Chapter X: Part III: The α Rays (2)

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.