This phenomenon is most easily studied in the case of the photo electrons liberated by X-rays and y-rays, when the velocities are considerable and the electrons have sufficient energy to penetrate several centimetres of a gas. The most fruitful method of investi gation is by the Wilson cloud track method, which has already been referred to. If a thin pencil of unpolarized X-rays is sent through a Wilson chamber and the tracks photographed, we can determine at once what is called the longitudinal distribution. The exact direction of the electric vector is always changing, but of necessity it must be always at right-angles to the direction of propagation. If the cloud tracks are photographed with a stereo scope camera we can count the fraction of electrons which are emitted with their directions initially within say 5° of the direc tion of propagation, between 5° and 1o°, and so on, obtaining in this way a distribution curve. The general results are as would be anticipated. Very few electrons travel near the direction of propagation either forward or backwards, the greater number tending to go off more at right-angles in the direction of the elec tric vector. The distribution curve therefore shows a marked maximum for directions at right-angles to the direction of propa gation.
However this is not all, there is a small subsidiary effect which seems to be of great importance. This maximum of the distribu tion curve is not exactly at right-angles to the direction of propa gation, it is shifted a few degrees forward, so that rather more electrons go forward than go back. This becomes more pro nounced as the wave-length gets shorter. While for light and soft X-rays it is not to be detected, it may amount to o°, 2o° or 3o° for hard X-rays or 7-rays. The primary cause of this asymmetry is to be found in the magnetic forces in the wave-front, but a simple description can also be given on the light-quantum picture. Imagine a quantum of energy hv impinging on an electron, being absorbed, and communicating all its energy to the electron. This quantum is not only characterized by its energy, it will also have momentum of amount hv/c. If we assume that the other causes responsible for the distribution would only produce a symmetrical spread about the direction of the electric vector, we can say that owing to the momentum of the quantum there should finally be an average forward momentum of amount hv/c. This does shift the maximum forward by about the right amount ; but according to some new measurements by Williams there is not exact agree ment—the predicted shift is not large enough. Either some other cause is at work or the electrons in the atom, which are moving forward at the instant the wave passes over them, have a prefer ential chance of absorbing. This is an interesting point and seems likely to shed fresh light on the details of the interaction of radia tion and matter.
Another type of asymmetry has also been investigated. By suitable. arrangements a beam of polarized X-rays can be ob tained. Suppose this is travelling along the direction of x, and the electric vector in the polarized beam is parallel to the y axis. By
taking Wilson cloud photographs close to the direction of the x-axis we can now find how the photoelectrons are distributed in the yz plane. As before a distribution is found, but this time, as would be expected, it is symmetrical. The maximum number occurs parallel to the electric vector and there appear to be very few indeed which come off at right angles to this.
Number of Photoelectrons Ejected.—The discussion so far given has centred round the elementary process of the conversion of a quantum and liberation of a photoelectron, and this process has been shown to be described completely by Einstein's equation. Thus, having treated what happens when a quantum is absorbed, the question now arises how often quanta are absorbed. It is the essential peculiarity of the photoelectric effect that these two points can be separated so completely, the energy of the ejected electron depending only on the frequency and being entirely inde pendent of the intensity of the radiation, whereas the number of electrons ejected is directly proportional to the intensity.
In considering the number of photoelectrons set free it is sim plest to go at once to the conception of an absorption coefficient. Suppose 1 ergs per sec. are incident upon each square centimetre of a very thin slab of matter, of thickness ox, then the number 6n of photoelectrons set free per second will be whereµ is called the absorption coefficient and is a characteristic constant of the material and of the frequency of the radiation. If this is applied to a gas it will give exactly the number of tracks that would be observed by a Wilson cloud apparatus. In the case of a solid it is usually rather complicated to deduce the actual number of electrons that emerge, since the scattering and absorp tion of the electrons liberated inside the solid are difficult to follow in detail.
It is simplest to consider first the case of the X-rays and y-rays, and afterwards the absorption effect of one particular set of electrons in the atom, say the K or L electrons. The total absorption of the material is then obtained by adding together the absorption of all the different sets of electrons in the atom. The first point to notice is that absorption, for example by the K electrons of tin, does not start until the frequency is increased to a certain limit. This limit which is characteristic for tin is determined by the condition that the hv of the radiation shall be just equal to the work necessary to remove a K electron to the surface of the atom ; i.e., absorption commences with the pro duction of photoelectrons of zero energy. From this point on wards, when the absorption is a maximum, it decreases steadily at first about as and later, in the 7-ray region, rather less rapidly. The attempt to extend these results towards the region of visible light meets with considerable experimental difficulties, but recently approximate values for the absorption by potassium vapour in the near ultra-violet have been obtained, which may be considered as the extension of the preceding results.