chapter XIII.

=96. Experiments with a zinc sulphide screen.= A screen of Sidot’s hexagonal blend (phosphorescent crystalline zinc sulphide) lights up brightly under the action of the α rays of radium and polonium. If the surface of the screen is examined with a magnifying glass, the light from the screen is found not to be uniformly distributed but to consist of a number of scintillating points of light. No two flashes succeed one another at the same point, but they are scattered over the surface, coming and going rapidly without any movement of translation. This remarkable action of the radium and polonium rays on a zinc sulphide screen was discovered by Sir William Crookes[152], and independently by Elster and Geitel[153], who observed it with the rays given out from a wire which has been charged negatively either in the open air or in a vessel containing the emanation of thorium.

In order to show the scintillations of radium on the screen, Sir William Crookes has devised a simple apparatus which he has called the “Spinthariscope.” A small piece of metal, which has been dipped in a radium solution, is placed several millimetres away from a small zinc sulphide screen. This screen is fixed at one end of a short brass tube and is looked at through a lens fixed at the other end of the tube. Viewed in this way, the surface of the screen is seen as a dark background, dotted with brilliant points of light which come and go with great rapidity. The number of points of light per unit area to be seen at one time falls off rapidly as the distance from the radium increases, and, at several centimetres distance, only an occasional one is seen. The experiment is extremely beautiful, and brings vividly before the observer the idea that the radium is shooting out a stream of projectiles, the impact of each of which on the screen is marked by a flash of light.

The scintillating points of light on the screen are the result of the impact of the α particles on its surface. If the radium is covered with a layer of foil of sufficient thickness to absorb all the α rays the scintillations cease. There is still a phosphorescence to be observed on the screen due to the β and γ rays, but this luminosity is not marked by scintillations to any appreciable extent. Sir William Crookes showed that the number of scintillations was about the same in vacuo as in air at atmospheric pressure. If the screen was kept at a constant temperature, but the radium cooled down to the temperature of liquid air, no appreciable difference in the number of scintillations was observed. If, however, the screen was gradually cooled to the temperature of liquid air, the scintillations diminished in number and finally ceased altogether. This is due to the fact that the screen loses to a large extent its power of phosphorescence at such a low temperature.

Not only are scintillations produced by radium, actinium, and polonium, but also by the emanations and other radio-active products which emit α rays. In addition, F. H. Glew[154] has found that they can be observed from the metal uranium, thorium compounds and various varieties of pitchblende. In order to show the scintillations produced by pitchblende, a flat surface was ground, and a transparent screen, whose lower surface was coated with zinc sulphide, placed upon it. Glew has designed a modified and very simple form of spinthariscope. A transparent screen, coated on one side with a thin layer of zinc sulphide, is placed in contact with the active material, and the scintillations observed by a lens in the usual way.

Since there is no absorption in the air, the luminosity is a maximum. The relative transparency of different substances placed between the active material and the screen may, in this way, be directly studied.

The production of scintillations appears to be a general property of the α rays from all radio-active substances. The scintillations are best shown with a zinc sulphide screen; but are also observed with willemite (zinc silicate), powdered diamond, and potassium platinocyanide (Glew, _loc. cit._). If a screen of barium platinocyanide is exposed to the α rays from radium, the scintillations are difficult to observe, and the luminosity is far more persistent than for a zinc sulphide screen exposed under the same conditions. The duration of the phosphorescence in this case probably accounts for the absence of visible scintillations.

There can be no doubt that the scintillations result from the continuous bombardment of the sensitive screen by the α particles. Each of these particles moves with enormous velocity, and has a considerable energy of motion. On account of the ease with which these particles are stopped, most of this energy is given up at the surface of the screen, and a portion of the energy is in some way transformed into light. Zinc sulphide is very sensitive to mechanical shocks. Luminosity is observed if a penknife is drawn across the screen, or if a current of air is directed on to the screen. The disturbance effected by the impact of the α particle extends over a distance very large compared with the size of the impinging particle, so that the spots of light produced have an appreciable area. Recently Becquerel[155] has made an examination of the scintillations produced by different substances, and has concluded that the scintillations are due to irregular cleavages in the crystals composing the screen, produced by the action of the α rays. Scintillations can be mechanically produced by crushing a crystal. Tommasina[156] found that a zinc sulphide screen removed from the action of the radium rays for several days, showed the scintillations again when an electrified rod was brought near it.

The number of scintillations produced in zinc sulphide depends upon the presence of a slight amount of impurity and on its crystalline state. It can be shown that even with the most sensitive zinc sulphide screens, the number of scintillations is probably only a small fraction of the total number of α particles which fall upon it. It would appear that the crystals are in some way altered by the bombardment of the α particles, and that some of the crystals occasionally break up with emission of light[157].

Although the scintillations from a particle of pure radium bromide are very numerous, they are not too numerous to be counted. Close to the radium, the luminosity is very bright, but by using a high power microscope the luminosity can still be shown to consist of scintillations. Since the number of scintillations probably bears no close relation to the number of α particles emitted, a determination of the number of scintillations would have no special physical significance. The relation between the number of α particles and the number of scintillations would probably be variable, depending greatly on the exact chemical composition of the sensitive substance and also upon its crystalline state.

=97. Absorption of the α rays by matter=. The α rays from the different radio-active substances can be distinguished from one another by the relative amounts of their absorption by gases or by thin screens of solid substances. When examined under the same conditions, the α rays from the active substances can be arranged in a definite order with reference to the amount of absorption in a given thickness of matter.

In order to test the amount of absorption of the α rays for different thicknesses of matter, an apparatus similar to that shown in Fig. 17, p. 98, was employed[158]. A thin layer of the active material was spread uniformly over an area of about 30 sq. cms., and the saturation current observed between two plates 3·5 cms. apart. With a thin layer[159] of active material, the ionization between the plates is due almost entirely to the α rays. The ionization due to the β and γ rays is generally less than 1% of the total.

The following table shows the variation of the saturation current between the plates due to the α rays from radium and polonium, with successive layers of aluminium foil interposed, each ·00034 cm. in thickness. In order to get rid of the ionization due to the β rays from radium, the radium chloride employed was dissolved in water and evaporated. This renders the active compound, for the time, nearly free from β rays.

The initial current with 1 layer of aluminium over the active material is taken as 100. It will be observed that the current due

_Polonium._ _Radium._

Layers of Current Ratio of Layers of Current Ratio of aluminium decrease aluminium decrease for each for each layer layer

0 100 0 100 ·41 ·48 1 41 1 48 ·31 ·48 2 12·6 2 23 ·17 ·60 3 2·1 3 13·6 ·067 ·47 4 ·14 4 6·4 ·39 5 0 5 2·5 ·36 6 ·9

7 0

to the radium rays decreases very nearly by half its value for each additional thickness until the current is reduced to about 6% of the maximum. It then decays more rapidly to zero. Thus, for radium, over a wide range, the current decreases approximately according to an exponential law with the thickness of the screen, or

$$ \frac {i} {i₀} = e^{λ d} $$,

where _i_ is the current for a thickness _d_, and _i₀_ the initial current. In the case of polonium, the decrease is far more rapid than would be indicated by the exponential law. By the first layer, the current is reduced to the ratio ·41. The addition of the third layer cuts the current down to a ratio of ·17. For most of the active bodies, the current diminishes slightly faster than the exponential law would lead one to expect, especially when the radiation is nearly all absorbed.

=98.= The increase of absorption of the α rays of polonium with the thickness of matter traversed has been very clearly shown in some experiments made by Mme Curie. The apparatus employed is shown in Fig. 34.

The saturation current was measured between two parallel plates _PP´_ 3 cms. apart. The polonium _A_ was placed in the metal box _CC_, and the rays from it, after passing through an opening in the lower plate _P´_, covered with a layer of thin foil _T_, ionized the gas between the plates. For a certain distance _AT_, of 4 cms. or more, no appreciable current was observed between _P_ and _P´_. As the distance _AT_ was diminished, the current increased in a very sudden manner, so that for a small variation of the distance _AT_ there was a large increase of current. With still further decrease of distance the current increases in a more regular manner. The results are shown in the following table, where the screen _T_ consisted of one and two layers of aluminium foil respectively. The current due to the rays, without the aluminium screen, is in each case taken as 100.

Distance AT in cms. 3·5 2·5 1·9 1·45 0·5

For 100 rays 0 0 5 10 25 transmitted by one layer

For 100 rays 0 0 0 0 0·7 transmitted by two layers

The metallic screen thus cuts off a greater proportion of the rays the greater the distance of air which the radiations traverse. The effects are still more marked if the plates _PP´_ are close together. Results similar but not so marked are found if radium is substituted for the polonium.

It follows from these experiments that the ionization per unit volume, due to a large plate uniformly covered with the radio-active matter, falls off rapidly with the distance from the plate. At a distance of 10 cms. the α rays from uranium, thorium, or radium have been completely absorbed in the gas, and the small ionization then observed in the gas is due to the more penetrating β and γ rays. The relative amount of the ionization observed at a distance from the source will increase with the thickness of the layer of active matter, but will reach a maximum for a layer of a certain thickness. The greater proportion of the ionization, due to unscreened active matter, is thus entirely confined to a shell of air surrounding it not more than 10 cms. in depth.

=99.= The α rays from different compounds of the same active element, although differing in amount, have about the same average penetrating power. Experiments on this point have been made by the writer[160] and by Owens[161]. Thus in comparing the relative power of penetration of the α rays from the different radio-elements, it is only necessary to determine the penetrating power for one compound of each of the radio-elements. Rutherford and Miss Brooks[162] have determined the amount of absorption of the α rays from the different active substances in their passage through successive layers of aluminium foil ·00034 cm. thick. The curves of absorption are given in Fig. 35. For the purpose of comparison in each case, the initial current with the bare active compound was taken as 100. A very thin layer of the active substance was used, and, in the case of thorium and radium, the emanations given off were removed by a slow current of air through the testing vessel. A potential difference of 300 volts was applied between the plates, which was sufficient to give the maximum current in each case.

Curves for the minerals organite and thorite were very nearly the same as for thoria.

For comparison, the absorption curves of the excited radiations of thorium and radium are given, as well as the curve for the radio-elements uranium, thorium, radium, and polonium. The α radiations may be arranged in the following order, as regards their power of penetration, beginning with the most penetrating.

Thorium} Radium } excited radiation. Thorium. Radium. Polonium. Uranium.

The same order is observed for all the absorbing substances examined, viz., aluminium, Dutch metal, tinfoil, paper, and air and other gases. The differences in the absorption of the α rays from the active bodies are thus considerable, and must be ascribed either to a difference of mass or of velocity of the α particles or to a variation in both these quantities.

Since the α rays differ either in mass or velocity, it follows that they cannot be ascribed to any single radio-active impurity common to all radio-active bodies.

=100. Absorption of the α rays by gases=. The α rays from the different radio-active substances are quickly absorbed in their passage through a few centimetres of air at atmospheric pressure and temperature. In consequence of this, the ionization of the air, due to the α rays, is greatest near the surface of the radiating body and falls off very rapidly with the distance (see section 98).

A simple method of determining the absorption in gases is shown in Fig. 36. The maximum current is measured between two parallel plates _A_ and _B_ kept at a _fixed_ distance of 2 cms. apart, and then moved by means of a screw to different distances from the radio-active surface. The radiation from this active surface passed through a circular opening in the plate _A_, covered with thin aluminium foil, and was stopped by the upper plate. For observations on other gases besides air, and for examining the effect at different pressures, the apparatus is enclosed in an air-tight cylinder.

If the radius of the active surface is large compared with the distance of the plate _A_ from it, the intensity of the radiation is approximately uniform over the opening in the plate _A_, and falls off with the distance _x_ traversed according to an exponential law. Thus

$$ \frac {I} {I₀} = e^{–λ x} $$,

where λ is the “absorption constant” of the radiation for the gas under consideration[163]. Let

_x_ = distance of lower plate from active material, _l_ = distance between the two fixed plates.

The energy of the radiation at the lower plate is then

$$ I₀ e^{–λ x} $$,

and at the upper plate

$$ I₀ e^{–λ (l + x)} $$ .

The total number of ions produced between the parallel plates _A_ and _B_ is therefore proportional to

$$ e^{–λ x} − e^{–λ (l + x)} = e^{–λ x} (1 - e^{–λ l}) $$ .

Since the factor

$$ 1 = e^{–λ l} $$

is a constant, the saturation current between _A_ and _B_ varies as

$$ e^{–λ x} $$,

_i.e._ it decreases according to an exponential law with the distance traversed.

The variation of the current between _A_ and _B_ with the distance from a thin layer of uranium oxide is shown in Fig. 37 for different gases. The initial measurements were taken at a distance of about 3·5 mms. from the active surface. The actual values of this initial current were different for the different gases, but, for the purposes of comparison, the value is in each case taken as unity.

It will be seen that the current falls off with the distance approximately in a geometrical progression, a result which is in agreement with the simple theory given above. The distance through which the rays pass before they are absorbed is given below for different gases.

Gas Distance in mms. to absorb half of radiation

Carbonic acid 3

Air 4·3

Coal-gas 7·5

Hydrogen 16

The results for hydrogen are only approximate, as the absorption is small over the distance examined.

The absorption is least in hydrogen and greatest in carbonic acid, and follows the same order as the densities of the gases. In the case of air and carbonic acid, the absorption is proportional to the density, but this rule is widely departed from in the case of hydrogen. Results for the relative absorption by air of the α rays from the different active bodies are shown in Fig. 38.

The initial observation was made about 2 mms. from the active surface, and the initial current is in each case taken as 100. The current, as in the case of uranium, falls off at first approximately in geometrical progression with the distance. The thickness of air, through which the radiation passes before the intensity is reduced to half value, is given below.

Distance in mms.

Uranium 4·3

Radium 7·5

Thorium 10

Excited radiation 16·5 from Thorium and Radium

The order of absorption by air of the radiations from the active substances is the same as the order of absorption by the metals and solid substances examined.

=101. Connection between absorption and density.= Since in all cases the radiations first diminish approximately according to an exponential law with the distance traversed, the intensity _I_ after passing through a thickness _x_ is given by

$$ I = I₀ e^{–λ x} $$

where λ is the absorption constant and _I₀_ the initial intensity.

The following table shows the value of λ with different radiations for air and aluminium.

Radiation λ for λ for air aluminium

Excited radiation 830 ·42

Thorium 1250 ·69

Radium 1600 ·90

Uranium 2750 1·6

Taking the density of air at 20° C. and 760 mms. as 0·00120 compared with water as unity, the following table shows the value of λ divided by density for the different radiations.

Radiation Aluminium Air Excited radiation 320 350 Thorium 480 550 Radium 620 740 Uranium 1060 1300

Comparing aluminium and air, the absorption is thus roughly proportional to the density for all the radiations. The divergence, however, between the absorption-density numbers is large when two metals like tin and aluminium are compared. The value of λ for tin is not much greater than for aluminium, although the density is nearly three times as great.

If the absorption is proportional to the density, the absorption in a gas should vary directly as the pressure, and this is found to be the case. Some results on this subject have been given by the writer (_loc. cit._) for uranium rays between pressures of ¼ and 1 atmosphere. Owens (_loc. cit._) examined the absorption of the α radiation in air from thoria between the pressures of 0·5 to 3 atmospheres and found that the absorption varied directly as the pressure.

The variation of absorption with density for the projected positive particles is thus very similar to the law for the projected negative particles and for cathode rays. The absorption, in both cases, depends mainly on the density, but is not in all cases directly proportional to it. Since the absorption of the α rays in gases is probably mainly due to the exhaustion of the energy of the rays by the production of ions in the gas, it seems probable that the absorption in metals is due to a similar cause.

=102. Relation between ionization and absorption in gases.= It has been shown (section 45) that if the α rays are completely absorbed in a gas, the _total_ ionization produced is about the same for all the gases examined. Since the rays are unequally absorbed in different gases, there should be a direct connection between the relative ionization and the relative absorption. This is seen to be the case if the results of Strutt (section 45) are compared with the relative absorption constants (section 100).

Gas Relative Relative absorption ionization

Air 1 1

Hydrogen ·27 ·226

Carbon dioxide 1·43 1·53

Considering the difficulty of obtaining accurate determinations of the absorption, the relative ionization in a gas is seen to be directly proportional to the relative absorption within the limits of experimental error. This result shows that the energy absorbed in producing an ion is about the same in air, hydrogen, and carbon dioxide.

=103. Mechanism of the absorption of α rays by matter=. The experiments, already described, show that the ionization of the gas, due to the α rays from a large plane surface of radio-active matter, falls off in most cases approximately according to an exponential law, until most of the rays are absorbed, whereupon the ionization decreases at a much faster rate. In the case of polonium, the ionization falls off more rapidly than is to be expected on the simple exponential law.

The ionization produced in the gas is due to the collision of the rapidly moving α particles with the molecules of the gas in their path. On account of its large mass, the α particle is a far more efficient ionizer than the β particle moving at the same speed. It can be deduced from the results of experiment that each projected α particle is able to produce about 100,000 ions in passing through a few centimetres of the gas before its velocity is reduced to the limiting value, below which it no longer ionizes the gas in its path.

Energy is required to ionize the gas, and this energy can only be obtained at the expense of the kinetic energy of the projected α particle. Thus it is to be expected that the α particle should gradually lose its velocity and energy of motion in its passage through the gas.

Since the rate of absorption of the α rays in gases is deduced from measurements of the ionization of the gas at different distances from the source of radiation, a knowledge of the law of variation of the ionizing power of the projected α particle with its speed is required in order to interpret the results. The experimental data on this question are, however, too incomplete to be applied directly to a solution of this question. Townsend[164] has shown that a moving electron produces ions in the gas after a certain limiting velocity is reached. The number of ions produced per centimetre of its path through the gas then rises to a maximum, and for still higher speeds continuously decreases. For example, Townsend found that the number of ions produced by an electron moving in an electric field was small at first for weak fields, but increased with the strength of the electric field to a maximum corresponding to the production of 20 ions per cm. of path in air at a pressure of 1 mm. of mercury. Durack[165] found that the electrons, generated in a vacuum tube, moving with a velocity of about 5 × 10⁹ cms. per second produced a pair of ions every 5 cms. of path at 1 mm. pressure. In a later paper, Durack showed that for the electrons from radium, which are projected with a velocity greater than half the velocity of light, a pair of ions was produced every 10 cms. of path. The high speed electron from radium is thus a very inefficient ionizer and produces only about ¹⁄₁₀₀ of the ionization per unit path observed by Townsend for the slow moving electron.

=104.= In the case of the α particle, no direct measurements have been made upon the variation of the ionization with the velocity of the particle, so that the law of absorption of the rays cannot be deduced directly. An indirect attack upon the question has, however, been made recently by Bragg and Kleeman[166] who have formulated a simple theory to account for the experimental results which they have obtained upon the absorption of the α rays. The α particles from each simple type of radio-active matter are supposed to be projected with the same velocity, and to pass through a definite distance a in air at atmospheric pressure and temperature before they are all absorbed. As a first approximation the ionization per unit path is supposed to be the same over the whole length traversed before absorption, and to cease fairly suddenly at a definite distance from the source of radiation. This is in agreement with the observed fact that the ionization between parallel plates increases very rapidly when it approaches nearer than a certain distance to the radiant source. The range _a_ depends upon the initial energy of motion of the α particle and will thus be different for different kinds of radio-active matter. If a thick layer of radio-active matter is employed, only the α particles from the surface have a range _a_. Those which reach the surface from a depth _d_ have their range diminished by an amount ρ_d_, where ρ is the density of the radio-active matter compared with air. This is merely an expression of the fact that the absorption of the α rays is proportional to the thickness and density of matter traversed. The rays from a thick layer of active matter will thus be complex, and will consist of particles of different velocity whose ranges have all values between 0 and _a_.

Suppose that a narrow pencil of α rays is emitted from a thick layer of radio-active material, and confined by metal stops as in Fig. 39.

The pencil of rays passes into an ionization vessel _AB_ through a fine wire gauze _A_. The amount of ionization is to be determined between _A_ and _B_ for different distances _h_ from the source of the rays _R_ to the plate _A_.

All the particles coming from a depth _x_ of the material given by _h_ = _a_ − ρ_x_ will enter the ionization vessel. The number of ions produced in a depth _dh_ of the ionization vessel is equal to _nxdh_, _i.e._ to

_a_ − _h_ _n_ --------- _dh_, ρ

where _n_ is a constant.

If the depth of the ionization vessel be _b_, the total number of ions produced in the vessel is

$$ \int_h^{h+b} n \frac {a-h} {\rho} dh = \frac {nb} {\rho} (a − h - \frac {b} {2}) $$ .

This supposes that the stream of particles passes completely across the vessel. If not, the expression becomes

$$ \int_h^a n \frac {a − h} {\rho} dh = \frac {n (a − h)^2} {2\rho} $$ .

If the ionization in the vessel _AB_ is measured, and a curve plotted showing its relation to _h_, the curve in the former case should be a straight line whose slope is _nb_/ρ and in the latter a parabola.

Thus if a thin layer of radio-active material is employed and a shallow ionization vessel, the ionization would be represented by a curve such as _APM_ (Fig. 40), where the ordinates represent distances from the source of radiation, and the abscissae the ionization current between the plates _AB_.

In this case, _PM_ is the range of the α particles from the lowest layer of the radio-active matter. The current should be constant for all distances less than _PM_.

For a thick layer of radio-active matter, the curve should be a straight line such as _APB_.

Curves of the above character should only be obtained when definite cones of rays are employed, and where the ionization vessel is shallow and includes the whole cone of rays. In such a case the inverse square law need not be taken into account.

In the experiments previously recorded (sections 99 and 100), the ionization was measured between parallel plates several centimetres apart for a large area of radio-active material. Such an arrangement was necessary at the time at which the experiments were made, as only weak radio-active material was available. Measurable electrical effects could not then be obtained with narrow cones of rays and shallow ionization vessels, but this disadvantage is removed by the advent of pure radium bromide as a source of radiation.

The interesting experiments described by Bragg and Kleeman show that the theoretical curves are approximately realized in practice. The chief difficulty experienced in the analysis of the experimental results was due to the fact that radium is a complex radio-active substance and contains four radio-active products each of which gives rise to α rays which have different ranges. The general character of the results obtained from radium are shown graphically in Fig. 41, curves _A_, _B_, _C_, _D_.

The ordinates represent the distance between the radium and the gauze of the testing vessel; the abscissae the current in the ionization vessel in arbitrary units. Five milligrams of radium bromide were used, and the depth of the ionization vessel was about 5 mms. Curve _A_ is for a cone of rays of angle 20°. The initial current at a distance of 7 cms. is due to the β and γ rays and natural leak. This curve is initially parabolic, and then is made up of two straight lines. Curve _B_ is for a smaller cone, and shows the straight line character of the curve to within a short distance of the radium. Curve _C_ was obtained under the same condition as curve _A_, but with a layer of gold beater’s skin placed over the radium. The effect of this is to reduce all the ordinates of curve _A_ by the same quantity. This is to be expected on the simple theory already considered. Curve _D_ was obtained when the radium was heated so as to get rid of the emanation and its products. The α particles of greatest range are quite absent and the curve is simpler in character.

The complex character of the radium curves are more clearly brought out by a careful examination of a portion of the curve at distances between 2 and 5 cms. from the radium, using an ionization vessel of depth only 2 mms. The results are shown in Fig. 42, where the curve is seen to consist approximately of four straight lines of different slopes represented by _PQ_, _QR_, _RS_, _ST_.

Such a result is to be expected, for it will be shown later that four distinct α ray products exist in radium when in radio-active equilibrium. Each of these products of radium emits an equal number of α particles per second, but the range of each is different. If _a₁_ is the range of one stream, _a₂_ of another, the ionization in the vessel _AB_, when two streams enter the vessel, should be

_nb_ _nb_ ---- (_a₁_-_h_-_b_/2) + ----- (_a₂_ − _h_ − _b_/2), ρ ρ

_i.e._

_nb_ ---- (_a₁_ + _a₂_ − 2_h_ − _b_) . ρ

Thus the slope of the curve should in this case be 2_nb_/ρ, while if only one stream enters, it should be _nb_/ρ. When three reach it, the slope should be 3_nb_/ρ and for four 4_nb_/ρ. These results are realized fairly closely in practice. The curve (Fig. 42) consists of four parts, whose slopes are in the proportion 16, 34, 45, 65, _i.e._ very nearly in the ratio 1, 2, 3, 4.

Experiments were also made with very thin layers of radium bromide, when, as we have seen (Fig. 40) a very different shape of curve is to be expected. An example of the results is shown in Fig. 43, curves I., II. and III. Curve I. is obtained from radium bromide which has been heated to drive off the emanation, and curves II. and III. from the same substance several days later, when the emanation was again accumulating. The portion _PQ_, which is absent in the first curve, is probably due to the “excited” activity produced by the emanation. By careful examination of the successive changes in the curves after the radium has been heated to drive off the emanation, it is possible to tell the range of the α rays from each of the different products, and this has been done to some extent by Bragg and Kleeman.

It will be seen later that the results here obtained support in a novel way the theory of radio-active changes which has been advanced from data of quite a different character.

The inward slope of the curve in Fig. 43 due to the radium indicates that the α particles become more efficient ionizers as their velocity decreases. This is in agreement with observations on the β rays. In some cases Bragg also observed that the α particles are the most efficient ionizers just before they lose their power of ionizing the gas.

Thus we may conclude from these experiments that the α particles from a simple radio-active substance traverse a definite distance in air, at a definite pressure and temperature, and that the ionization ends fairly abruptly. If the rays traverse a sheet of metal, the effective range of ionization is diminished by a distance corresponding to ρ_d_, where ρ is the density of the material compared with air and _d_ its thickness. The α rays from a thick layer of a simple radio-active substance consist of α particles of different velocities, which have ranges in air lying between 0 and the maximum range. The ionization of the particles per unit path is greatest near the end of its range, and decreases somewhat as we approach the radiant source. A complex source of rays like radium gives out four types of rays, each of which has a different but distinct range.

From this theory it is possible to calculate approximately the decrease of current to be observed when sheets of metal foil are placed over a large area of radio-active substance. This is the method that has been employed to obtain the curves of Figs. 35 and 38.

Suppose a very thin layer of simple radio-active matter is employed (for example a bismuth plate covered with radio-tellurium or a metal plate made active by exposure to the presence of the thorium or radium emanations) and that the ionization vessel is of sufficient depth to absorb the α rays completely.

Let _d_ be the thickness of the metal plate, ρ its density compared with air. Consider a point _P_ close to the upper side of the plate. The range of the particles moving from a point, when the path makes an angle θ with the normal at _P_, is _a_ − ρ_d_ sec θ, where _a_ is the range in air. The rays coming from points such that the paths make an angle with the normal greater than

$$ \cos^{−1} \frac {\rho d} {a} $$

will thus be absorbed in the plate. By integrating over the circular area under the point _P_, it is easy to show that the total ionization in the vessel is proportional to

$$ \int₀^{\cos^{−1} \frac {\rho d} {a}} 2 \pi \sin \theta \cos \theta (a − \rho d \sec \theta) d\theta = \frac {\pi (a − \rho d)^2} {a} $$ .

The curves showing the relation between current and distance of metal traversed should thus be parabolic with respect to _d_. This is approximately the case for a simple substance like radio-tellurium. The curve for a thick layer of radium would be difficult to calculate on account of the complexity of the rays, but we know from experiment that it is approximately exponential. An account of some recent investigations made to determine the range of velocity over which the α particle is able to ionize the gas is given in Appendix A. The results there given strongly support the theory of absorption of the α rays discussed above.