energy of such electrons is given by

…

In the body is charged to a positive potential Π and is surrounded by conductors at zero potential, and if Π is just large enough to prevent loss of electricity by the body, if follows that:

…

where ε is the electrical mass of the electron, or

…

where E is the charge of one gram equivalent of a single-valued ion and P’ is the potential of this amount of negative electricity with respect to this body. [8]

If one takes E = 9.6 × 103, then Π · 10−8 is the potential in volts which the body assumes when irradiated in a vacuum.

In order to see whether the derived relation yields an order of magnitude consistent with experience, we take P0 = 0, ν = 1.03×1015 (corresponding to the limit of the solar spectrum toward the ultraviolet) and β = 4.866×10−11.

We obtain Π·107 = 4.3 volts, a result agreeing in order magnitude with those of Lenard.9

If the derived formula is correct, then Π, when represented in Cartesian coordinates as a function of the frequency of the incident light, must be a straight line whose slope is independent of the nature of the emitting substance.

As far as I can see, there is no contradiction between these conceptions and the properties of the photoelectric observed by Herr Lenard. If each energy quantum of the incident light, independently of everything else, delivers its energy of electrons, then the velocity distribution of the ejected electrons will be independent of the intensity of the incident light.

On the other hand the number of electrons leaving the body will, if other conditions are kept constant, be proportional to the intensity of the incident light.10

Remarks similar to those made concerning hypothetical deviations from Stokes’s Rule can be made with regard to hypothetical boundaries of validity of the law set forth above.

In the foregoing it has been assumed that the energy of at least some of the quanta of the incident light is delivered completely to individual electrons. If one does not make this obvious assumption, one obtains, in place of the last equation:

…

For fluorescence induced by cathode rays, which is the inverse process to the one discussed above, one obtains by analogous considerations

…

In the case, of the substances investigated by Herr Lenard, P E 11is always significantly greater than Rβν, since the potential difference, which the cathode rays must traverse in order to produce visible light, amounts in some cases to hundreds and in others to thousands of volts.12

It is therefore to be assumed that the kinetic energy of an electron goes into the production of many light energy quanta.

9 Ionization of Gases by Ultraviolet Light

I assume that in the ionization of a gas by UV light, an individual light energy quantum is used for the ionization of an individual gas molecule.

From this is follows immediately that the work of ionization (i.e., the work theoretically needed for ionization) of a molecule cannot be greater than the energy of an absorbed light quantum capable of producing this effect. If one denotes by J the (theoretical) work of ionization per gram equivalent, then it follows that:

We have to assume that in ionization of a gas by ultraviolet light always one absorbed light energy quantum is used for the ionization of just one gas molecule. Firstly it follows that the ionization energy (that is, the theoretically necessary energy to ionize) of a molecule cannot be larger than the energy of an absorbed light energy quantum. Taking J as the (theoretical) ionization energy per gram equivalent, we have:

According to Lenard’s measurements for air the largest wavelength that has an effect is about 1.9·10-5 cm, so

An upper limit for the ionization energy can also be obtained from the ionization voltage in rarefied gases. According to Stark [12] the smallest measured ionization voltage (for platinum anodes) is for air about 10 volt. [13] We have thus for J an upper limit 9.6·1012, which is nearly the same as the one just found. There is another consequence that in my mind is very important to verify. If every light energy quantum ionizes one molecule then the following relation must exist between the absorbed quantity of light L and the number j of thereby ionized gram molecules:

If our understanding reflects reality this relation must hold for every gas that (at the particular frequency) has no absorption that isn’t accompanied by ionization.

According to Maxwell, energy is a continuous spatial function in the case of electromagnetism.

Material energy:

• is the sum of energy in its atoms.
• cannot be subdivided arbitrarily

EM light energy is continuously spread over an increasing volume.

The wave theory of light works optically. But optical observations are time averages and not instantaneous values.

The energy of light is discontinuously distributed in space.

• Instead, it has a finite energy quanta

Quanta are:

• localized points in space which move without dividing
• these move without dividing
• there act as complete units

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For small wavelengths..