PART II.
The β or Cathodic Rays.
75. Discovery of the β rays. A discovery which gave a great impetus to the study of the radiations from active bodies was made in 1899, almost simultaneously in Germany, France, and Austria. It was observed that preparations of radium gave out some rays which were deviable by a magnetic field, and very similar in character to the cathode rays produced in a vacuum tube. The observation of Elster and Geitel that a magnetic field altered the conductivity produced in air by radium rays, led Giesel[[113]] to examine the effect of a magnetic field on the radiations. In his experiments, the radio-active preparation was placed in a small vessel between the poles of an electromagnet. The vessel was arranged to give a pencil of rays which was approximately perpendicular to the field. The rays caused a small fluorescent patch on the screen. On exciting the electromagnet, the fluorescent zone was observed to broaden out on one side. On reversing the field, the extension of the zone was in the opposite direction. The deviation of the rays thus indicated was in the same direction and of the same order of magnitude as that for cathode rays.
S. Meyer and Schweidler[[114]] also obtained similar results. They showed, in addition, the deviation of the rays by the alteration of the conductivity of the air when a magnetic field was applied. Becquerel[[115]], a little later, showed the magnetic deflection of the radium rays by using the photographic method. P. Curie[[116]], by the electrical method, showed furthermore that the rays from radium consisted of two kinds, one apparently non-deviable and easily absorbed (now known as the α rays), and the other penetrating and deviable by a magnetic field (now known as the β rays). The ionization effect due to the β rays was only a small fraction of that due to the α rays. At a later date Becquerel, by the photographic method, showed that uranium gave out some deflectable rays. It had been shown previously[[117]] that the rays from uranium consisted of α and β rays. The deflected rays in Becquerel’s experiment consisted entirely of β rays, as the α rays from uranium produce no appreciable photographic action. Rutherford and Grier[[118]], using the electric method, showed that compounds of thorium, like those of uranium, gave out, besides α rays, some penetrating β rays, deviable in a magnetic field. As in the case of radium, the ionization due to the α rays of uranium and thorium is large compared with that due to the β rays.
76. Examination of the magnetic deviation by the photographic method. Becquerel has made a very complete study, by the photographic method, of the β rays from radium, and has shown that they behave in all respects like cathode rays, which are known to be negatively charged particles moving with a high velocity. The motion of a charged ion acted on by a magnetic field has been discussed in section 49. It has been shown that if a particle of mass m and charge e is projected with a velocity u, at an angle α with the direction of a uniform field of strength H, it will describe a helix round the magnetic lines of force. This helix is wound on a cylinder of radius R, with the axis parallel to the field, where R is given by
mu
R = ---- sin α.
He
When α = π/2, i.e. when the rays are projected normally to the field, the particles describe circles of radius
mu
R = ----
He
The planes of these circles are normal to the field. Thus, for a particular velocity u, the value of R varies inversely as the strength of the field. In a uniform field the rays projected normally to the field describe circles, and their directions of projection are the tangents at the origin.
This conclusion has been verified experimentally by Becquerel for the β rays of radium, by an arrangement similar to that shown in [Fig. 23].
Fig. 23.
A photographic plate P, with the film downwards, is enveloped in black paper and placed horizontally in the uniform horizontal magnetic field of an electromagnet. The magnetic field is supposed to be uniform, and, in the figure, is at right angles to the plane of the paper. The plate was covered with a sheet of lead, and on the edge of the plate, in the centre of the magnetic field, is placed a small lead vessel R containing the radio-active matter.
On exciting the magnet, so that the rays are bent to the left of the figure, it is observed that a photographic impression is produced directly below the source of the rays, which have been bent round by the magnetic field. The active matter sends out rays equally in all directions. The rays perpendicular to the field describe circles, which strike the plate immediately under the source. A few of these rays, A1, A2, A3, are shown in the figure. The rays, normal to the plate, strike the plate almost normally, while the rays nearly parallel to the plate strike the plate at grazing incidence. The rays, inclined to the direction of the field, describe spirals and produce effects on an axis parallel to the field passing through the source. In consequence of this, any opaque screen placed in the path of the rays has its shadow thrown near the edge of the photographic plate.
77. Complexity of the rays. The deviable rays from radium are complex, i.e. they are composed of a flight of particles projected with a wide range of velocity. In a magnetic field every ray describes a path, of which the radius of curvature is directly proportional to the velocity of projection. The complexity of the radiation has been shown very clearly by Becquerel[[119]] in the following way.
An uncovered photographic plate, with the film upwards, was placed horizontally in the horizontal uniform magnetic field of an electromagnet. A small, open, lead box, containing the radio-active matter, was placed in the centre of the field, on the photographic plate. The light, due to the phosphorescence of the radio-active matter, therefore, could not reach the plate. The whole apparatus was placed in a dark room. The impression on the plate took the form of a large, diffuse, but continuous band, elliptic in shape, produced on one side of the plate.
Such an impression is to be expected if the rays are sent out in all directions, even if their velocities of projection are the same, for it can readily be shown theoretically, that the path of the rays is confined within an ellipse whose minor axis, which is at right angles to the field, is equal to 2R, and whose major axis is equal to πR. If, however, the active matter is placed in the bottom of a deep lead cylinder of small diameter, the rays have practically all the same direction of projection, and in that case each part of the plate is acted on by rays of a definite curvature.
In this case also, a diffuse impression is observed on the plate, giving, so to speak, a continuous spectrum of the rays and showing that the radiation is composed of rays of widely different curvatures. [Fig. 24] shows a photograph of this kind obtained by Becquerel, with strips of paper, aluminium, and platinum placed on the plate.
Fig. 24.
If screens of various thickness are placed on the plate, it is observed that the plate is not appreciably affected within a certain distance from the active matter, and that this distance increases with the thickness of the screen. This distance is obviously equal to twice the radius of curvature of the path of the rays, which are just able to produce an impression through the screen.
These experiments show very clearly that the most deviable rays are those most readily absorbed by matter. By observations of this kind Becquerel has determined approximately the inferior limit of the value of HR for rays which are transmitted through different thicknesses of matter.
The results are given in the table below:
| Substance | Thickness in mms. | Inferior limit of HR for transmitted rays |
|---|---|---|
| Black paper | 0·065 | 650 |
| Aluminium | 0·010 | 350 |
| “ | 0·100 | 1000 |
| ” | 0·200 | 1480 |
| Mica | 0·025 | 520 |
| Glass | 0·155 | 1130 |
| Platinum | 0·030 | 1310 |
| Copper | 0·085 | 1740 |
| Lead | 0·130 | 2610 |
If e/m is a constant for all the rays, the value of HR is proportional to the velocity of the rays, and it follows from the table that the velocity of the rays which just produce an effect on the plate through ·13 mms. of lead is about 7 times that of the rays which just produce an impression through ·01 mm. of aluminium. It will be shown, however, in [section 82], that e/m is not a constant for all speeds, but decreases with increase of velocity of the rays. The difference in velocity between the rays is in consequence not as great as this calculation would indicate. On examination of the rays from uranium, Becquerel found that the radiation is not as complex as that from radium, but consists wholly of rays for which the value of HR is about 2000.
78. Examination of the β rays by the electric method. The presence of easily deviable rays given off from an active substance can most readily be shown by the photographic method, but it is necessary, in addition, to show that the penetrating rays which produce the ionization in the gas are the same as those which cause the photographic action. This can be conveniently tested in an arrangement similar to that shown in [Fig. 25].
Fig. 25.
The radio-active matter A is placed on a lead block B´´ between the two parallel lead plates BB´. The rays pass between the parallel plates and ionize the gas between the plates PP´ of the testing vessel. The magnetic field is applied at right angles to the plane of the paper. The dotted rectangle EEEE represents the position of the pole piece. If a compound of radium or thorium is under investigation, a stream of air is required to prevent the diffusion of the radio-active emanations into the testing vessel. When a layer of uranium, thorium or radium compound is placed at A, the ionization in the testing vessel is due mainly to the action of the α and β rays. The α rays are cut off by adding a layer of aluminium ·01 cm. thick over the active material. When the layer of active matter is not more than a few millimetres thick, the ionization due to the γ rays is small compared with that produced by the β rays, and may be neglected. On the application of a magnetic field at right angles to the mean direction of the rays, the ionization in the testing vessel due to the rays steadily decreases as the strength of the field increases, and in a strong field it is reduced to a very small fraction of its original value. In this case the rays are bent so that none of them enter the testing vessel.
Examined in this way, it has been found that the β rays of uranium, thorium, and radium consist entirely of rays readily deflected by a magnetic field. The rays from polonium consist entirely of α rays, the deviation of which can be detected only in very intense magnetic fields.
When the screen covering the active material is removed, in a strong magnetic field, the ionization in the vessel is mainly due to the α rays. On account of the slight deviation of the α rays under ordinary experimental conditions, a still greater increase of the magnetic field does not appreciably alter the current due to them in the testing vessel.
The action of a magnetic field on a very active substance like radium is easily shown by the electrical method, as the ionization current due to the deviable rays is large. With substances of small activity like uranium and thorium, the ionization current due to the deviable rays is very small, and a sensitive electrometer or an electroscope is required to determine the variation, in a magnetic field, of the very small current involved. This is especially the case for thorium oxide, which gives out only about ⅕ of the amount of deviable rays given out by the same weight of uranium oxide.
79. Experiments with a fluorescent screen. The β rays from a few milligrams of pure radium bromide produce intense fluorescence in barium platinocyanide and other substances which can be made luminous under the influence of the cathode rays. Using a centigram of radium bromide, the luminosity on a screen, placed upon it, is bright enough to be observed in daylight. With the aid of such a screen in a dark room many of the properties of the β rays may be simply illustrated and their complex nature clearly shown. A small quantity of radium is placed in the bottom of a short, narrow, lead tube open at one end. This is placed between the pole pieces of an electromagnet, and the screen placed below it. With no magnetic field, a faint luminosity of the screen is observed due to the very penetrating γ rays which readily pass through the lead. When the magnetic field is put on, the screen is brightly lighted up on one side over an area elliptical in shape ([section 77]). The direction of deviation is reversed by reversal of the field. The broad extent of the illumination shows the complex nature of the β rays. On placing a metallic object at various points above the screen, the trajectory of the rays can readily be traced by noticing the position of the shadow cast upon the screen. By observing the density of the shadow, it can be seen that the rays most easily deviated are the least penetrating.
Comparison of the β rays with cathode rays.
80. Means of comparison. In order to prove the identity of the β rays from active bodies with the cathode rays produced in a vacuum tube, it is necessary to show
(1) That the rays carry with them a negative charge;
(2) That they are deviated by an electric as well as by a magnetic field;
(3) That the ratio e/m is the same as for the cathode rays.
Electric charge carried by the β rays. The experiments of Perrin and J. J. Thomson have shown that the cathode rays carry with them a negative charge. In addition, Lenard has shown that the rays still carry a charge after traversing thin layers of matter. When the rays are absorbed, they give up their charge to the body which absorbs them. The total amount of charge carried by the β rays from even a very active preparation of radium is, in general, small compared with that carried by the whole of the cathode rays in a vacuum tube, and can be detected only by delicate methods.
Suppose that a layer of very active radium is spread on a metal plate connected to earth, and that the β rays are absorbed by a parallel plate connected with an electrometer. If the rays are negatively charged, the top plate should receive a negative charge increasing with the time. On account, however, of the great ionization produced by the rays between the plates, any charge given to one of them is almost instantly dissipated. In many cases, the plate does become charged to a definite positive or negative potential depending on the metal, but this is due to the contact difference of potential between the plates, and would be produced whether the rays were charged or not. The ionization of the gas is greatly diminished by placing over the active material a metal screen which absorbs the α rays, but allows the β rays to pass through with little absorption.
The rapid loss of any charge communicated to the top plate can be very much reduced, either by diminishing the pressure of the gas surrounding it or by enclosing the plate with suitable insulators. In their experiments to determine the amount of charge carried by the radium rays, M. and Mme Curie[[120]] used the second method.
A metal disc MM ([Fig. 26]) is connected with an electrometer by the wire T. The disc and wire are completely surrounded by insulating matter ii. The whole is surrounded by a metal envelope EEEE connected with earth. On the lower side of the disc, the insulator and the metallic covering are very thin. This side is exposed to the rays of the radium R placed in a depression in a lead plate AA.
Fig. 26.
The rays of the radium pass through the metal cover and insulator with little absorption, but they are completely absorbed by the disc MM. It was observed that the disc received a negative charge which increased uniformly with the time, showing that the rays carry with them a negative charge. The current observed was very small. With an active preparation of radium[[121]], forming a layer 2·5 sq. cms. in area and 2 mms. thick, a current of the order of 10-11 amperes was observed after the rays had traversed a layer of aluminium ·01 mm. thick and a layer of ebonite ·3 mm. thick. The current was the same with discs of lead, copper, and zinc, and also when the ebonite was replaced by paraffin.
Curie also observed in another experiment of a similar character that the radium itself acquired a positive charge. This necessarily follows if the rays carry with them a negative charge. If the β rays alone carried with them a charge, a pellet of radium, if perfectly insulated, and surrounded by a non-conducting medium, would in the course of time be raised to a high positive potential. Since, however, the α rays carry with them a charge opposite in sign to the β rays, the ratio of the charge carried off by the two types of rays must be determined, before it can be settled whether the radium would acquire a positive or a negative charge. If, however, the radium is placed in an insulated metal vessel of a thickness sufficient to absorb all the α rays, but not too thick to allow most of the β rays to escape, the vessel will acquire a positive charge in a vacuum.
An interesting experimental result bearing upon this point has been described by Dorn[[122]]. A small quantity of radium was placed in a sealed glass tube and left for several months. On opening the tube with a file, a bright electric spark was observed at the moment of fracture, showing that there was a large difference of potential between the inside of the tube and the earth.
In this case the α rays were absorbed in the walls of the tube, but a large proportion of the β rays escaped. The inside of the tube thus became charged, in the course of time, to a high positive potential; a steady state would be reached when the rate of escape of negative electricity was balanced by the leakage of positive electricity through the walls of the tube. The external surface of the glass would be always practically at zero potential, on account of the ionization of the air around it.
Strutt[[123]] has recently described a simple and striking experiment to illustrate still more clearly that a radium preparation acquires a positive charge, if it is enclosed in an envelope thick enough to absorb all the α particles, but thin enough to allow most of the β particles to escape. The experimental arrangement is clearly seen in [Fig. 27]. A sealed tube AA containing the radium, was attached at one end to a pair of thin gold leaves in metallic connection with the radium, and was insulated inside a larger tube by means of a quartz rod B. The inner surface of the tube was coated with tinfoil EE connected to earth. The glass surface of AA was made conducting by a thin coating of phosphoric acid. The air in the outer tube was exhausted as completely as possible by means of a mercury pump, in order to reduce the ionization in the gas, and consequently the loss of any charge gained by the gold leaves. After an interval of 20 hours, the gold leaves were observed to diverge to their full extent, indicating that they had acquired a large positive charge. In this experiment Strutt used ½ gram of radiferous barium of activity only 100 times that of uranium.
Fig. 27.
If the tube is filled with 30 mgrs. of pure radium bromide, the leaves diverge to their full extent in the course of about a minute. If it is arranged that the gold leaf, at a certain angle of divergence, comes in contact with a piece of metal connected with earth, the apparatus can be made to work automatically. The leaf diverges, touches the metal, and at once collapses, and this periodic movement of the leaf will continue, if not indefinitely, at any rate as long as the radium lasts. This “radium clock” should work at a sensibly uniform rate for many years, but, from evidence considered later ([Section 261]), there is reason to believe that the number of β particles emitted would decrease exponentially with the time, falling to half value in about 1200 years. The period of movement of the leaf should thus gradually increase with the time, and ultimately the effect would become too small to observe.
The action of this radium clock is the nearest approach to an apparent perpetual motion that has so far been observed.
A determination of the amount of the charge carried off by the β rays of radium has been made by Wien[[124]]. A small quantity of radium, placed in a sealed platinum vessel, was hung by an insulating thread inside a glass cylinder, which was exhausted to a low pressure. A connection between the platinum vessel and an electrode sealed on to the external glass cylinder could be made, when required, by tilting the tube. Wien found that in a good vacuum the platinum vessel became charged to about 100 volts. The rate of escape of negative electricity from the platinum vessel containing 4 milligrams of radium bromide corresponded to 2·91 × 10-12 amperes. If the charge on each particle is taken as 1·1 × 10-20 electromagnetic units, this corresponds to an escape of 2·66 × 107 particles per second. From 1 gram of radium bromide the corresponding number would be 6·6 × 109 per second. Since some of the β rays are absorbed in their passage through the walls of the containing vessel and through the radium itself, the actual number projected per second from 1 gram of radium bromide must be greater than the above value. This has been found by the writer to be the case. The method employed reduced the absorption of the β rays to a minimum, and the total number emitted per second by 1 gram of radium bromide in radio-active equilibrium was found to be 4·1 × 1010, or about six times the number found by Wien. A detailed account of the method employed cannot be given with advantage at this stage, but will be found later in [Section 253].
81. Determination of e/m. We have seen ([Section 50]) that, in their passage between the plates of a condenser, the cathode rays are deflected towards the positive plate. Shortly after the discovery of the magnetic deviation of the β rays from radium, Dorn[[125]] and Becquerel[[126]] showed that they also were deflected by an electric field.
By observing separately the amount of the electric and magnetic deviation, Becquerel was able to determine the ratio of e/m and the velocity of the projected particles. Two rectangular copper plates, 3·45 cms. high and 1 cm. apart, were placed in a vertical plane and insulated on paraffin blocks. One plate was charged to a high potential by means of an influence machine, and the other was connected with earth. The active matter was placed in a narrow groove cut in a lead plate parallel to the copper plates and placed midway between them. The photographic plate, enveloped in black paper, was placed horizontally above the plate containing the active substance. The large and diffuse pencil of rays thus obtained was deflected by the electric field, but the deviation amounted to only a few millimetres and was difficult to measure. The method finally adopted was to place vertically above the active matter a thin screen of mica, which cut the field into two equal parts. Thus, in the absence of an electric field, a narrow rectangular shadow was produced on the plate.
When the electric field was applied, the rays were deflected and a part of the pencil of rays was stopped by the mica screen. A shadow was thus cast on the plate which showed the direction of deviation and corresponded to the least deviable rays which gave an impression through the black paper.
If a particle of mass m, charge e, and velocity u, is projected normally to an electric field of strength X, the acceleration α is in the direction of the field, and is given by
Xe
α = ----- .
m
Since the particle moves with a constant acceleration parallel to the field, the path of the particle is the same as that of a body projected horizontally from a height with a constant velocity and acted on by gravity. The path of the particle is thus a parabola, whose axis is parallel to the field and whose apex is at the point where the particle enters the electric field. The linear deviation d1 of the ray parallel to the field after traversing a distance l is given by
1 Xe l2
d1 = -- ----- -- .
2 m u2
On leaving the electric field, the particle travels in the direction of the tangent to the path at that point. If θ is the angular deviation of the path at that point
eXl
tan θ = ----- .
mu2
The photographic plate was at a distance h above the extremity of the field. Thus the particles struck the plate at a distance d2 from the original path given by
In the experimental arrangement the values were
d2 = ·4 cms.;
X = 1·02 × 1012;
l = 3·45 cms.;
h = 1·2 cms.
If the radius R of curvature of the path of the same rays is observed in a magnetic field of strength H perpendicular to the rays,
e V
--- = ----
m HR
Combining these two equations we get
A difficulty arose in identifying the part of the complex pencil of rays for which the electric and magnetic deviations were determined. Becquerel estimated that the value of HR for the rays deflected by the electric field was about 1600 C.G.S. units. Thus
u = 1·6 × 1010 cms. per second,
and
e
--- = 107.
m
Thus these rays had a velocity more than half the velocity of light, and an apparent mass about the same as the cathode ray particles, i.e. about ¹⁄₁₀₀₀ of the mass of the hydrogen atom. The β ray is therefore analogous in all respects to the cathode ray, except that it differs in velocity. In a vacuum tube the cathode rays generally have a velocity of about 2 × 109 cms. per sec. In special tubes with strong fields the velocity may be increased to about 1010 cms. per sec. These β particles, then, behave like isolated units of negative electricity, identical with the electrons set free by an electric discharge in a vacuum tube. The electrons projected from radium have velocities varying from about 0·2V to at least 0·96V, where V is the velocity of light, and thus have an average speed considerably greater than that of the electrons produced in a vacuum tube. These moving electrons are able to pass through much greater thicknesses of matter before they are absorbed than the slower electrons produced in a vacuum tube, but the difference is one merely of degree and not of kind. Since electrons are continuously and spontaneously expelled from radium with enormous velocities, they must acquire their energy of motion from the matter itself. It is difficult to avoid the conclusion, that this velocity has not been suddenly impressed on the electron. Such a sudden gain of velocity would mean an immense and sudden concentration of energy on a small particle, and it is more probable that the electron before its expulsion has been in rapid orbital or oscillatory motion in the atom, and, by some means, suddenly escapes from its orbit. According to this view, the energy of the electron is not suddenly created but is only made obvious by its escape from the system to which it belongs.
82. Variation of e/m with the velocity of the electron. The fact that radium throws off electrons with rates of speed varying from ⅕ to ⁹⁄₁₀ the velocity of light has been utilised by Kaufmann[[127]] to examine whether the ratio e/m of the electrons varies with the speed. We have seen ([Section 48]) that, according to the electromagnetic theory, a charge of electricity in motion behaves as if it had apparent mass. For small speeds, this additional electrical mass is equal to
2 e2
- --- ,
3 a
where a is the radius of the body, but it increases rapidly as the speed of light is approached. It is very important to settle whether the mass of the electron is due partly to mechanical and partly to electrical mass, or whether it can be explained by virtue of electricity in motion independently of the usual conception of mass.
Slightly different formulae expressing the variation of mass with speed have been developed by J. J. Thomson, Heaviside, and Searle. To interpret his results Kaufmann used a formula developed by M.
Abraham[[128]].
Let m₀ = mass of electron for slow speeds;
m = apparent mass of electron at any speed;
u = velocity of electron;
V = velocity of light.
Let β = u/V; then it can be shown that
where
The experimental method employed to determine e/m and u is similar to the method of crossed spectra. Some strongly active radium was placed at the bottom of a brass box. The rays from this passed between two brass plates insulated and about 1·2 mm. apart. These rays fell on a platinum diaphragm, containing a small tube about 0·2 mm. in diameter, which allowed a narrow bundle of rays to pass. The rays then struck a photographic plate enveloped in a thin layer of aluminium.
In the experiments the diaphragm was about 2 cms. from the active material and at the same distance from the photographic plate. When the whole apparatus was placed in a vacuum, a P.D. of from 2000 to 5000 volts could be applied between the plates without a spark. The rays were deflected in their passage through the electric field, and produced what may be termed an electric spectrum on the plate.
Fig. 28.
If a magnetic field is superimposed parallel to the electric field by means of an electromagnet, a magnetic spectrum is obtained perpendicular to the electric spectrum. The combination of the two spectra gives rise to a curved line on the plate. The double trace obtained on the photographic plate with reversal of the magnetic field is shown in [Fig. 28]. Disregarding some small corrections, it can readily be shown that if y and z are the electric and magnetic deviations respectively,
z
β = κ1 ----- (3),
y
and
e z2
-- = κ --- (4).
m y
From these two equations, combined with (1), we obtain
where κ, κ1, κ2 are constants.
Equation (5) gives the curve that should be obtained on the plate according to the electromagnetic theory. This is compared by trial with the actual curve obtained on the plate.
In this way Kaufmann[[129]] found that the value of e/m decreased with the speed, showing that, assuming the charge constant, the mass of the electron increased with the speed.
The following numbers give some of the preliminary results obtained by this method.
| Velocity of electron | e/m |
|---|---|
| 2·36 × 1010 cms. per sec. | 1·31 × 107 |
| 2·48 „ „ | 1·17 × 107 |
| 2·59 „ „ | 0·97 × 107 |
| 2·72 „ „ | 0·77 × 107 |
| 2·85 „ „ | 0·63 × 107 |
For the cathode rays S. Simon[[130]] obtained a value for e/m of 1·86 × 107 for an average speed of about 7 × 109 cms. per second.
In a later paper[[131]] with some very active radium, more satisfactory photographs were obtained, which allowed of accurate measurement. The given equation of the curve was found to agree satisfactorily with experiment.
The table given below, deduced from the results given by Kaufmann, shows the agreement between the theoretical and experimental values, u being the velocity of the electron and V that of light.
The average percentage error between the observed and calculated value is thus not much more than one per cent. It is remarkable how nearly the velocity of the electron has to approach the velocity of light before the value of m/m₀ becomes large. This is shown in the following table which gives the calculated values of m/m₀ for different velocities of the electron.
| Value of u/V | Observed value of m/m₀ | Percentage difference from theoretical values |
|---|---|---|
| Small | 1 | |
| ·732 | 1·34 | -1·5 % |
| ·752 | 1·37 | -0·9 „ |
| ·777 | 1·42 | -0·6 „ |
| ·801 | 1·47 | +0·5 „ |
| ·830 | 1·545 | +0·5 „ |
| ·860 | 1·65 | 0 „ |
| ·883 | 1·73 | +2·8 „ |
| ·933 | 2·05 | -7·8 „ ? |
| ·949 | 2·145 | -1·2 „ |
| ·963 | 2·42 | +0·4 „ |
| Value of u/V | small | ·1 | ·5 | ·9 | ·99 | ·999 | ·9999 | ·999999 |
| Calculated value m/m₀ | 1·00 | 1·015 | 1·12 | 1·81 | 3·28 | 4·96 | 6·68 | 10·1 |
Thus for velocities varying from 0 to ⅒ the velocity of light, the mass of the electron is practically constant. The increase of mass becomes appreciable at about half the velocity of light, and increases steadily as the velocity of light is approached. Theoretically the mass becomes infinite at the velocity of light, but even when the velocity of the electron only differs from that of light by one part in a million, its mass is only 10 times the value for slow speeds.
The above results are therefore in agreement with the view that the mass of the electron is altogether electrical in origin and can be explained purely by electricity in motion. The value of e/m₀, for slow speeds, deduced from the results was 1·84 × 107, which is in very close agreement with the value obtained by Simon for the cathode rays, viz. 1·86 × 107.
If the electricity carried by the electron is supposed to be distributed uniformly over a sphere of radius a, for speeds slow compared with the velocity of light, the apparent mass
2 e2
m₀ = --- ----
3 a
Therefore
2 e
a = --- ---- . e
3 m₀
Taking the value of e as 1·13 × 10-20, a is 1·4 × 10-13 cms.
Thus the diameter of an electron is minute compared with the diameter of an atom.
83. Distribution of velocity amongst the β particles. Some interesting experiments have been recently made by Paschen[[132]] to determine the relative number of β particles which are expelled from radium at the different speeds. The experimental arrangement is shown in [Fig. 29].
Fig. 29.
A small thin silvered glass tube b, containing 15 mgrs. of radium bromide, was placed in the axis of a number of lead vanes arranged round a cylinder of diameter 2 cms. and length 2·2 cms. When no magnetic field was acting, the β particles from the radium passed through the openings and were absorbed in an outer concentric cylinder aa of lead of inner diameter 3·7 cms. and of thickness 5·5 mms. This outer cylinder was rigidly connected to the inner cylinder cc by quartz rods ii, which also served to insulate it. The cylinder c and the radium were connected with earth. A gold-leaf electroscope E was attached to a, and the whole apparatus was enclosed in a glass vessel which was exhausted to a low vacuum by means of a mercury pump. The glass vessel was placed in the uniform field of a large electromagnet, so that the axis of the lead cylinder was parallel to the lines of force.
The outer cylinder gains a negative charge on account of the particles which are absorbed in it. This negative charge, which is indicated by the movement of the gold-leaf, tends to be dissipated by the small ionization produced in the residual gas by the passage of the β rays. This action of the gas can be eliminated by observing the rate of movement of the gold leaf when charged alternately to an initial positive and negative potential. The mean of the two rates is proportional to the number of β particles which give up their charge to the lead cylinder. This is evidently the case, since, when the charge is positive, the ionization of the gas assists the rate of movement of the gold-leaf, and, when negative, diminishes it to an equal extent.
When a magnetic field is applied, each of the particles describes a curved path, whose radius of curvature depends on the velocity of the particle. For weak fields, only the particles of smallest velocity will be deflected sufficiently not to strike the outer cylinder, but, as the field is raised, the number will increase until finally all the β particles fail to reach the outer cylinder. The decrease of the charge communicated to the outer cylinder with the increase of the strength of the magnetic field is shown graphically in [Fig. 30], Curve I.
The ordinates represent in arbitrary units the charge communicated to the lead cylinder per second, and thus serve as a measure of the number of β particles which reach the cylinder. Knowing the dimensions of the apparatus, and assuming the value e/m found by Kaufmann, the velocity of the particles which just fail to reach the lead cylinder can be deduced from any strength of the magnetic field. Curve II, [Fig. 30] is the first differential of Curve I, and the ordinates represent the relative number of β particles which are projected at each velocity.
Fig. 30.
From the data given by Kaufmann (see [section 82]) Paschen deduced that the group of rays examined by the former, which had velocities lying between 2·12 × 1010 and 2·90 × 1010 cms. per second, corresponded to the group of rays between the points A and B, that is, to the group of rays which were completely deflected from the lead cylinder between the magnetic fields of strengths of 1875 and 4931 C.G.S. units. Since radium gives off β particles which require a field of strength over 7000 units to deflect them, Paschen concluded that β particles are expelled from radium with still greater velocities than the highest recorded by Kaufmann.
Paschen considered that the small charge observed in still higher fields was mainly due to the γ rays. The effect is small and is probably not due to an actual charge carried by the γ rays but to a secondary effect produced by them. This question will be discussed in more detail in [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.