215. Radio-activity of radium. Notwithstanding the enormous difference in their relative activities, the radio-activity of radium presents many close analogies to that of thorium and actinium. Both substances give rise to emanations which in turn produce “excited activity” on bodies in their neighbourhood. Radium, however, does not give rise to any intermediate product between the element itself and the emanation it produces, or in other words there is no product in radium corresponding to Th X in thorium.

If now the compound is again dissolved or heated, the emanation escapes. Since the active deposit is not volatile and is insoluble in water, it is not removed by the process of solution or heating. Since, however, the parent matter is removed, the activity due to the active deposit will immediately begin to decay, and in the course of a few hours will have almost disappeared. The activity of the radium measured by the α rays is then found to be about 25 per cent. of its original value. This residual activity of radium, consisting entirely of α rays, is non-separable, and has not been further diminished by chemical or physical means. Rutherford and Soddy^[314] examined the effect of aspiration for long intervals through a radium chloride solution. After the first few hours the activity was found to be reduced to 25 per cent., and further aspiration for three weeks did not produce any further diminution. The radium was then evaporated to dryness, and the rise of its activity with time determined. The results are shown in the following table. The final activity in the second column is taken as one hundred. In column 3 is given the percentage proportion of the activity recovered.

The results are shown graphically in Fig. 85.

The decay curve of the radium emanation is shown in the same figure. The curve of recovery of the lost activity of radium is thus analogous to the curves of recovery of uranium and thorium which have been freed from the active products Ur X and Th X respectively. The intensity I_t of the recovered activity at any time is given by

where I₀ is the final value, and λ is the radio-active constant of the emanation. The decay and recovery curves are complementary to one another.

Knowing the rate of decay of activity of the radium emanation, the recovery curve of the activity of radium can thus at once be deduced, provided all of the emanation formed is occluded in the radium compound.

When the emanation is removed from a radium compound by solution or heating, the activity measured by the β rays falls almost to zero, but increases in the course of a month to its original value. The curve showing the rise of β and γ rays with time is practically identical with the curve, Fig. 85, showing the recovery of the lost activity of radium measured by the α rays. The explanation of this result lies in the fact that the β and γ rays from radium only arise from the active deposit, and that the non-separable activity of radium gives out only α rays. On removal of the emanation, the activity of the active deposit decays nearly to zero, and in consequence the β and γ rays almost disappear. When the radium is allowed to stand, the emanation begins to accumulate, and produces in turn the active deposit, which gives rise to β and γ rays. The amount of β and γ rays (allowing for a period of retardation of a few hours) will then increase at the same rate as the activity of the emanation, which is continuously produced from the radium.

216. Effect of escape of emanation. If the radium allows some of the emanation produced to escape into the air, the curve of recovery will be different from that shown in Fig. 85. For example, suppose that the radium compound allows a constant fraction α of the amount of emanation, present in the compound at any time, to escape per second. If n is the number of emanation particles present in the compound at the time t, the number of emanation particles changing in the time dt is λndt, where λ is the constant of decay of activity of the emanation. If q is the rate of production of emanation particles per second, the increase of the number dn in the time dt is given by

The same equation is obtained when no emanation escapes, with the difference that the constant λ + α is replaced by λ. When a steady state is reached, dn/dt is zero, and the maximum value of n is equal to q/(λ + α).

If no escape takes place, the maximum value of n is equal to q/λ. The escape of emanation will thus lower the amount of activity recovered in the proportion λ/(λ + α). If n₀ is the final number of emanation particles stored up in the compound, the integration of the above equation gives

The curve of recovery of activity is thus of the same general form as the curve when no emanation escapes, but the constant λ is replaced by λ + α.

For example, if α = λ = ¹⁄₄₆₃₀₀₀, the equation of rise of activity is given by

and, in consequence, the increase of activity to the maximum will be far more rapid than in the case of no escape of emanation.

A very slight escape of emanation will thus produce large alterations both in the final maximum and in the curve of recovery of activity.

A number of experiments have been described by Mme Curie in her Thèse présentée à la Faculté des Sciences de Paris on the effect of solution and of heat in diminishing the activity of radium. The results obtained are in general agreement with the above view, that 75 per cent. of the activity of radium is due to the emanation and the excited activity it produces. If the emanation is wholly or partly removed by solution or heating, the activity of the radium is correspondingly diminished, but the activity of the radium compound is spontaneously recovered owing to the production of fresh emanation. A state of radio-active equilibrium is reached, when the rate of production of fresh emanation balances the rate of change in the emanation stored up in the compound. The differences observed in the rate of recovery of radium under different conditions were probably due to variations in the rate of escape of the emanation.

217. It has been shown in section 152 that the emanation is produced at the same rate in the solid as in the solution, and all the results obtained point to the conclusion that the emanation is produced from radium at a constant rate, which is independent of physical conditions. Radium, like thorium, shows a non-separable activity of 25 per cent. of the maximum activity, and consisting entirely of α rays. The β and γ rays arise only from the active deposit. The emanation itself (section 156) gives out only α rays. These results thus admit of the explanation given in the case of thorium (section 136). The radium atoms break up at a constant rate with the emission of α particles. The residue of the radium atom becomes the atom of the emanation. This in turn is unstable and breaks up with the expulsion of an α particle. The emanation is half transformed in four days. We have seen that this emanation gives rise to an active deposit. The results obtained up to this stage are shown diagrammatically below.

218. Analysis of the active deposit from radium. We have seen in chapter VIII that the excited activity produced on bodies, by the action of the radium emanation, is due to a thin film of active matter deposited on the surface of bodies. This active deposit is a product of the decomposition of the radium emanation, and is not due to any action of the radiations on the surface of the matter.

The curves showing the variation of the excited activity with time are very complicated, depending not only upon the time of exposure in the presence of the emanation, but also upon the type of radiation used for measurement. The greater portion of the activity of this deposit dies away in the course of 24 hours, but a very small fraction still remains, which then changes very slowly.

It will be shown in this chapter that at least six successive transformations occur in the active deposit. The matter initially produced from the emanation is called radium A, and the succeeding products B, C, D, E, F. The equations expressing the quantity of A, B, C,...... present at any time are very complicated, but the comparison of theory with experiment may be much simplified by temporarily disregarding some unimportant terms: for example, the products A, B, C are transformed at a very rapid rate compared with D. The activity due to D + E + F is, in most cases, negligible compared with that of A or C, being usually less than ¹⁄₁₀₀₀₀₀ of the initial activity observed for A or C. The analysis of the active deposit of radium may thus be conveniently divided into two stages:

(1) Analysis of the deposit of rapid change, which is mainly composed of radium A, B, and C;

(2) Analysis of the deposit of slow change, which is composed of radium D, E, and F.

219. Analysis of the deposit of rapid change. In the experiments described below, a radium solution was placed in a closed glass vessel. The emanation then collected in the air space above the solution. The rod, to be made active, was introduced through an opening in the stopper and exposed in the presence of the emanation for a definite interval. If the decay was to be measured by the α rays, the rod was made the central electrode in a cylindrical vessel such as is shown in Fig. 18. A saturating voltage was applied, and the current between the cylinders measured by an electrometer. If a very active rod is to be tested, a sensitive galvanometer can be employed, but, in such a case, a large voltage is required to produce saturation. A slow current of dust-free air was continuously circulated through the cylinder, in order to remove any emanation that may have adhered to the rod. For experiments on the β and γ rays, it was found advisable to use an electroscope, such as is shown in Fig. 12, instead of an electrometer. For measurements with the γ rays, the active rod was placed under the electroscope, and before entering the vessel the rays passed through a sheet of metal of sufficient thickness to absorb all the α rays. For measurements with the γ rays, the electroscope was placed on a lead plate 0·6 cms. thick, and the active rod placed under the lead plate. The α and β rays were completely stopped by the lead, and the discharge in the electroscope was then due to the γ rays alone. The electroscope is very advantageous for measurements of this character, and accurate observations can be made simply and readily.

The curve of decay of activity, measured by the α rays, for an exposure of 1 minute in the presence of the radium emanation is shown in Fig. 86, curve BB.

The curve exhibits three stages:—

(1) A rapid decay in the course of 15 minutes to less than 10 per cent. of the value immediately after removal;

(2) A period of 30 minutes in which the activity varies very little;

(3) A gradual decrease almost to zero.

The initial drop decays very approximately according to an exponential law with the time, falling to half value in about 3 minutes. Three or four hours after removal the activity again decays according to an exponential law with the time, falling to half value in about 28 minutes. The family of curves obtained for different times of exposure have already been shown in Fig. 67. These results thus indicate:—

(1) An initial change in which half the matter is transformed in 3 minutes;

(2) A final change in which half the matter is transformed in 28 minutes.

Before considering the explanation of the intermediate portion of the curve further experimental results will be considered.

The curve of decay of the excited activity for a long exposure (24 hours) is shown graphically in Fig. 86, curve AA. There is at first a rapid decrease for the first 15 minutes to about 50 per cent. of the initial value, then a slower decay, and, after an interval of about 4 hours, a gradual decay nearly to zero, according to an exponential law with the time, falling to half value in 28 minutes.

The curves of variation with time of the excited activity when measured by the β rays are shown graphically in Figs. 87 and 88.

Fig. 87 is for a short exposure of 1 minute. Fig. 88 shows the decay for a long exposure of about 24 hours.

The curves obtained for the β rays are quite different from those obtained for the α rays. For a short exposure, the activity measured by the β rays is at first small, then passes through a maximum about 36 minutes after removal. There is then a gradual decrease, and after several hours the activity decays according to an exponential law, falling, as in the other cases, to half value in 28 minutes.

The curve shown in Fig. 88 for the β rays is very similar in shape to the corresponding curve, Fig. 86, curve AA, for the α rays, with the exception that the rapid initial drop observed for the α-ray curve is quite absent. The later portions of the curve are similar in shape, and, disregarding the first 15 minutes after removal, the activity decays at exactly the same rate in both cases.

The curves obtained by means of the γ rays are identical with those obtained for the β rays. This shows that the β and γ rays always occur together and in the same proportion.

For increase of the time of exposure from 1 minute to 24 hours the curves obtained are intermediate in shape between the two representative limiting curves, Figs. 87 and 88. Some of these curves have already been shown in Fig. 68.

220. Explanation of the curves. It has been pointed out that the rapid initial drop for curves A and B, Fig. 86, is due to a change giving rise to α rays, in which half of the matter is transformed in about 3 minutes. The absence of the drop in the corresponding curves, when measured by the β rays, shows that the first 3-minute change does not give rise to β rays; for if it gave rise to β rays, the activity should fall off at the same rate as the corresponding α-ray curve.

It has been shown that the activity several hours after removal decays in all cases according to an exponential law with the time, falling to half value in about 28 minutes. This is the case whether for a short or long exposure, or whether the activity is measured by the α, β, or γ rays. This indicates that the final 28-minute change gives rise to all three types of rays.

It will be shown that these results can be completely explained on the supposition that three successive changes occur in the deposited matter of the following character^[315]:—

(1) A change of the matter A initially deposited in which half is transformed in about 3 minutes. This gives rise only to α rays.

(2) A second “rayless” change in which half the matter B is transformed in 21 minutes.

(3) A third change in which half the matter C is transformed in 28 minutes. This gives rise to α, β, and γ rays.

221. Analysis of the β-ray curves. The analysis of the changes is much simplified by temporarily disregarding the first 3-minute change. In the course of 6 minutes after removal, three quarters of the matter A has been transformed into B and 20 minutes after removal all but 1 per cent. has been transformed. The variation of the amount of matter B or C present at any time agrees more closely with the theory, if the first change is disregarded altogether. A discussion of this important point is given later (section 228).

The explanation of the β-ray curves (see Figs. 87 and 88), obtained for different times of exposure, will be first considered. For a very short exposure, the activity measured by the β rays is small at first, passes through a maximum about 36 minutes later, and then decays steadily with the time.

The curve shown in Fig. 87 is very similar in general shape to the corresponding thorium and actinium curves. It is thus necessary to suppose that the change of the matter B into C does not give rise to β rays, while the change of C into D does. In such a case the activity (measured by the β rays) is proportional to the amount of C present. Disregarding the first rapid change, the activity I_t at any time t should be given by an equation of the same form (section 207) as for thorium and actinium, viz.,

where I_T is the maximum activity observed, which is reached after an interval T. Since the activity finally decays according to an exponential law (half value in 28 minutes), one of the values of λ is equal to 4·13 × 10^-4. As in the case of thorium and actinium, the experimental curves do not allow us to settle whether this value of λ is to be given to λ₂ or λ₃. From other data (see section 226) it will be shown later that it must refer to λ₃. Thus λ₃ = 4·13 × 10^-4 (sec)^-1.

The experimental curve agrees very closely with theory if λ₂ = 5·38 × 10^-4 (sec)^-1.

The agreement between theory and experiment is shown by the table given below. The maximum value I_T (which is taken as 100) is reached at a time T = 36 minutes.

In order to obtain the β-ray curve, the following procedure was adopted. A layer of thin aluminium was placed inside a glass tube, which was then exhausted. A large quantity of radium emanation was then suddenly introduced by opening a stop-cock communicating with the emanation vessel, which was at atmospheric pressure. The emanation was left in the tube for 1·5 minutes and then was rapidly swept out by a current of air. The aluminium was then removed and was placed under an electroscope, such as is shown in Fig. 12. The α rays from the aluminium were cut off by an interposed screen of aluminium ·1 mm. thick. The time was reckoned from a period of 45 seconds after the introduction of the emanation.

There is thus a good agreement between the calculated and observed values of the activity measured by the β rays.

The results are satisfactorily explained if it is supposed:—

(1) That the change B into C (half transformed in 21 minutes) does not give rise to β rays;

(2) That the change C into D (half transformed in 28 minutes) gives rise to β rays.

222. These conclusions are very strongly supported by observations of the decay measured by the β rays for a long exposure. The curve of decay is shown in Fig. 88 and Fig. 89, curve I.

P. Curie and Danne made the important observation that the curve of decay C, corresponding to that shown in Fig. 88, for a long exposure, could be accurately expressed by an empirical equation of the form

where λ₂ = 5·38 × 10^-4 (sec)^-1 and λ₃ = 4·13 × 10^-4 (sec)^-1, and α = 4·20 is a numerical constant.

I have found that within the limit of experimental error this equation represents the decay of excited activity of radium for a long exposure, measured by the β rays. The equation expressing the decay of activity, measured by the α rays, differs considerably from this, especially in the early part of the curve. Several hours after removal the activity decays according to an exponential law with the time, decreasing to half value in 28 minutes. This fixes the value of λ₃. The constant α and the value of λ₂ are deduced from the experimental curve by trial. Now we have already shown (section 207) that in the case of the active deposit from thorium, where there are two changes of constants λ₂ and λ₃, in which only the second change gives rise to a radiation, the intensity of the radiation is given by

for a long time of exposure (see equation 8, section 198). This is an equation of the same form as that found experimentally by Curie and Danne. On substituting the values λ₂, λ₃ found by them,

Thus the theoretical equation agrees in form with that deduced from observation, and the values of the numerical constants are also closely concordant. If the first as well as the second change gave rise to a radiation, the equation would be of the same general form, but the value of the numerical constants would be different, the values depending upon the ratio of the ionization in the first and second changes. If, for example, it is supposed that both changes give out β rays in equal amounts, it can readily be calculated that the equation of decay would be

Taking the values of λ₂ and λ₃ found by Curie, the numerical factor

becomes 2·15 instead of 4·3 and 1·15 instead of 3·3. The theoretical curve of decay in this case would be readily distinguishable from the observed curve of decay. The fact that the equation of decay found by Curie and Danne involves the necessity of an initial rayless change can be shown as follows:—

Curve I (Fig. 89) shows the experimental curve. At the moment of removal of the body from the emanation (disregarding the initial rapid change), the matter must consist of both B and C. Consider the matter which existed in the form C at the moment of removal. It will be transformed according to an exponential law, the activity falling by one-half in 28 minutes. This is shown in curve II. Curve III represents the difference between the ordinates of curves I and II. It will be seen that it is identical in shape with the curve (Fig. 87) showing the variation of the activity for a short exposure, measured by the β rays. It passes through a maximum at the same time (about 36 minutes). The explanation of such a curve is only possible on the assumption that the first change is a rayless one. The ordinates of curve III express the activity added in consequence of the change of the matter B, present after removal, into the matter C. The matter B present gradually changes into C, and this, in its change to D, gives rise to the radiation observed. Since the matter B alone is considered, the variation of activity with time due to its further changes, shown by curve III, should agree with the curve obtained for a short exposure (see Fig. 87), and this, as we have seen, is the case.

The agreement between theory and experiment is shown in the following table. The first column gives the theoretical curve of decay for a long exposure deduced from the equation

taking the value of λ₂ = 5·38 × 10^-4 and λ₃ = 4·13 × 10^-4.

The second column gives the observed activity (measured by means of an electroscope) for a long exposure of 24 hours in the presence of the emanation.

In cases where a steady current of air is drawn over the active body, the observed values are slightly lower than the theoretical. This is probably due to a slight volatility of the product radium B at ordinary temperatures.

223. Analysis of the α-ray curves. The analysis of the decay curves of the excited activity of radium, measured by the α rays, will now be discussed. The following table shows the variation of the intensity of the radiation after a long exposure in the presence of the radium emanation. A platinum plate was made active by exposure for several days in a glass tube containing a large quantity of emanation. The active platinum after removal was placed on the lower of two parallel insulated lead plates, and a saturating electromotive force of 600 volts was applied. The ionization current was sufficiently large to be measured by means of a sensitive high-resistance galvanometer, and readings were taken as quickly as possible after removal of the platinum from the emanation vessel. The initial value of the current (taken as 100) was deduced by continuing the curves backwards to meet the vertical axis (see Fig. 90), and was found to be 3 × 10^-8 ampere.

These results are shown graphically in the upper curve of Fig. 90. The initial rapid decrease is due to the decay of the activity of the matter A. If the slope of the curve is produced backwards from a time 20 minutes after removal, it cuts the vertical axis at about 50. The difference between the ordinates of the curves A + B + C and LL at any time is shown in the curve AA. The curve AA represents the activity at any time supplied by the change in radium A. The curve LL starting from the vertical axis is identical with the curve already considered, representing the decay of activity measured by the β rays for a long exposure (see Fig. 88).

This is shown by the agreement of the numbers in the above table. The first column in the table above gives the theoretical values of the activity deduced from the equation

for the values of λ₂, λ₃ previously employed. The second column gives the observed values of the activity deduced from the decay curve LL.

The close agreement of the curve LL with the theoretical curve deduced on the assumption that there are two changes, the first of which does not emit rays, shows that the change of radium B into C does not emit α rays. In a similar way, as in the curve I, Fig. 89, the curve LL may be analysed into its two components represented by the two curves CC and BB. The curve CC represents the activity supplied by the matter C present at the moment of removal. The curve BB represents the activity resulting from the change of B into C and is identical with the corresponding curve in Fig. 89. Using the same line of reasoning as before, we may thus conclude that the change of B into C is not accompanied by α rays. It has already been shown that it does not give rise to β rays, and the identity of the β and γ-ray curves shows that it does not give rise to γ rays. The change of B into C is thus a “rayless” change, while the change of C into D gives rise to all three kinds of rays.

An analysis of the decay of the excited activity of radium thus shows that three distinct rapid changes occur in the matter deposited, viz.:—

(1) The matter A, derived from the change in the emanation, is half transformed in 3 minutes and is accompanied by α rays alone;

(2) The matter B is half transformed in 21 minutes and gives rise to no ionizing rays;

(3) The matter C is half transformed in 28 minutes and is accompanied by α, β, and γ rays;

(4) A fourth very slow change will be discussed later.

224. Equations representing the activity curves. The equations representing the variation of activity with time are for convenience collected below, where λ₁ = 3·8 × 10^-3, λ₂ = 5·38 × 10^-4, λ₃ = 4·13 × 10^-4:—

(1) Short exposure: activity measured by β rays,

where I_T is the maximum value of the activity;

(2) Long exposure: activity measured by β rays,

where I₀ is the initial value;

(3) Any time of exposure T: activity measured by the β rays,

where

(4) Activity measured by α rays: long time of exposure,

The equations for the α rays for any time of exposure can be readily deduced, but the expressions are somewhat complicated.

225. Equations of rise of excited activity. The curves expressing the gradual increase to a maximum of the excited activity produced on a body exposed in the presence of a constant amount of emanation are complementary to the curves of decay for a long exposure. The sum of the ordinates of the rise and decay curves is at any time a constant. This follows necessarily from the theory and can also be deduced simply from à priori considerations. (See section 200.)

The curves of rise and decay of the excited activity for both the α and β rays are shown graphically in Fig. 91. The thick line curves are for the α rays. The difference between the shapes of the decay curves when measured by the α or β rays is clearly brought out in the figure. The equations representing the rise of activity to a maximum are given below.

For the β and γ rays,