where N₀ is the initial number of particles present. When a steady state is reached, the rate of production q₀ of fresh emanation particles is exactly balanced by the rate of change of the particles N₀ already present, i.e.
N₀ in this case represents the amount of emanation “occluded” in the compound. Substituting the value of λ found for the radium emanation in section 145,
The amount of emanation stored in a non-emanating radium compound should therefore be nearly 500,000 times the amount produced per second by the compound. This result was tested in the following way[247].
A weight of ·03 gr. of radium chloride of activity 1000 times that of uranium was placed in a Drechsel bottle and a sufficient amount of water drawn in to dissolve it. The released emanation was swept out by a current of air into a small gas holder and then into a testing cylinder. The initial saturation current was proportional to N₀. A rapid current of air was then passed through the radium solution for some time in order to remove any slight amount of emanation which had not been removed initially. The Drechsel bottle was closed air-tight, and allowed to stand undisturbed for a definite time t. The accumulated emanation was then swept out as before into the testing vessel. The new ionization current represents the value of Nt the amount of emanation formed in the compound during the interval t.
Assuming that there is no decay during the interval,
Making the small correction for the decay of activity during the interval,
We have previously shown that from the theory
The agreement between theory and experiment is thus as close as could be expected from the nature of the experiments. This experiment proves conclusively that the rate of production of emanation in the solid compound is the same as in the solution. In the former case it is occluded, in the latter it escapes as fast as it is produced.
It is remarkable how little emanation, compared with the amount stored up in the compound, escapes from solid radium chloride in a dry atmosphere. One experiment showed that the emanating power in the dry solid state was less than ½% of the emanating power of the solution. Since nearly 500,000 times as much emanation is stored up in the solid compound as is produced per second, this result showed that the amount of emanation which escaped per second was less than 10-8 of that occluded in the compound.
If a solid radium chloride compound is kept in a moist atmosphere, the emanating power becomes comparable with the amount produced per second in the solution. In such a case, since the rate of escape is continuous, the amount occluded will be much less than the amount for the non-emanating material.
The phenomenon of occlusion of the radium emanation is probably not connected in any way with its radio-activity, although this property has here served to measure it. The occlusion of helium by minerals presents almost a complete analogy to the occlusion of the radium emanation. Part of the helium is given off by fergusonite, for example, when it is heated and all of it when the mineral is dissolved.
153. Similar results hold for thorium, but, on account of the rapid loss of activity of the emanation, the amount of emanation occluded in a non-emanating compound is very small compared with that observed for radium. If the production of the thorium emanation proceeds at the same rate under all conditions, the solution of a solid non-emanating compound should be accompanied by a rush of emanation greater than that subsequently produced. With the same notation as before we have for the thorium emanation,
This result was tested as follows: a quantity of finely powdered thorium nitrate, of emanating power ¹⁄₂₀₀ of ordinary thoria, was dropped into a Drechsel bottle containing hot water and the emanation rapidly swept out into the testing vessel by a current of air. The ionization current rose quickly to a maximum, but soon fell again to a steady value; showing that the amount of emanation released when the nitrate dissolves, is greater than the subsequent amount produced from the solution.
The rapid loss of the activity of the thorium emanation makes a quantitative comparison like that for radium very difficult. By slightly altering the conditions of the experiment, however, a definite proof was obtained that the rate of production of emanation is the same in the solid compound as in the solution. After dropping in the nitrate, a rapid air stream was blown through the solution for 25 seconds into the testing vessel. The air stream was stopped and the ionization current immediately measured. The solution was then allowed to stand undisturbed for 10 minutes. In that time the accumulation of the emanation again attained a practical maximum and again represented a steady state. The stream of air was blown through, as before, for 25 seconds, stopped and the current again measured. In both cases, the electrometer recorded a movement of 14·6 divisions per second. By blowing the same stream of air continuously through the solution the final current corresponded to 7·9 divisions per second or about one-half of that observed after the first rush.
Thus the rate of production of emanation is the same in the solid nitrate as in the solution, although the emanating power, i.e. the rate of escape of the emanation, is over 600 times greater in the solution than in the solid.
It seems probable that the rate of production of emanation by thorium, like the rate of production of Ur X and Th X, is independent of conditions. The changes of emanating power of the various compounds by moisture, heat, and solution must therefore be ascribed solely to an alteration in the rate of escape of the emanation into the surrounding gas and not to an alteration in the rate of its production in the compound.
On this view, it is easy to see that slight changes in the mode of preparation of a thorium compound may produce large changes in emanating power. Such effects have been often observed, and must be ascribed to slight physical changes in the precipitate. The fact that the rate of production of the emanation is independent of the physical or chemical conditions of the thorium, in which it is produced, is thus in harmony with what had previously been observed for the radio-active products Ur X and Th X.
Source of the Thorium Emanation.
154. Some experiments of Rutherford and Soddy[248] will now be considered, which show that the thorium emanation is produced, not directly by the thorium itself, but by the active product Th X.
When the Th X, by precipitation with ammonia, is removed from a quantity of thorium nitrate, the precipitated thorium hydroxide does not at first possess appreciable emanating power. This loss of emanating power is not due, as in the case of the de-emanated oxide, to a retardation in the rate of escape of the emanation produced; for the hydroxide, when dissolved in acid, still gives off no emanation. On the other hand, the solution, containing the Th X, possesses emanating power to a marked degree. When the precipitated hydroxide and the Th X is left for some time, it is found that the Th X decreases in emanating power, while the hydroxide gradually regains its emanating power. After about a month’s interval, the emanating power of the hydroxide has nearly reached a maximum, while the emanating power of the Th X has almost disappeared.
The curves of decay and recovery of emanating power with time are found to be exactly the same as the curves of decay and recovery of activity of Th X and the precipitated hydroxide respectively, shown in Fig. 47. The emanating power of Th X, as well as its activity, falls to half value in four days, while the hydroxide regains half its final emanating power as well as half its lost activity in the same interval.
It follows from these results that the emanating power of Th X is directly proportional to its activity, i.e. that the rate of production of emanating particles is always proportional to the number of α particles, projected from the Th X per second. The radiation from Th X thus accompanies the change of the Th X into the emanation. Since the emanation has chemical properties distinct from those of the Th X, and also a distinctive rate of decay, it cannot be regarded as a vapour of Th X, but it is a distinct chemical substance, produced by the changes occurring in Th X. On the view advanced in section 136, the atom of the emanation consists of the part of the atom of Th X left behind after the expulsion of one or more α particles. The atoms of the emanation are unstable, and in turn expel α particles. This projection of α particles constitutes the radiation from the emanation, which serves as a measure of the amount of emanation present. Since the activity of the emanation falls to half value in one minute while that of Th X falls to half value in four days, the emanation consists of atoms which disintegrate at intervals nearly 6000 times shorter than those of the atoms of Th X.
Source of the Radium and Actinium Emanation.
155. No intermediate stage—Radium X—between radium and its emanation, corresponding to the Th X for thorium, has so far been observed. The emanation from radium is probably produced directly from that element. In this respect, the radium emanation holds the same position in regard to radium as Th X does to thorium, and its production from radium can be explained on exactly similar lines. It will be shown later in chapter X, that the emanation of actinium, like that of thorium, does not arise directly from the parent element but from an intermediate product actinium X, which is very analogous in physical and chemical properties to Th X.
Radiations from the Emanations.
156. Special methods are necessary to examine the nature of the radiation from the emanations, for the radiations arise from the volume of the gas in which the emanations are distributed. Some experiments to examine the radiations from the thorium emanation were made by the writer in the following way.
Fig. 55.
A highly emanating thorium compound wrapped in paper was placed inside a lead box B about 1 cm. deep, shown in Fig. 55. An opening was cut in the top of the box, over which a very thin sheet of mica was waxed. The emanation rapidly diffused through the paper into the vessel, and after ten minutes reached a state of radio-active equilibrium. The penetrating power of the radiation from the emanation which passed through the thin mica window was examined by the electrical method in the usual way by adding screens of thin aluminium foil. The results are expressed in the following table:
| Layers of foil | Current |
| 0 | 100 |
| 1 | 59 |
| 2 | 30 |
| 3 | 10 |
| 4 | 3·2 |
The greater proportion of the conductivity is thus due to α rays, as in the case of the radio-active elements. The amount of absorption of these α rays by aluminium foil is about the same as that of the rays from the active bodies. No direct comparison can be made, for the α rays from the emanation show the characteristic property of increased rate of absorption with thickness of matter traversed. Before testing, the rays have been largely absorbed by the mica window, and the penetrating power has consequently decreased.
No alteration in the radiation from the emanation was observed on placing an insulated wire inside the emanation vessel, and charging it to a high positive or negative potential. When a stream of air through the vessel carried away the emanation as fast as it was produced, the intensity of the radiation fell to a small fraction of its former value.
No evidence of any β rays in the radiations was found in these experiments, although a very small effect would have been detected. After standing some hours, however, β rays began to appear. These were due to the excited activity deposited on the walls of the vessel from the emanation, and not directly to the emanation itself.
The radium emanation, like that of thorium, only gives rise to α rays. This was tested in the following way[249]:
A large amount of emanation was introduced into a cylinder made of sheet copper ·005 cm. thick, which absorbed all the α rays but allowed the β and γ rays, if present, to pass through with but little loss. The external radiation from the cylinder was determined at intervals, commencing about two minutes after the introduction of the emanation. The amount observed at first was extremely small, but increased rapidly and practically reached a maximum in three or four hours. Thus the radium emanation only gives out α rays, the β rays appearing as the excited activity is produced on the walls of the vessel. On sweeping out the emanation by a current of air, there was no immediately appreciable decrease of the radiation. This is another proof that the emanation does not emit any β rays. In a similar way it can be shown that the emanation does not give out γ rays; these rays always make their appearance at the same time as the β rays.
The method of examination of the radiations from the emanations has been given in some detail, as the results are of considerable importance in the discussion, which will be given later in chapters X and XI, of the connection between the changes occurring in radio-active products and the radiations they emit. There is no doubt that the emanations, apart from the excited activity to which they give rise, only give out α rays, consisting most probably of positively charged bodies projected with great velocity.
Effect of pressure on the rate of production of the Emanation.
157. It has already been mentioned that the conductivity due to the thorium emanation is proportional to the pressure of the gas, pointing to the conclusion that the rate of production of the emanation is independent of the pressure, as well as of the nature of the surrounding gas. This result was directly confirmed with the apparatus of Fig. 55. When the pressure of the gas under the vessel was slowly reduced, the radiation, tested outside the window, increased to a limit, and then remained constant over a wide range of pressure. This increase, which was far more marked in air than in hydrogen, is due to the fact that the α rays from the emanation were partially absorbed in the gas inside the vessel when at atmospheric pressure. At pressures of the order of 1 millimetre of mercury the external radiation decreased, but experiment showed that this must be ascribed to a removal of the emanation by the pump, and not to a change in the rate of production. The thorium compounds very readily absorb water-vapour, which is slowly given off at low pressures, and in consequence some of the emanation is carried out of the vessel with the water-vapour.
Curie and Debierne[250] found that both the amount of excited activity produced in a closed vessel containing active samples of radium, and also the time taken to reach a maximum value, were independent of the pressure and nature of the gas. This was true in the case of a solution down to the pressure of the saturated vapour, and in the case of solid salts to very low pressures. When the pump was kept going at pressures of the order of ·001 mm. of mercury, the amount of excited activity was much diminished. This was probably not due to any alteration of the rate of escape of the emanation, but to the removal of the emanation by the action of the pump as fast as it was formed.
Since the amount of excited activity, when in a state of radio-active equilibrium, is a measure of the amount of emanation producing it, these results show that the amount of emanation present when the rate of production balances the rate of decay is independent of the pressure and nature of the gas. It was also found that the time taken to reach the point of radio-active equilibrium was independent of the size of the vessel or the amount of active matter present. This proves that the state of equilibrium cannot in any way be ascribed to the possession by the emanation of any appreciable vapour pressure; for if such were the case, the time taken to reach the equilibrium value should depend on the size of the vessel and the amount of active matter present. The results are, however, in agreement with the view that the emanation is present in minute quantity in the tube, and that the equilibrium is governed purely by the radio-active constant λ, the constant of decay of activity of the emanation. This has been seen to be the same under all conditions of concentration, pressure and temperature, and, provided the rate of supply of the emanation from the active compound is not changed, the time-rate of increase of activity to the equilibrium value will always be the same, whatever the size of the vessel or the nature and pressure of the surrounding gas.
Chemical Nature of the Emanations.
158. We shall now consider some experiments on the physical and chemical properties of the emanations themselves, without reference to the material producing them, in order to see if they possess any properties which connect them with any known kind of matter.
It was soon observed that the thorium emanation passed unchanged through acid solutions, and later the same result was shown to hold true in the case of both emanations for every reagent that was tried. Preliminary observations[251] showed that the thorium emanation, obtained in the usual way by passing air over thoria, passed unchanged in amount through a platinum tube heated electrically to the highest temperature obtainable. The tube was then filled with platinum-black, and the emanation passed through it in the cold, and with gradually increasing temperatures, until the limit was reached. In another experiment, the emanation was passed through a layer of red-hot lead-chromate in a glass tube. The current of air was replaced by a current of hydrogen, and the emanation was sent through red-hot magnesium-powder and red-hot palladium-black, and, by using a current of carbon dioxide, through red-hot zinc-dust. In every case the emanation passed through without sensible change in the amount. If anything, a slight increase occurred, owing to the time taken for the gas-current to pass through the tubes when hot being slightly less than when cold, the decay en route being consequently less. The only known gases capable of passing in unchanged amount through all the reagents employed are the recently discovered members of the argon family.
But another possible interpretation might be put upon the results. If the emanation were the manifestation of a type of excited radio-activity on the surrounding atmosphere, then, since from the nature of the experiments it was necessary to employ in each case as the atmosphere, a gas not acted on by the reagent employed, the result obtained might be expected. Red-hot magnesium would not retain an emanation consisting of radio-active hydrogen, nor red-hot zinc-dust an emanation consisting of radio-active carbon dioxide. The incorrectness of this explanation was shown in the following way. Carbon dioxide was passed over thoria, then through a T-tube, where a current of air met and mixed with it, both passing on to the testing-cylinder. But between this and the T-tube a large soda-lime tube was introduced, and the current of gas was thus freed from its admixed carbon dioxide, before being tested in the cylinder for the emanation. The amount of emanation found was quite unchanged, whether carbon dioxide was sent over thoria in the manner described, or whether, keeping the other arrangements as before, an equally rapid current of air was substituted for it. The theory that the emanation is an effect of the excited activity on the surrounding medium is thus excluded.
Experiments of a similar kind on the radium emanation were made later. A steady stream of gas was passed through a radium chloride solution and then through the reagent to be employed, into a testing-vessel of small volume, so that any change in the amount of emanation passing through could readily be detected. The radium emanation, like that of thorium, passed unchanged in amount through every reagent used.
In later experiments by Sir William Ramsay and Mr Soddy[252], the emanation from radium was exposed to still more drastic treatment. The emanation in a glass tube was sparked for several hours with oxygen over alkali. The oxygen was then removed by ignited phosphorus and no visible residue was left. When, however, another gas was introduced, mixed with the minute amount of emanation in the tube and withdrawn, the activity of emanation was found to be unaltered. In another experiment, the emanation was introduced into a magnesium lime tube, which was heated for three hours at a red heat. The emanation was then removed and tested, but no diminution in its discharging power was observed.
The emanations of thorium and radium thus withstand chemical treatment in a manner hitherto unobserved except in gases of the argon family.
159. Ramsay and Soddy (loc. cit.) record an interesting experiment to illustrate the gaseous nature of the emanation. A large amount of the radium emanation was collected in a small glass tube. This tube phosphoresced brightly under the influence of the rays from the emanation. The passage of the emanation from point to point was observed in a darkened room by the luminosity excited in the glass. On opening the stop-cock connecting with the Töpler pump, the slow flow through the capillary tube was noticed, the rapid passage along the wider tubes, the delay in passing through a plug of phosphorous pentoxide, and the rapid expansion into the reservoir of the pump. When compressed, the luminosity of the emanation increased, and became very bright as the small bubble containing the emanation was expelled through the fine capillary tube.
Diffusion of the Emanations.
160. It has been shown that the emanations of thorium and radium behave like radio-active gases, distributed in minute amount in the air or other gas in which they are tested. With the small quantities of active material so far investigated, the emanations have not yet been collected in sufficient amount to determine their density. Although the molecular weight of the emanations cannot yet be obtained by direct chemical methods, an indirect estimate of it can be made by determining the rate of their inter-diffusion into air or other gases. The coefficients of inter-diffusion of various gases have long been known, and the results show that the coefficient of diffusion of one gas into another is, for the simpler gases, approximately inversely proportional to the square root of the product of their molecular weights. If, therefore, the coefficient of diffusion of the emanation into air is found to have a value, lying between that of two known gases A and B, it is probable that the molecular weight of the emanation lies between that of A and B.
Although the volume of the emanation given off from radium is very small, the electrical conductivity produced by the emanation in the gas, with which it is mixed, is often very large, and offers a ready means of measuring the emanation present.
Some experiments have been made by Miss Brooks and the writer[253] to determine the rate of the diffusion of the radium emanation into air, by a method similar to that employed by Loschmidt[254] in 1871, in his investigations of the coefficient of inter-diffusion of gases.
Fig. 56.
Fig. 56 shows the general arrangement. A long brass cylinder AB, of length 73 cms., and diameter 6 cms., was divided into two equal parts by a moveable metal slide S. The ends of the cylinder were closed with ebonite stoppers. Two insulated brass rods, a and b, each half the length of the tube, passed through the ebonite stoppers and were supported centrally in the tube. The cylinder was insulated and connected with one pole of a battery of 300 volts, the other pole of which was earthed. The central rods could be connected with a sensitive quadrant electrometer. The cylinder was covered with a thick layer of felt, and placed inside a metal box filled with cotton wool in order to keep temperature conditions as steady as possible.
In order to convey a sufficient quantity of emanation into the half-cylinder A, it was necessary to heat the radium slightly. The slide S was closed and the side tubes opened. A slow current of dry air from a gasometer was passed through a platinum tube, in which a small quantity of radium compound was placed. The emanation was carried with the air into the cylinder A. When a sufficient quantity had been introduced, the stream of air was stopped. The side tubes were closed by fine capillary tubes. These prevented any appreciable loss of gas due to the diffusion, but served to keep the pressure of the gas inside A at the pressure of the outside air. The three entrance tubes into the cylinder, shown in the figure, were for the purpose of initially mixing the emanation and gas as uniformly as possible.
After standing several hours to make temperature conditions steady, the slide was opened, and the emanation began to diffuse into the tube B. The current through the tubes A and B was measured at regular intervals by an electrometer, with a suitable capacity in parallel. Initially there is no current in B, but after the opening of the slide, the amount in A decreased and the amount in B steadily increased. After several hours the amount in each half is nearly the same, showing that the emanation is nearly uniformly diffused throughout the cylinder.
It can readily be shown[255] that if
then
Now the values of S1 and S2 are proportional to the saturation ionization currents due to the emanations in the two halves of the cylinder. From this equation K can be determined, if the relative values of S1 and S2 are observed after diffusion has been in progress for a definite interval t.
The determination of S1 and S2 is complicated by the excited activity produced on the walls of the vessel. The ionization due to this must be subtracted from the total ionization observed in each half of the cylinder, for the excited activity is produced from the material composing the emanation, and is removed to the electrodes in an electric field. The ratio of the current due to excited activity to the current due to the emanation depends on the time of exposure to the emanation, and is only proportional to it for exposures of several hours.
The method generally adopted in the experiments was to open the slide for a definite interval, ranging in the experiments from 15 to 120 minutes. The slide was then closed and the currents in each half determined at once. The central rods, which had been kept negatively charged during the experiments, had most of the excited activity concentrated on their surfaces. These were removed, new rods substituted and the current immediately determined. The ratio of the currents in the half cylinders under these conditions was proportional to S1 and S2, the amounts of emanation present in the two halves of the cylinder.
The values of K, deduced from different values of t, were found to be in good agreement. In the earlier experiments the values of K were found to vary between ·08 and ·12. In some later experiments, where great care was taken to ensure that temperature conditions were very constant, the values of K were found to vary between ·07 and ·09. The lower value ·07 is most likely nearer the true value, as temperature disturbances tend to give too large a value of K. No certain differences were observed in the value of K whether the air was dry or damp, or whether an electric field was acting or not.
161. Some experiments on the rate of diffusion of the radium emanation into air were made at a later date by P. Curie and Danne[256]. If the emanation is contained in a closed reservoir, it has been shown that its activity, which is a measure of the amount of emanation present, decreases according to an exponential law with the time. If the reservoir is put in communication with the outside air through a capillary tube, the emanation slowly diffuses out, and the amount of emanation in the reservoir is found to decrease according to the same law as before, but at a faster rate. Using tubes of different lengths and diameters, the rate of diffusion was found to obey the same laws as a gas. The value of K was found to be 0·100. This is a slightly greater value of K than the lowest value 0·07 found by Rutherford and Miss Brooks. No mention is made by Curie and Danne of having taken any special precautions against temperature disturbances, and this may account for the higher value of K obtained by them.
They also found that the emanation, like a gas, always divided itself between two reservoirs, put in connection with one another, in the proportion of their volumes. In one experiment one reservoir was kept at a temperature of 10° C. and the other at 350° C. The emanation divided itself between the two reservoirs in the same proportion as would a gas under the same conditions.
162. For the purpose of comparison, a few of the coefficients of inter-diffusion of gases, compiled from Landolt and Bernstein’s tables, are given below.
| Gas or vapour | Coefficient of diffusion into air | Molecular weight |
|---|---|---|
| Water vapour | 0·198 | 18 |
| Carbonic acid gas | 0·142 | 44 |
| Alcohol vapour | 0·101 | 46 |
| Ether vapour | 0·077 | 74 |
| Radium emanation | 0·07 | ? |
The tables, although not very satisfactory for the purpose of comparison, show that the coefficient of inter-diffusion follows the inverse order of the molecular weights. The value of K for the radium emanation is slightly less than for ether vapour, of which the molecular weight is 74. We may thus conclude that the emanation is of greater molecular weight than 74. It seems likely that the emanation has a molecular weight somewhere in the neighbourhood of 100, and is probably greater than this, for the vapours of ether and alcohol have higher diffusion coefficients compared with carbonic acid than the theory would lead us to anticipate. Comparing the diffusion coefficients of the emanation and carbonic acid into air, the value of the molecular weight of the emanation should be about 176 if the result observed for the simple gases, viz. that the coefficient of diffusion is inversely proportional to the square root of the molecular weights, holds true in the present case. Bumstead and Wheeler[257] compared the rates of diffusion of the radium emanation and of carbon dioxide through a porous plate, and concluded that the molecular weight of the emanation was about 180. On the disintegration theory, the atom of the emanation is derived from the radium atom by the expulsion of one α particle. Thus, it is to be expected that its molecular weight would be over 200.
It is of interest to compare the value of K = ·07 with the value of K determined by Townsend (section 37) for the gaseous ions produced in air at ordinary pressure and temperature, by Röntgen rays or by the radiations from active substances. Townsend found that the value of K in dry air was ·028 for the positive ions and ·043 for the negative ions. The radium emanation thus diffuses more rapidly than the ions produced by its radiation in the gas, and behaves as if its mass were smaller than that of the ions produced in air, but considerably greater than that of the air molecules with which it is mixed.
It is not possible to regard the emanation as a temporarily modified condition of the gas originally in contact with the active body. Under such conditions a much larger value of K would be expected. The evidence derived from the experiments on diffusion strongly supports the view that the emanation is a gas of heavy molecular weight.
Makower[258] has recently attacked the question of the molecular weight of the radium emanation by another method. The rate of diffusion of the emanation through a porous plug of plaster-of-Paris was compared with that of the gases oxygen, carbon dioxide, and sulphur dioxide. It was found that Graham’s law, viz. that the coefficient of diffusion K is inversely proportional to the square root of its molecular weight M, was not strictly applicable. The value of K √M was not found to be constant for these gases, but decreased with increase of molecular weight of the gas. If, however, a curve was plotted with K √M as ordinate and K as abscissa, the points corresponding to the values of O, CO2 and SO2 were found to lie on a straight line. By linear extrapolation, the molecular weight of the emanation was estimated. The value obtained from experiments on three different porous plugs was 85·5, 97, and 99 respectively. This method indicates that the molecular weight of the radium emanation is about 100; but in all the experiments on diffusion, it must be remembered that the emanation, whose rate of inter-diffusion is being examined, exists in minute quantity mixed with the gas, and is compared with the rate of inter-diffusion of gases which are present in large quantity. For this reason, deductions of the molecular weight of the emanation may be subject to comparatively large errors, for which it is difficult to make correction.
Diffusion of the Thorium Emanation.
163. On account of the rapid decay of the activity of the thorium emanation, it is not possible to determine the value of K its coefficient of diffusion into air by the methods employed for the radium emanation. The value of K has been determined by the writer in the following way. A plate C, Fig. 57, covered with thorium hydroxide, was placed horizontally near the base of a long vertical brass cylinder P. The emanation released from the thorium compound diffuses upwards in the cylinder.
Fig. 57.
Let p be the partial pressure of the emanation at a distance x from the source C. This will be approximately uniform over the cross section of the cylinder. From the general principles of diffusion we get the equation
The emanation is continuously breaking up and expelling α particles. The emanation-residue gains a positive charge, and, in an electric field, is removed at once from the gas to the negative electrode.
Since the activity of the emanation at any time is always proportional to the number of particles which have not broken up, and since the activity decays with the time according to an exponential law,
where p1 is the value of p when t = 0 and λ is the radio-active constant of the emanation.
Thus
Since p = 0 when x = ∞. B = 0. If p = p₀ when x = 0, A = p₀.
Thus
It was not found convenient in the experiments to determine the activity of the emanation along the cylinder, but an equivalent method was used which depends upon measuring the distribution of “excited activity,” produced along a central rod AB, which is charged negatively.
It will be shown later (section 177) that the amount of excited activity at any point is always proportional to the amount of emanation at that point. The distribution of “excited activity” along the central rod from the plate C upwards thus gives the variation of p for the emanation along the tube.
In the experiments, the cylinder was filled with dry air at atmospheric pressure and was kept at a constant temperature. The central rod was charged negatively and exposed from one to two days in the presence of the emanation. The rod was then removed, and the distribution of the excited activity along it determined by the electric method. It was found that the amount of excited activity fell off with the distance x according to an exponential law, falling to half value in about 1·9 cms. This is in agreement with the above theory.
Since the activity of the emanation falls to half value in 1 minute, λ = ·0115. The value K = ·09 was deduced from the average of a number of experiments. This is a slightly greater value than K = ·07, obtained for the radium emanation, but the results show that the two emanations do not differ much from one another in molecular weight.
Makower (loc. cit.) compared the rates of diffusion of the thorium and radium emanation through a porous plate, and concluded that the two emanations were of about the same molecular weight, thus confirming the results obtained by the above method.
Diffusion of the Emanation into Liquids.
164. Experiments have been made by Wallstabe[259] on the coefficient of diffusion of the radium emanation into various liquids. The radium emanation was allowed to diffuse into a closed reservoir, containing a cylinder of the liquid under observation. The cylinder was provided with a tube and a stop-cock extending beyond the closed vessel, so that different layers of the liquid could be removed. The liquid was then placed in a closed testing vessel, where the ionization current due to the escape of the emanation from the liquid was observed to rise to a maximum after several hours, and then to decay. This maximum value of the current was taken as a measure of the amount of emanation absorbed in the liquid.
The coefficient of diffusion K of the emanation into the liquid can be obtained from the same equation used to determine the diffusion of the thorium emanation into air,