Chapter XI: Transformation Products of Radium (1)

=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.

Giesel first drew attention to the fact that a radium compound gradually increased in activity after preparation, and only reached a constant value after a month’s interval. If a radium compound is dissolved in water and boiled for some time, or a current of air drawn through the solution, on evaporation it is found that the activity has been diminished. The same result is observed if a solid radium compound is heated in the open air. This loss of activity is due to the removal of the emanation by the process of solution or heating. Consider the case of a radium compound which has been kept for some time in solution in a shallow vessel, exposed to the open air, and then evaporated to dryness. The emanation which, in the state of solution, was removed as fast as it was formed, is now occluded, and, together with the active deposit which it produces, adds its radiations to that of the original radium. The activity will increase to a maximum value when the rate of production of fresh emanation balances the rate of change of that already produced.

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.

Time in Activity Percentage
days Activity
recovered

0 25·0 0

0·70 33·7 11·7

1·77 42·7 23·7

4·75 68·5 58·0

7·83 83·5 78·0

16·0 96·0 95·0

21·0 100·0 100·0

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

$$ \frac {I_t} {I₀} = 1 − e^{–λt} $$,

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 λ_ndt_, 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

_dn_ = _qdt_ − λ_ndt_ − α_ndt_,

or _dn_
----- = _q_ − (λ + α)_n_.
_dt_

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

$$ \frac {n} {n₀} = 1 − e^{-(λ + \alpha) t} $$ .

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

$$ \frac {n} {n₀} = 1 − e^{−2λ t} $$,

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.

α _particle_ α _particle_
/ /
/ /
RADIUM ATOM ——> ATOM OF EMANATION ——> ATOM OF ACTIVE DEPOSIT

=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.,

$$ \frac {I_t} {I_T} = \frac {e^{–λ_3 t} − e^{–λ_2 t}} {e^{–λ_3 T} − e^{–λ_2 T}} $$,

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.

Time in Theoretical Observed
minutes value of value of
activity activity

0 0 0

10 58·1 55

20 88·6 86

30 97·3 97

36 100 100

40 99·8 99·5

50 93·4 92

60 83·4 82

80 63·7 61·5

100 44·8 42·5

120 30·8 29

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

$$ \frac {I_t} {I₀} = ae^{–λ_3 t} − (a − 1) e^{–λ_2 t} $$,

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

$$ \frac {I_t} {I₀} = \frac {λ_2} {λ_2 − λ_3} e^{–λ_3 t} − \frac {λ_3} {λ_2 − λ_3} e^{–λ_2 t} $$

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,

$$ \frac {λ_2} {λ_2 − λ_3} = 4\cdot3 $$, and

$$ \frac {λ_1} {λ_1 − λ_3} = 3\cdot3 $$ .

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

$$ \frac {I_t} {I₀} = \frac {\cdot5λ_2} {λ_2 − λ_3} e^{–λ_3 t} − \cdot5 (\frac {λ_3} {λ_2 − λ_3} - 1) e^{–λ_2 t} $$ .

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

$$ e^{–λ_2 t} $$

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

$$ \frac {I_t} {I₀} = \frac {λ_2} {λ_2 − λ_3} e^{–λ_3 t} − \frac {λ_3} {λ_2 − λ_3} e^{–λ_2 t} $$

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

Time in Calculated Observed
minutes values values

0 100 100

10 96·8 97·0

20 89·4 88·5

30 78·6 77·5

40 69·2 67·5

50 59·9 57·0

60 49·2 48·2

80 34·2 33·5

100 22·7 22·5

120 14·9 14·5

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.

Time in Current
minutes

0 100

2 80

4 69·5

6 62·4

8 57·6

10 52·0

15 48·4

20 45·4

30 40·4

40 35·6

50 30·4

60 25·4

80 17·4

100 11·6

120 7·6

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).

Time in Calculated Observed
minutes value of value of
activity activity

0 100 100

10 96·8 97·0

20 89·4 89·2

30 78·6 80·8

40 69·2 71·2

50 59·9 60·8

60 49·2 50·1

80 34·2 34·8

100 22·7 23·2

120 14·9 15·2

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

$$ \frac {I_t} {I₀} = \frac {λ_2} {λ_2 − λ_3} e^{–λ_3 t} − \frac {λ_3} {λ_2 − λ_3} e^{–λ_2 t} $$

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,

$$ \frac {I_t} {I_T} = 10\cdot3 (e^{–λ_3 t} − e^{–λ_2 t}) $$

where _I_{T}_ is the maximum value of the activity;

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

$$ \frac {I_t} {I₀} = 4\cdot3 (e^{–λ_3 t} − 3\cdot3 e^{–λ_2 t}) $$,

where _I₀_ is the initial value;

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

$$ \frac {I_t} {I₀} = \frac {ae^{–λ_3 t} − be^{–λ_2 t}} {a − b} $$,

where

$$ a = \frac {1 − e^{–λ_3 T}} {λ_3} $$,

$$ b = \frac {1 − e^{–λ_2 T}} {λ_2} $$;

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

$$ \frac {I_t} {I₀} = \frac {1}{2} e^{–λ_1 t} + \frac {1}{2} (4\cdot3 e^{–λ_3 t} − 3\cdot3 e^{–λ_2 t}) $$ .

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,

$$ \frac {I_t} {I_{max}} = 1 − (4\cdot3 e^{–λ_3 t} − 3\cdot3 e^{–λ_2 t}) $$ .

For the α rays,

$$ \frac {I_t} {I_{max}} = 1 − \frac {1}{2} e^{–λ_1 t} − \frac {1}{2} (4\cdot3 e^{–λ_3 t} − 3\cdot3 e^{–λ_2 t}) $$ .

=226. Effect of temperature.= We have so far not considered the evidence on which the 28-minute rather than the 21-minute change is supposed to take place in the matter C. This evidence has been supplied by some recent important experiments of P. Curie and Danne[316] on the volatilization of the active matter deposited by the emanation. Miss Gates[317] showed that this active matter was volatilized from a platinum wire above a red heat and deposited on the surface of a cold cylinder surrounding the wire. Curie and Danne extended these results by subjecting an active platinum wire _for a short time_ to the action of temperatures varying between 15° C. and 1350° C., and then examining at room temperatures the decay curves not only for the active matter remaining on the wire, but also for the volatilized part. They found that the activity of the distilled part always increased after removal, passed through a maximum, and finally decayed according to an exponential law to half value in 28 minutes. At a temperature of about 630° C. the active matter left behind on the wire decayed at once according to an exponential law, falling to half value in 28 minutes. P. Curie and Danne showed that the matter B is much more volatile than C. The former is completely volatilized at about 600° C., while the latter is not completely volatilized even at a temperature of 1300° C. The fact that the matter C, left behind when B is completely volatilized, decays at once to half value in 28 minutes shows that the matter C itself and not B is half transformed in 28 minutes.

Curie and Danne also found that the rate of decay of the active matter varied with the temperature to which the platinum wire had been subjected. At 630° C. the rate of decay was normal, at 1100° C. the activity fell to half value in about 20 minutes, while at 1300° C. it fell to about half value in about 25 minutes.

I have repeated the experiments of Curie and Danne and obtained very similar results. It was thought possible that the measured rate of decay observed after heating might be due to a permanent increase in the rate of volatilization of C at ordinary temperatures. This explanation, however, is not tenable, for it was found that the activity decreased at the same rate whether the activity of the wire was tested in a closed tube or in the open with a current of air passed over it.

These results are of great importance, for they indicate that the rate of change of the product C is not a constant, but is affected by differences of temperature. This is the first case where temperature has been shown to exert an appreciable influence on the rate of change of any radio-active product.

=227. Volatility of radium B at ordinary temperature.= Miss Brooks[318] has observed that a body, made active by exposure to the radium emanation, possesses the power of exciting secondary activity on the walls of a vessel in which it is placed. This activity was usually about ¹⁄₁₀₀₀ of the whole, but the amount was increased to about ¹⁄₂₀₀ if the active wire was washed in water and dried over a gas flame—the method often adopted to free the wire of any trace of the radium emanation. This effect of producing activity was most marked immediately after removal of the wire from the emanation, and was almost inappreciable ten minutes afterwards.

The effect was particularly noticeable in some experiments with a copper plate, which was made active by leaving it a short time in a solution of the active deposit from radium. This active solution was obtained by placing an active platinum wire in dilute hydrochloric acid. On placing the copper plate in a testing vessel for a few minutes, and then removing it, activity was observed on the walls of the vessel amounting to about one per cent. of the activity of the copper plate.

It was found that this effect was not due to the emission of an emanation from the active body, but must be ascribed to a slight volatility of radium B at ordinary temperatures. This was proved by observations on the variation of the activity of the matter deposited on the walls of the vessel. The activity was small at first, but rose to a maximum after about 30 minutes, and then decayed with the time. The curve of rise was very similar to that shown in Fig. 87, and shows that the inactive matter radium B was carried to the walls and there changed into C, which gave rise to the radiation observed.

The product B only escapes from the body for a short time after removal. This is a strong indication that its apparent volatility is connected with the presence of the rapidly changing product radium A. Since A breaks up with an expulsion of an α particle, some of the residual atoms constituting radium B may acquire sufficient velocity to escape into the gas, and are then transferred by diffusion to the walls of the vessel.

Miss Brooks observed that the activity was not concentrated on the negative electrode in an electric field but was diffused uniformly over the walls of the vessel. This observation is of importance in considering the explanation of the anomalous effects exhibited by the active deposit of radium, which will be discussed in the following section.

=228. Effect of the first rapid change.= We have seen that the law of decay of activity, measured by the β or γ rays, can be explained very satisfactorily if the first 3-minute change is disregarded. The full theoretical examination of the question given in sections 197 and 198 and the curves of Figs. 72 and 73 show, however, that the presence of the first change should exercise an effect of sufficient magnitude to be detected in measurements of the activity due to the succeeding changes. The question is of great interest, for it involves the important theoretical point whether the substances A and B are produced independently of one another, or whether A is the parent of B. In the latter case, the matter A which is present changes into B, and, in consequence, the amount of B present after A is transformed should be somewhat greater than if B were produced independently. Since the change of A is fairly rapid, the effect should be most marked in the early part of the curve.

In order to examine this point experimentally, the curve of rise of activity, measured by the β rays, was determined immediately after the introduction of a large quantity of the radium emanation into a closed vessel. The curve of decay of activity on a body for a long exposure after removal of the emanation, and the rise of activity after the introduction of the emanation, are in all cases complementary to one another. While, however, it is difficult to measure with certainty whether the activity has fallen in a given time, for example, from 100 to 99 or 98·5, it is easy to be sure whether the corresponding rise of activity in the converse experiment is 1 or 1·5 per cent. of the final amount. Fig. 92, curve I, shows the rise of activity (measured by the β rays) obtained for an interval of 20 minutes after the introduction of the emanation. The ordinates represent the percentage amount of the final activity regained at any time.

Curve III shows the theoretical curve obtained on the assumption that A is a parent of B. This curve is calculated from equation (9) discussed in section 198, and λ₁, λ₂, λ₃ are the values previously found.

Curve II gives the theoretical activity at any time on the assumption that the substances A and B arise independently. This is calculated from an equation of the same form as (8), section 198.

It is seen that the experimental results agree best with the view that A and B arise independently. Such a conclusion, however, is of too great importance to be accepted before examining closely whether the theoretical conditions are fulfilled in the experiments. In the first place, it is assumed that the carriers which give rise to excited activity are deposited on the surface of the body, to be made active immediately after their formation. There is some evidence, however, that some of these carriers exist for a considerable interval in the gas before their deposit on the body. For example, it is found that if a body is introduced for a short interval, about 1 minute, into a vessel containing the radium emanation, which has remained undisturbed for several hours, the activity after the first rapid decay (see Fig. 86, curve _B_) is in much greater proportion than if an electric field had been acting for some time previously. This result indicates that the carriers of B and C both collect in the gas and are swept to the electrode when an electric field is applied. I have also observed that if radium emanation, which has stood undisturbed for some time, is swept into a testing vessel, the rise curve is not complementary to the decay curve, but indicates that a large amount of radium B and C was present with the emanation. The experiments of Miss Brooks, previously referred to, indicate that radium B does not obtain a charge and so will remain in the gas. Dr Bronson, working in the laboratory of the writer, has obtained evidence that a large amount of radium D remains in the gas even in a strong electric field. If the matter B exists to some extent in the gas, the difference between the theoretical curves for three successive changes would be explained; for, in transferring the emanation to another vessel, the matter B mixed with it would commence at once to change into C and give rise to a part of the radiation observed.

The equal division of the activity between the products A and C (see Fig. 90) supports the view that C is a product of A, for when radio-active equilibrium is reached, the number of particles of A changing per second is equal to the number of B or C changing per second. If each atom of A and C expels an α particle of the same mass and with the same average velocity, the activity due to the matter A should be equal to that due to the matter C; and this, as we have seen, is the case.

While it is a matter of great difficulty to give a definite experimental proof that radium A and B are consecutive products, I think there is little doubt of its correctness. Accurate determinations of the curves of rise and decay may throw further light on the complicated processes which undoubtedly occur between the breaking up of the atoms of the emanation and the appearance of the active deposit on the electrodes.

=229. Relative activity supplied by the α-ray products of radium.= There are four products in radium which give out α rays, viz. radium itself, the emanation, radium A and C. If these products are in radio-active equilibrium, the same number of particles of each product are transformed per second and, if each atom breaks up with the emission of one α particle, the number of α particles expelled per second should be the same for each product.

Since, however, the α particles from the different products are not projected with the same velocity, the activity, measured by the ionization current in the usual manner, will not be the same for all products. The activity, when measured by the saturation current between parallel plates at sufficient distance apart to absorb all the α rays in the gas, is proportional to the energy of the α particles escaping into the gas.

It has been shown that the minimum activity of radium after removal of the emanation, measured by the α rays, is 25 per cent. of the maximum value. The remaining 75 per cent. is due to the α particles from the other products. Now the activity supplied by radium A and C is nearly the same (section 228). If the emanation is introduced into a cylindrical vessel about 5 cms. in diameter, the activity increases to about twice its initial value owing to the deposit of radium A and C on the surface of the vessel. This shows that the activity of the emanation is of about the same magnitude as that supplied by radium A or C, but an accurate comparison is beset with difficulty, for the emanation is distributed throughout the gas, while radium A and C are deposited on the walls of the vessel. In addition, the relative absorption of the emanation compared with that of radium A and C is not known.

The writer has made some experiments on the decrease of activity of radium immediately after heating to a sufficient temperature to drive off the emanation. The results obtained by this method are complicated by the alteration of the radiating surface in consequence of the heating, but indicate that the emanation supplies about 70 per cent. of the activity of radium A or C.

This points to the conclusion that the α particles from the emanation are projected with less velocity than those from radium C.

The following table shows approximately the activity supplied by the different products of radium in radio-active equilibrium.

Product Percentage
proportion
of total
activity

Radium 25 per
cent.

Emanation 17 „

Radium A 29 „

Radium B 0 „

Radium C 29 „

The products of radium and their radiation are graphically shown later in Fig. 95.

=230. Active deposit of radium of slow transformation.= It has been pointed out (section 183) that a body, exposed in the presence of the radium emanation, does not lose all its activity for a long time after removal; a small residual activity is always observed. The magnitude of this residual activity is dependent not only upon the amount of emanation employed, but also upon the time of exposure of the body in the presence of the emanation. For an exposure of several hours in the presence of the emanation, the residual activity is less than one-millionth of the activity immediately after removal.

An account will now be given of some investigations made by the writer[319] on the nature of this residual activity and the chemical properties of the active matter itself. It is first of all necessary to show that the residual activity arises in consequence of a deposit of radio-active matter, and is not due to some action of the intense radiations to which the body made active has been subjected.

The inside of a long glass tube was covered with equal areas of thin metal, including aluminium, iron, copper, silver, lead, and platinum. A large amount of radium emanation was introduced into the tube, and the tube closed. After seven days the metal plates were removed, and, after allowing two days to elapse for the ordinary excited activity to disappear, the residual activity of the plates was tested by an electrometer. The activity of the plates was found to be unequal, being greatest for copper and silver, and least for aluminium. The activity of copper was twice as great as that of aluminium. After standing for another week the activity of the plates was again tested. The activity of each had diminished in the interval to some extent, but the initial differences observed had to a large extent disappeared. After reaching a minimum value the activity of each plate slowly but steadily increased at the same rate. After a month’s interval the activity of each of the plates was nearly the same, and more than three times the minimum value. The initial irregularities in the decay curves of the different metals are, in all probability, due to slight but different degrees of absorption of the radium emanation by the metal plates, the absorption being greatest for copper and silver and least for aluminium. As the occluded emanation was slowly released or lost its activity, the activity of the metal fell to a limiting value. The absorption of the radium emanation by lead, paraffin, and caoutchouc has been noticed by Curie and Danne (section 182).

The residual activity on the plates comprised both α and β rays, the latter being present, in all cases, in a very unusual proportion. The equality of the activity and the identity of the radiation emitted from each plate show that the residual activity is due to changes of some form of matter deposited on the plates, and that it cannot be ascribed to an action of the intense radiations; for if such were the case, it would be expected that the activity produced on the different plates would vary not only in quantity, but also in quality. This result is confirmed by the observation that the active matter can be removed from a platinum plate by solution in sulphuric acid, and has other distinctive chemical and physical properties.

The variation with time of the residual activity measured by the α rays will first be considered. A platinum plate was exposed in the presence of the radium emanation for seven days. The amount of emanation initially present was equal to that obtained from about 3 milligrams of pure radium bromide. The plate immediately after removal gave a saturation-current, measured between parallel plates by a galvanometer, of 1·5 × 10⁻⁷ ampere. Some hours after removal, the activity decayed according to an exponential law with the time, falling to half value in 28 minutes. Three days after removal the active plate gave a saturation-current, measured by an electrometer, of 5 × 10⁻¹³ ampere; _i.e._ ¹⁄₃₀0,000 of the initial activity. The activity was observed to increase steadily with the time. The results are shown in Fig. 93, where the time is reckoned from the middle of the time of exposure to the emanation.

The curve is initially nearly a straight line passing through the origin. The activity increases with the time for the interval of eight months over which the observations have extended. The latter portions of the curve, however, fall below the tangent to the curve drawn through the origin, showing that the activity is not increasing proportionately with the time.

The active deposit, obtained in a different manner, has been examined for a still longer period. The emanation from 30 milligrams of radium bromide was condensed in a glass tube and then sealed. After a month’s interval, the tube was opened and dilute sulphuric acid introduced. The acid dissolved off the active deposit in the tube and on driving off the acid by heat, a radio-active residue was obtained. The activity of this residue, measured by the α rays, steadily increased for a period of 18 months, but the curve of variation of activity with time plotted as in Fig. 93 tends to become more flattened, and is obviously approaching a maximum value.

The explanation of this curve will be considered later in section 236.

=231. Variation of the β ray activity.= The residual activity consists of both α and β rays, the latter being present initially in an unusually large proportion. The proportion of α to β rays from the platinum plate, one month after removal, was at the most one-fiftieth of that from a thin film of radium bromide in radio-active equilibrium. Unlike the α ray activity, the activity measured by the β rays remains constant after the active deposit is about one month old, and, in consequence, the proportion of α to β rays steadily increases with the time. The experiments showed that the intensity of the β rays did not vary much, if at all, over a further period of eighteen months. The want of proportionality between the α and β rays shows that the two types of rays arise from different products. This conclusion is confirmed by experiments, to be described later, which show that the products giving rise to α and β rays can be temporarily separated from one another by physical and chemical means.