Radio-activity/Chapter 12

by Ernest Rutherford

 

CHAPTER XII.

RATE OF EMISSION OF ENERGY.

243. It was early recognised that a considerable amount of energy is emitted by the radio-active bodies in the form of their characteristic radiations. Most of the early estimates of the amount of this energy were based on the number and energy of the expelled particles, and were much too small. It has been pointed out (section 114) that the greater part of the energy emitted from the radio-active bodies in the form of ionizing radiations is due to the α rays, and that the β rays in comparison supply only a very small fraction.

Rutherford and McClung^[1] made an estimate of the energy of the rays, emitted by a thin layer of active matter, by determining the total number of ions produced by the complete absorption of the α rays. The energy required to produce an ion was determined experimentally by observations of the heating effect of X rays, and of the total number of ions produced when the rays were completely absorbed in air. The energy required to produce an ion in air was found to be 1·90 × 10^{-10} ergs. This, as will be shown in Appendix A, is probably an over-estimate, but was of the right order of magnitude. From this it was calculated that one gram of uranium oxide spread over a plate in the form of a thin powdered layer emitted energy into the air at the rate of 0·032 gram calories per year. This is a very small emission of energy, but in the case of an intensely radio-active substance like radium, whose activity is about two million times that of uranium, the corresponding emission of energy is 69000 gram calories per year. This is obviously an under-*

• estimate, for it includes only the energy radiated into the air.

The actual amount of energy released in the form of α rays is evidently much greater than this on account of the absorption of the α rays by the active matter itself.

It will be shown later that the heating effect of radium and of its products is a measure of the energy of the expelled α particles.

244. Heat emission of radium. P. Curie and Laborde^[2] first drew attention to the striking result that a radium compound kept itself continuously at a temperature several degrees higher than that of the surrounding atmosphere. Thus the energy emitted from radium can be demonstrated by its direct heating effect, as well as by photographic and electric means. Curie and Laborde determined the rate of the emission of heat in two different ways. In one method the difference of temperature was observed by means of an iron-constantine thermo-couple between a tube containing one gram of radiferous chloride of barium, of activity about 1/6 of pure radium, and an exactly similar tube containing one gram of pure barium chloride. The difference of temperature observed was 1·5° C. In order to measure the rate of emission of heat, a coil of wire of known resistance was placed in the pure barium chloride, and the strength of the electric current required to raise the barium to the same temperature as the radiferous barium was observed. In the other method, the active barium, enclosed in a glass tube, was placed inside a Bunsen calorimeter. Before the radium was introduced, it was observed that the level of the mercury in the stem remained steady. As soon as the radium, which had previously been cooled in melting ice, was placed in the calorimeter, the mercury column began to move at a regular rate. If the radium tube was removed, the movement of the mercury ceased. It was found from these experiments that the heat emission from the 1 gram of radiferous barium, containing about 1/6 of its weight of pure radium chloride, was 14 gram-calories per hour. Measurements were also made with 0·08 gram of pure radium chloride. Curie and Laborde deduced from these results that 1 gram of pure radium emits a quantity of heat equal to about 100 gram-calories per hour. This result was confirmed by the experiments of Runge and Precht^[3] and others. As far as observation has gone at present, this rate of emission of heat is continuous and unchanged with lapse of time. Therefore, 1 gram of radium emits in the course of a day 2400, and in the course of a year 876,000 gram-calories. The amount of heat evolved in the union of hydrogen and oxygen to form 1 gram of water is 3900 gram-calories. It is thus seen that 1 gram of radium emits per day nearly as much energy as is required to dissociate 1 gram of water.

In some later experiments using 0·7 gram of pure radium bromide, P. Curie^[4] found that the temperature of the radium indicated by a mercury thermometer was 3° C. above that of the surrounding air. This result was confirmed by Giesel, who obtained a difference of temperature of 5° C. with 1 gram of radium bromide. The actual rise of temperature observed will obviously depend upon the size and nature of the vessel containing the radium.

During their visit to England in 1903 to lecture at the Royal Institution, M. and Mme Curie performed some experiments with Professor Dewar, to test by another method the rate of emission of heat from radium at very low temperatures. This method depended on the measurement of the amount of gas volatilized when a radium preparation was placed inside a tube immersed in a liquefied gas at its boiling point. The arrangement of the calorimeter is shown in Fig. 97.

Fig. 97.

The small closed Dewar flask A contains the radium in a glass tube R, immersed in the liquid to be employed. The flask A is surrounded by another Dewar bulb B, containing the same liquid, so that no heat is communicated to A from the outside. The gas liberated in the tube A is collected in the usual way over water or mercury, and its volume determined. By this method, the rate of heat emission of the radium was found to be about the same in boiling carbon dioxide and oxygen, and also in liquid hydrogen. Especial interest attaches to the result obtained with liquid hydrogen, for at such a low temperature ordinary chemical activity is suspended. The fact that the heat emission of radium is unaltered over such a wide range of temperature indirectly shows that the rate of expulsion of α particles from radium is independent of temperature, for it will be shown later that the heating effect observed is due to the bombardment of the radium by the α particles.

The use of liquid hydrogen is very convenient for demonstrating the rate of heat emission from a small amount of radium. From 0·7 gram of radium bromide (which had been prepared only 10 days previously) 73 c.c. of gas were given off per minute.

In later experiments P. Curie (loc. cit.) found that the rate of emission of heat from a given quantity of radium depended upon the time which had elapsed since its preparation. The emission of heat was at first small, but after a month's interval practically attained a maximum. If a radium compound is dissolved and placed in a sealed tube, the rate of heat emission rises to the same maximum as that of an equal quantity of radium in the solid state.

245. Connection of the heat emission with the radiations. The observation of Curie that the rate of heat emission depended upon the age of the radium preparation pointed to the conclusion that the phenomenon of heat emission of radium was connected with the radio-activity of that element. It had long been known that radium compounds increased in activity for about a month after their preparation, when they reached a steady state. It has been shown (section 215), that this increase of activity is due to the continuous production by the radium of the radio-active emanation, which is occluded in the radium compound and adds its radiation to that of the radium proper. It thus seemed probable that the heating effect was in some way connected with the presence of the emanation. Some experiments upon this point were made by Rutherford and Barnes^[5]. In order to measure the small amounts of heat emitted, a form of differential air calorimeter shown in Fig. 98 was employed. Two equal glass flasks of about 500 c.c. were filled with dry air at atmospheric pressure. These flasks were connected through a glass U-tube filled with xylene, which served as a manometer to determine any variation of pressure of the air in the flasks. A small glass tube, closed at the lower end, was introduced into the middle of each of the flasks. When a continuous source of heat was introduced into the glass tube, the air surrounding it was heated and the pressure was increased. The difference of pressure, when a steady state was reached, was observed on the manometer by means of a microscope with a micrometer scale in the eye-piece. On placing the source of heat in the similar tube in the other flask, the difference in pressure was reversed. In order to keep the apparatus at a constant temperature, the two flasks were immersed in a water-*bath, which was kept well stirred.

Fig. 98.

Observations were first made on the heat emission from 30 milligrams of radium bromide. The difference in pressure observed on the manometer was standardized by placing a small coil of wire of known resistance in the place of the radium. The strength of the current through the wire was adjusted to give the same difference of pressure on the manometer. In this way it was found that the heat emission per gram of radium bromide corresponded to 65 gram-calories per hour. Taking the atomic weight of radium as 225, this is equivalent to a rate of emission of heat from one gram of metallic radium of 110 gram-calories per hour.

The emanation from the 30 milligrams of radium bromide was then removed by heating the radium (section 215). By passing the emanation through a small glass tube immersed in liquid air, the emanation was condensed. The tube was sealed off while the emanation was still condensed in the tube. In this way the emanation was concentrated in a small glass tube about 4 cms. long. The heating effects of the "de-emanated" radium and of the emanation tube were then determined at intervals. It was found that, after removal of the emanation, the heating effect of the radium decayed in the course of a few hours to a minimum, corresponding to about 25 per cent. of the original heat emission, and then gradually increased again, reaching its original value after about a month's interval. The heating effect of the emanation tube was found to increase for the first few hours after separation to a maximum, and then to decay regularly with the time according to an exponential law, falling to half its maximum value in about four days. The actual heat emission of the emanation tube was determined by sending a current through a coil of wire occupying the same length and position as the emanation tube.

The variation with time of the heating effect from 30 milligrams of radium and the emanation from it is shown in Fig. 99.

Fig. 99.

Curve A shows the variation with time of the heat emission of the radium and curve B of the emanation. The sum total of the rate of heat emission of the radium and the emanation together, was at any time found to be equal to that of the original radium. The maximum heating effect of the tube containing the emanation from 30 milligrams of radium bromide was 1·26 gram-calories per hour. The emanation together with the secondary products which arise from it, obtained from one gram of radium, would thus give out 42 gram-calories per hour. The emanation stored up in the radium is thus responsible for more than two-thirds of the total heat emission from radium. It will be seen later that the decrease to a minimum of the heating effect of radium, after removal of the emanation, is connected with the decay of the excited activity. In a similar way, the increase of the heating effect of the emanation to a maximum some hours after removal is also a result of the excited activity produced by the emanation on the walls of the containing vessel. Disregarding for the moment these rapid initial changes in heat emission, it is seen that the heating effect of the emanation and its further products, after reaching a maximum, decreases at the same rate as that at which the emanation loses its activity, that is, it falls to half value in four days. If Q_{max.} is the maximum heating effect and Q_{t} the heating effect at any time t later, then Q_{t}/Q_{max.} = e^{-λt} where λ is the constant of change of the emanation.

The curve of recovery of the heating effect of radium from its minimum value is identical with the curve of recovery of its activity measured by the α rays. Since the minimum heating effect is 25 per cent. of the total, the heat emission Q_{t} at any time t after reaching a minimum is given by

Q_{t}/Q_{max.} = ·25 + ·75(1 - e^{-λt}),

where Q_{max.} is the maximum rate of heat emission and λ, as before, is the constant of change of the emanation.

The identity of the curves of recovery and fall of the heating effect of radium and its emanation respectively with the corresponding curves for the rise and fall of radio-activity shows that the heat emission of radium and its products is directly connected with their radio-activity. The variation in the heat emission of both radium and its emanation is approximately proportional to their activity measured by the α rays. It is not proportional to the activity measured by the β or γ rays, for the intensity of these rays falls nearly to zero some hours after removal of the emanation, while the α ray activity, like the heating effect, is 25 per cent. of the maximum value. These results are thus in accordance with the view that the heat emission of radium accompanies the expulsion of α particles, and is approximately proportional to the number expelled. Before such a conclusion can be considered established, it is necessary to show that the heating effect of the active deposit from the emanation varies in the same way as its α ray activity. Experiments made to test this point will now be considered.

246. Heat emission of the active deposit from the emanation. New radium in radio-active equilibrium contains four successive products which break up with the emission of α particles, viz. radium itself, the emanation, radium A and C. Radium B does not emit rays at all. The effect of the later products radium D, E and F may be neglected, if the radium has not been prepared for more than a year.

It is not easy to settle definitely the relative activity supplied by each of these products when in radio-active equilibrium, but it has been shown in section 229 that the activity is not very different for the four α ray products. The α particles from radium A and C are more penetrating than those from radium itself and the emanation. The evidence at present obtained points to the conclusion that the activity supplied by the emanation is less than that supplied by the other products. This indicates that the α particles from the emanation are projected with less velocity than in the other cases.

When the emanation is suddenly released from radium by heat or solution, the products radium A, B and C are left behind. Since the parent matter is removed, the amount of the products A, B, C at once commences to diminish, and at the end of about three hours reaches a very small value. If the heating effect depends upon the α ray activity, it is thus to be expected that the heat emission of the radium should rapidly diminish to a minimum after the removal of the emanation.

When the emanation is introduced into a vessel, the products radium A, B and C at once appear and increase in quantity, reaching a practical maximum about 3 hours later. The heating effect of the emanation tube should thus increase for several hours after the introduction of the emanation.

In order to follow the rapid changes in the heating effect of radium, after removal of the emanation, Rutherford and Barnes (loc. cit.) used a pair of differential platinum thermometers. Each thermometer consisted of 35 cms. of fine platinum wire, wound carefully on the inside of a thin glass tube 5 mms. in diameter, forming a coil 3 cms. long. The glass tube containing the radium and also the tube containing the emanation were selected to slide easily into the interior of the coils, the wire thus being in direct contact with the glass envelope containing the source of heat. The change in resistance of the platinum thermometers, when the radium or emanation tube was transferred from one coil to the other, was readily measured.

Fig. 100.

The heating effect of the radium in radio-active equilibrium was first accurately determined. The radium tube was heated to drive off the emanation, which was rapidly condensed in a small glass tube 3 cms. long and 3 mms. internal diameter. After allowing a short time for temperature conditions to become steady, the heating effect of the radium tube was measured. The results are shown in Fig. 100. An observation could not be taken until about 12 minutes after the removal of the emanation, and the heating effect was then found to have fallen to about 55 per cent. of the maximum value. It steadily diminished with the time, finally reaching a minimum value of 25 per cent. several hours later.

It is not possible in experiments of this character to separate the heating effect of the emanation from that supplied by radium A. Since A is half transformed in three minutes, its heating effect will have largely disappeared after 10 minutes, and the decrease is then mainly due to changes in radium B and C.

The variation with time of the heating effect of the active deposit is still more clearly brought out by an examination of the rise of the heating effect when the emanation is introduced into a small tube, and of the decrease of the heating effect after the emanation is removed. The curve of rise is shown in the upper curve of Fig. 101. 40 minutes after the introduction of the emanation, the heating effect had risen to 75 per cent. of the maximum value which was reached after an interval of about 3 hours.

Fig. 101.

After the heating effect of the emanation tube had attained a maximum, the emanation was removed, and the decay with time observed as soon as possible afterwards. The results are shown in the lower curve of Fig. 101. It is seen that the two curves of rise and decay are complementary to one another. The first observation was made 10 minutes after removal, and the heating effect had then dropped to 47 per cent. of the original value This sudden drop is due partly to the removal of the emanation, and partly to the rapid transformation of radium A. The lower curve is almost identical in shape with the corresponding α ray curve for the decay of the excited activity after a long exposure (see Fig. 86) and clearly shows that the heating effect is directly proportional to the activity measured by the α rays over the whole range examined. The heating effect decreases according to the same law and at the same rate as the activity measured by the α rays.

Twenty minutes after the removal of the emanation, radium A has been almost completely transformed, and the activity is then proportional to the amount of radium C present, since the intermediate product B does not give out rays. The close agreement of the activity and heat emission curves shows that the heating effect is proportional also to the amount of radium C. We may thus conclude that the rayless product B supplies little if any of the heat emission observed. If radium B supplied the same amount as radium C, the curve of decrease of heating effect with time would differ considerably from the activity curve.

The conclusion that the transformation of radium B is not accompanied by the release of as much heat as the other changes is to be expected if the heating effect is mainly due to the energy of motion of the expelled α particles.

The relative heating effect due to the radium products is shown in the following table. The initial heating effect of C is deduced by comparison with the corresponding activity curve.

Products Radiation Initial rate of heat emission
Radium α rays 25 per cent. of total
Emanation α " }
Radium A α " } 44 " "
Radium B no rays 0 " "
Radium C α, β, γ rays 31 " "

Since radium A and C supply almost an equal proportion of activity, it is probable that they have equal initial heating effects. If this is the case, the heating effect of the emanation alone is 13 per cent. of the total. 247. Heating effects of the β and γ rays. It has been shown in section 114 that the kinetic energy of the β particles emitted from radium is probably not greater than one per cent. of that due to the α particles. If the heat emission is a result of bombardment by the particles expelled from its mass, it is to be expected that the heating effect of the β rays will be very small compared with that due to the α rays. This anticipation is borne out by experiment. Curie measured the heating effect of radium (1) when enclosed in a thin envelope, and (2) when surrounded by one millimetre of lead. In the former case a large proportion of the β rays escaped, and, in the latter, nearly all were absorbed. The increase of heating effect in case (2) was not more than five per cent., and this is probably an over-estimate.

In a similar way, since the total ionization due to the β rays is about equal to that produced by the γ rays, we should expect that the heating effect of the γ rays will be very small compared with that arising from the α rays.

Paschen made some experiments on the heating effect of radium in a Bunsen ice calorimeter where the radium was surrounded by a thickness of 1·92 cms. of lead—a depth sufficient to absorb a large proportion of the γ rays. In his first publication^[6], results were given which indicated that the heating effect of the γ rays was even greater than that of the α rays. This was not confirmed by later observations by the same method. He concluded that the ice calorimeter could not be relied on to measure such very small quantities of heat.

After the publication of Paschen's first paper Rutherford and Barnes^[7] examined the question by a different method. An air calorimeter of the form shown in Fig. 98 was employed which was found to give very satisfactory results. The heat emission of radium was measured (1) when the radium was surrounded by a cylinder of aluminium and (2) when surrounded by a cylinder of lead of the same dimensions. The aluminium absorbed only a small fraction of the γ rays while the lead stopped more than half. No certain difference between the heating effect in the two cases was observed, although from the earlier experiments of Paschen a difference of at least 50 per cent. was to be expected. We must therefore conclude that the β and γ rays together do not supply more than a small percentage of the total heat emission of radium—a result which is in accordance with the calculations based on the total ionization produced by the different types of rays.

248. Source of the energy. It has been shown that the heating effect of radium is closely proportional to the activity measured by the α rays. Since the activity is generally measured between parallel plates such a distance apart that most of the α particles are absorbed in the gas, this result shows that the heating effect is proportional to the energy of the emitted α particles. The rapid heat emission of radium follows naturally from the disintegration theory of radio-activity. The heat is supposed to be derived not from external sources, but from the internal energy of the radium atom. The atom is supposed to be a complex system consisting of charged parts in very rapid motion, and in consequence contains a large store of latent energy, which can only be manifested when the atom breaks up. For some reason, the atomic system becomes unstable, and an α particle, of mass about twice that of the hydrogen atom, escapes, carrying with it its energy of motion. Since the α particles would be practically absorbed in a thickness of radium of less than ·001 cm., the greater proportion of the α particles, expelled from a mass of radium, would be stopped in the radium itself and their energy of motion would be manifested in the form of heat. The radium would thus be heated by its own bombardment above the temperature of the surrounding air. The energy of the expelled α particles probably does not account for the whole emission of heat by radium. It is evident that the violent expulsion of a part of the atom must result in intense electrical disturbances in the atom. At the same time, the residual parts of the disintegrated atom rearrange themselves to form a permanently or temporarily stable system. During this process also some energy is probably emitted, which is manifested in the form of heat in the radium itself.

The view that the heat emission of radium is due very largely to the kinetic energy possessed by the expelled α particles is strongly confirmed by calculations of the magnitude of the heating effect to be expected on such an hypothesis. It has been shown in section 93 that one gram of radium bromide emits about 1·44 × 10^{11} α particles per second. The corresponding number for 1 gram of radium (Ra = 225) is 2·5 × 10^{11}. Now it has been calculated from experimental data in section 94, that the average kinetic energy of the α particles expelled from radium is 5·9 × 10^{-6} ergs. Since all of the α particles are absorbed either in the radium itself or the envelope surrounding it, the total energy of the α particles emitted per second is 1·5 × 10^6 ergs. This corresponds to an emission of energy of about 130 gram calories per hour. Now the observed heating effect of radium is about 100 gram calories per hour. Considering the nature of the calculation, the agreement between the observed and experimental values is as close as would be expected, and directly supports the view that the heat emission of radium is due very largely to the bombardment of the radium and containing vessel by the α particles expelled from its mass.

249. Heating effect of the radium emanation. The enormous amount of heat liberated in radio-active transformations which are accompanied by the expulsion of α particles is very well illustrated by the case of the radium emanation.

The heat emission of the emanation released from 1 gram of radium is 75 gram calories per hour at its maximum value. This heat emission is not due to the emanation alone, but also to its further products which are included with it. Since the rate of heat emission decays exponentially with the time to about half value in four days, the total amount of heat liberated during the life of the emanation from 1 gram of radium is equal to

[integral]_{0}^[infinity] 75e^{-λt}dt = 75/λ = 10,000 gram calories approximately,

since λ = ·0072(hour)^{-1}. Now the volume of the emanation from 1 gram of radium is about 1 cubic millimetre at standard pressure and temperature (section 172). Thus 1 cubic centimetre of the emanation would during its transformation emit 10^7 gram calories. The heat emitted during the combination of 1 c.c. of hydrogen and oxygen to form water is about 2 gram calories. The emanation thus gives out during its changes 5 × 10^6 times as much energy as the combination of an equal volume of hydrogen and oxygen to form water, although this latter reaction is accompanied by a larger release of energy than any other known to chemistry.

The production of heat from 1 c.c. of the radium emanation is about 21 gram calories per second. This generation of heat would be sufficient to heat to redness, if not to melt down, the walls of the glass tube containing the emanation.

The probable rate of heat emission from 1 gram weight of the emanation can readily be deduced, assuming that the emanation has about 100 times the molecular weight of hydrogen. Since 100 c.c. of the emanation would weigh about 1 gram, the total heat emission from 1 gram of the emanation is about 10^9 gram calories.

It can readily be calculated that one pound weight of the emanation would, at its maximum, radiate energy at the rate of about 10,000 horse-power. This radiation of energy would fall off with the time, but the total emission of energy during the life of the emanation would correspond to 60,000 horse-power days.

250. Heating effects of uranium, thorium, and actinium. Since the heat emission of radium is a direct consequence of its bombardment by the α particles expelled from its mass, it is to be expected that all the radio-elements which emit α rays should also emit heat at a rate proportional to their α ray activity.

Since the activity of pure radium is probably about two million times that of uranium or thorium, the heat emission from 1 gram of thorium or uranium should be about 5 × 10^{-5} gram calories per hour, or about 0·44 gram calories per year. This is a very small rate of generation of heat, but it should be detectable if a large quantity of uranium or thorium is employed. Experiments to determine the heating effect of thorium have been made by Pegram^[8]. Three kilograms of thorium oxide, enclosed in a Dewar bulb, were kept in an ice-bath, and the difference of temperature between the thorium and ice-bath determined by a set of iron-constantine thermo-electric couples. The maximum difference of temperature observed was 0·04° C., and, from the rate of change of temperature, it was calculated that one gram of thorium oxide liberated 8 × 10^{-5} gram calories per hour. A more accurate determination of the heat emission is in progress, but the results obtained are of the order of magnitude to be expected. 251. Energy emitted by a radio-active product. An important consequence follows from the fact that the heat emission is a measure of the energy of the expelled α particles. If each atom of each product emits α particles, the total emission of energy from 1 gram of the product can at once be determined. The α particles from the different products are projected with about the same velocity, and consequently carry off about the same amount of energy. Now it has been shown that the energy of each α particle expelled from radium is about 5·9 × 10^{-6} ergs. Most of the products probably have an atomic weight in the neighbourhood of 200. Since there are 3·6 × 10^{19} molecules in one cubic centimetre of hydrogen, it can easily be calculated that there are about 3·6 × 10^{21} atoms in one gram of the product.

If each atom of the product expels one α particle, the total energy emitted from 1 gram of the matter is about 2 × 10^{16} ergs or 8 × 10^8 gram calories. The total emission of energy from a product which emits only β rays is probably about one-hundredth of the above amount.

In this case we have only considered the energy emitted from a single product independently of the successive products which may arise from it. Radium, for example, may be considered a radio-active product which slowly breaks up and gives rise to four subsequent α ray products. The total heat emission from one gram of radium and products is thus about five times the above amount, or 4 × 10^9 gram calories.

The total emission of energy from radium is discussed later in section 266 from a slightly different point of view.

252. Number of ions produced by an α particle. In the first edition of this book it was calculated by several independent methods that 1 gram of radium emitted about 10^{11} α particles per second. Since the actual number has later been determined by measuring the charge carried by the α rays (section 93) we can, conversely, use this number to determine with more certainty some of the constants whose values were assumed in the original calculation.

For example, the total number of ions produced by an α particle in the gas can readily be determined. The method employed is as follows. 0·484 mgr. of radium bromide was dissolved in water and then spread uniformly over an aluminium plate. After evaporation, the saturation ionization current, due to the radium at its minimum activity, was found to be 8·4 × 10^{-8} ampere. The plates of the testing vessel were sufficiently far apart to absorb all the α rays in the gas. The number of α particles expelled per second into the gas was found experimentally to be 8·7 × 10^6. Taking the charge on an ion as 1·13 × 10^{-19} coulombs (section 36), the total number of ions produced per second in the gas was 7·5 × 10^{11}. Thus each α particle on an average produced 86,000 ions in the gas before it was absorbed.

Now Bragg (section 104) has shown that the α particles from radium at its minimum activity are stopped in about 3 cms. of air. The results obtained by him indicate that the ionization of the particles per cm. of path is less near the radium than some distance away. Assuming, however, as a first approximation that the ionization is uniform along the path, the number of ions produced per cm. of path by the α particle is 29,000. Since the ionization varies directly as the pressure, at a pressure of 1 mm. of mercury the number of ions per unit path would be about 38. Now Townsend (section 103) found that the maximum number of ions produced per unit path of air at 1 mm. pressure by an electron in motion was 20, and in this case a fresh pair of ions was produced at each encounter of the electron with the molecules in its path. In the present case the α particle, which has a very large mass compared with the electron, appears to have a larger sphere of influence than the electron and to ionize twice as many molecules.

In addition, the α particle produces many more ions per unit path than an electron moving with the same velocity, for it has been shown (section 103) that the electron becomes a less efficient ionizer after a certain velocity is reached. As Bragg (loc. cit.) has pointed out, this is to be expected, since the α particle consists of a large number of electrons and consequently would be a far more efficient ionizer than an isolated electron. A calculation of the energy required to produce an ion by an α particle is given in Appendix A. 253. Number of β particles expelled from one gram of radium. It is of importance to compare the total number of β particles expelled from one gram of radium in radio-active equilibrium, as, theoretically, this number should bear a definite relation to the total number of α particles emitted. We have seen that new radium in radio-active equilibrium contains four products which emit α rays, viz. radium itself, the emanation, radium A and radium C. On the other hand, β rays are expelled from only one product, radium C. The same number of atoms of each of these successive products in equilibrium break up per second. If the disintegration of each atom is accompanied by the expulsion of one α particle and, in the case of radium C, also of one β particle, the number of α particles emitted from radium in radio-active equilibrium will be four times the number of β particles.

The method employed by Wien to determine the number of β particles emitted from a known quantity of radium has already been discussed in section 80. On account of the absorption of some of the β particles in the radium envelope and in the radium itself, the number found by him is far too small. It has been shown in section 85 that a number of easily absorbed β rays are projected from radium, many of which would be stopped in the radium itself or in the envelope containing it.

In order to eliminate as far as possible the error due to this absorption, in some experiments made by the writer, the active deposit obtained from the radium emanation rather than radium itself was used as a source of β rays. A lead rod, 4 cms. long and 4 mms. in diameter, was exposed as the negative electrode in a large quantity of the radium emanation for three hours. The rod was then removed and the γ ray effect from it immediately measured by an electroscope and compared with the corresponding γ ray effect from a known weight of radium bromide in radio-active equilibrium. Since the active deposit contains the product radium C which alone emits β rays, and, since the intensities of the β and γ rays are always proportional to each other, the number of β particles expelled from the lead rod per second is equal to the corresponding number from the weight of radium bromide which gives the same γ ray effect as the lead rod.

The rod was then enveloped in a thickness of aluminium foil of ·0053 cms.—a thickness just sufficient to absorb the α rays—and made the insulated electrode in a cylindrical metal vessel which was rapidly exhausted to a low pressure. The current in the two directions was measured at intervals by an electrometer, and, as we have seen in section 93, the algebraic sum of these currents is proportional to ne, where n is the number of β particles expelled per second from the lead rod, and e the charge on each particle. The activity of the radium C decayed with the time, but, from the known curve of decay, the results could be corrected in terms of the initial value immediately after the rod was removed from the emanation.

Taking into account that half of the β particles emitted by the active deposit were absorbed in the radium itself, and reckoning the charge on the β particle as 1·13 × 10^{-19} coulombs, two separate experiments gave 7·6 × 10^{10} and 7·0 × 10^{10} as the total number of β particles expelled per second from one gram of radium. Taking the mean value, we may conclude that the total number of β particles expelled per second from one gram of radium in radio-active equilibrium is about 7·3 × 10^{10}.

The total number of α particles expelled from one gram of radium at its minimum activity has been shown to be 6·2 × 10^{10} (section 93). The approximate agreement between these numbers is a strong indication of the correctness of the theoretical views previously discussed. It is to be expected that the number of β particles, deduced in this way, will be somewhat greater than the true value, since the β particles give rise to a secondary radiation consisting also of negatively charged particles moving at a high speed. These secondary β particles, arising from the impact of the β particles on the lead, will pass through the aluminium screen and add their effect to the primary β rays.

The results, however, indicate that four α particles are expelled from radium in radio-active equilibrium for each β particle and thus confirm the theory of successive changes.

1. Phil. Trans. A. p. 25, 1901.
2. P. Curie and Laborde, C. R. 136, p. 673, 1903.
3. Runge and Precht, Sitz. Ak. Wiss. Berlin, No. 38, 1903.
4. P. Curie, Société de Physique, 1903.
5. Rutherford and Barnes, Nature, Oct. 29, 1903. Phil. Mag. Feb. 1904.
6. Paschen, Phys. Zeit. Sept. 15, 1904.
7. Rutherford and Barnes, Nature, Dec. 18, 1904; Phil. Mag. May, 1905.
8. Pegram, Science, May 27, 1904.