section 112.

There is a group of low velocity β particles emitted by radium (see Fig. 30) which have about the same speed as the electrons set free in a vacuum tube. In consequence of their small velocity, these probably produce a large proportion of the ionization due to the β rays at short distances from the radium, for it will be shown (section 103) that the ionization produced by an electron per unit length of path steadily decreases with increase of its velocity above a small limiting value. This observation is confirmed by experiments on the absorption of the β rays in passing through matter.

In Paschen’s experiments, the glass tube containing the radium was ·5 mms. thick, so that a considerable proportion of the low velocity β particles must have been stopped by it. This is borne out by some later experiments of Seitz which will be described in section 85.

=84. Absorption of the β rays by matter=. The β particles produce ions in their passage through the gas and their energy of motion is consequently diminished. A similar action takes place also when the β rays pass through solid and liquid media, and the mechanism of absorption is probably similar in all cases. Some of the particles in their passage through matter are completely stopped, while others have their velocity reduced. In addition, there is a considerable scattering or diffuse reflection of the rays in traversing matter. The amount of this scattering depends upon the density of the substance and also upon the angle of incidence of the rays. This scattering of the rays will be discussed later in section 111.

There are two general methods of determining the absorption of the β rays. In the first method, the variation of the ionization current is observed in a testing vessel when the active matter is covered by screens differing in material and thickness. This ionization in the vessel depends upon two quantities, viz. the number of β particles which pass through the matter and also upon the number of ions produced by them per unit path. In the absence of any definite information in regard to the variation of ionization by the electron with its velocity, no very definite conclusions can be drawn from such experiments.

The advent of pure radium-bromide has made it possible to determine the actual number of electrons which are absorbed in their passage through a definite thickness of matter, by measuring the negative charge carried by the issuing rays. Experiments of this character have been made by Seitz and will be considered later.

These two methods of determining the absorption of β rays are quite distinct in principle, and it is not to be expected that the values of the coefficients of absorption obtained in the two cases should be the same. The whole question of the absorption of electrons by matter is very complicated, and the difficulty is still further increased by the complexity of the β rays emitted by the radio-active substances. Many of the results obtained by different methods, while pointing to the same general conclusion, are quantitatively in wide disagreement. Before any definite advance can be made to a better understanding of the mechanism of absorption, it will be necessary to determine the variation of the ionization with the speed of the electron over a very wide range. Some work has already been done in this direction but not between sufficiently wide limits.

Ionization method.

We shall first consider the results obtained on the absorption of β rays by measuring the variation of the ionization current, when screens of different thickness are placed over the active substance. When the active matter is covered with aluminium foil of thickness ·1 mm., the current in a testing vessel such as is shown in Fig. 17, is due almost entirely to the β rays. If a uranium compound is used, it is found that the saturation current decreases with the thickness of matter traversed nearly according to an exponential law. Taking the saturation current as a measure of the intensity of the rays, the intensity I after passing through a thickness d of matter is given by

$$ \frac {I} {I₀} = e^{–λ d} $$,

where λ is the constant of absorption of the rays and I₀ is the initial intensity. For uranium rays, the current is reduced to half its value after passing through about ·5 mm. of aluminium.

If a compound of thorium or radium is examined in the same way, it is found that the current does not decrease regularly according to the above equation. Results of this kind for radium rays have been given by Meyer and Schweidler. The amount of absorption of the rays by a certain thickness of matter decreases with the thickness traversed. This is exactly opposite to what is observed for the α rays. This variation in the absorption is due to the fact that the β rays are made up of rays which vary greatly in penetrating power. The rays from uranium are fairly homogeneous in character, i.e. they consist of rays projected with about the same velocity. The rays from radium and thorium are complex, i.e. they consist of rays projected with a wide range of velocity and consequently with a wide range of penetrating power. The electrical examination of the deviable rays thus leads to the same results as their examination by the photographic method.

Results on the absorption of cathode rays have been given by Lenard, who has shown that the absorption of cathode rays is nearly proportional to the density of the absorbing matter, and is independent of its chemical state. If the deviable rays from active bodies are similar to cathode rays, a similar law of absorption is to be expected. Strutt, working with radium rays, has determined the law of absorption, and has found it roughly proportional to the density of matter over a range of densities varying from 0·041 for sulphur dioxide to 21·5 for platinum. In the case of mica and cardboard, the values of λ divided by the density were 3·94 and 3·84 respectively, while the value for platinum was 7·34. In order to deduce the absorption coefficient, he assumed that the radiation fell off according to an exponential law with the distance traversed. As the rays from radium are complex, we have seen that this is only approximately the case.

Since the β rays from uranium are fairly homogeneous, and are at the same time penetrating in character, they are more suitable for such a determination than the complex rays of radium. I have in consequence made some experiments with uranium rays to determine the dependence of absorption on the density. The results obtained are given in the following table, where λ is the coefficient of absorption.

Substance λ Density λ/Density

Glass 14·0 2·45 5·7 Mica 14·2 2·78 5·1 Ebonite 6·5 1·14 5·7 Wood 2·16 ·40 5·4 Cardboard 3·7 ·70 5·3 Iron 44 7·8 5·6 Aluminium 14·0 2·60 5·4 Copper 60 8·6 7·0 Silver 75 10·5 7·1 Lead 122 11·5 10·8 Tin 96 7·3 13·2

It will be observed that the value of the absorption constant divided by the density is very nearly the same for such different substances as glass, mica, ebonite, wood, iron and aluminium. The divergences from the law are great, however, for the other metals examined, viz. copper, silver, lead and tin. In tin the value of λ divided by the density is 2·5 times its value for iron and aluminium. These differences show that a law for the absorption of the β rays depending only on the density does not hold for all substances. With an exception in the case of tin, the value of λ divided by the density for the metals increases in the same order as their atomic weights.

The absorption of the β rays by matter decreases very rapidly with increase of speed. For example, the absorption of cathode rays in Lenard’s experiment (loc. cit.) is about 500 times as great as for the uranium β rays. The velocity of the β rays of uranium was found by Becquerel to be about 1·6 × 10¹⁰ cms. per sec. The velocity of the cathode rays used in Lenard’s experiment was certainly not less than ⅒ of this, so that, for a decrease of speed of less than 10 times, the absorption has increased over 500 times.

=85. Number of electrons stopped by matter.= An account will now be given of the experiments made by Seitz, to determine the relative number of electrons which are stopped in their passage through different thicknesses of matter. The experimental arrangement is shown in Fig. 31.

The radium was placed outside a glass vessel containing an insulated brass plate P, the connection of which with a wire leading to the electrometer could be made or broken by a simple electromagnetic device. The β rays from the radium R, after passing through openings in a brass plate A, covered with thin aluminium foil, were absorbed in the plate P. The glass vessel was exhausted, and the charge communicated to P by the β rays was measured by an electrometer.

In a good vacuum, the magnitude of the current observed is a measure of the number of β particles absorbed by the upper plate. The following table shows the results obtained when different thicknesses of tin foil were placed over the radium. The second table gives the ratio I/I₀ where I₀ is the rate of discharge observed before the absorbing screen is introduced. The mean value of the absorption constant λ was deduced from the equation

$$ \frac {I} {I₀} = e^{–λ d} $$

where d is the thickness of matter traversed.

The values included in the brackets have not the same accuracy as the others. There is thus a wide difference in penetrating power of the β particles emitted from radium, and some of them are very readily absorbed.

When a lead screen 3 mms. thick was placed over the radium—a thickness sufficient to absorb all the readily deflectable β rays—a small negative charge was still given to the plate, corresponding to ·29 per cent. of the maximum. This is a very much smaller value than was observed by Paschen (see Fig. 30).

Thickness of I/I₀ λ Tin in mms.

0·00834 ·869 175

0·0166 ·802 132·5

0·0421 ·653 101·5

0·0818 ·466 93·5

0·124 ·359 82·5

0·166 ·289 74·9

0·205 ·230 71·5

0·270 ·170 65·4

0·518 ·065 53

0·789 ·031 44

1·585 ·0059 32

2·16 ·0043 25

This difference may, in part, be due to the fact that, in Paschen’s experiments, a large proportion of the slow velocity electrons were absorbed in the glass tube of ·5 mm. thickness containing the radium.

Seitz also determined the relative thickness, compared with tin, of different substances which reduced the negative charge communicated to P by a definite amount. A few of the numbers are given below, and expressed in terms of tin as unity.

Substance Thickness Tin = 1

Lead ·745

Gold ·83

Platinum ·84

Silver 1

Steel 1·29

Aluminium 1·56

Water 1·66

Paraffin 1·69

The thickness required to stop a given proportion of the β rays thus decreases with the density, but not nearly so fast as the density increases. These results are difficult to reconcile with the density-law of absorption found by Lenard from the cathode rays, or with the results of the ionization method already considered. A further experimental examination of the whole question is very much to be desired.

=86. Variation of the amount of radiation with the thickness of the layer of radiating material.= The radiations are sent out equally from all portions of the active mass, but the ionization of the gas which is measured is due only to the radiations which escape into the air. The depth from which the radiations can reach the surface depends on the absorption of the radiation by the active matter itself.

Let λ be the absorption constant of the homogeneous radiation by the active material. It can readily be shown that the intensity I of the rays issuing from a layer of active matter, of thickness d, is given by

$$ \frac {I} {I_{0}} = 1 − e^{–λ d} $$,

where I₀ is the intensity at the surface due to a very thick layer.

This equation has been confirmed experimentally by observing the current due to the β rays for different thicknesses of uranium oxide. In this case I = (½)I₀ for a thickness of oxide corresponding to ·11 gr. per sq. cm. This gives a value of λ divided by density of 6·3. This is a value slightly greater than that observed for the absorption of the same rays in aluminium. Such a result shows clearly that the substance which gives rise to the β rays does not absorb them to a much greater extent than does ordinary matter of the same density.

The value of λ will vary, not only for the different active substances, but also for the different compounds of the same substance.