XI. TRANSFORMATION PRODUCTS OF RADIUM
=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.
If observations of the active deposit are begun shortly after its formation, it is found that the activity, measured by the β rays, is small at first, but increases with the time, reaching a practical maximum about 40 days later. Experiments were made on a platinum plate, which was exposed for 3·75 days in a vessel containing the radium emanation. The observations of the β ray activity began 24 hours after removal. The results are shown in Fig. 94, where the time was measured from the middle of the time of exposure to the emanation. Similar results were obtained for a negatively charged wire exposed to the emanation. The curve, if produced back to the origin, is seen to be very similar to the recovery curves of Ur X, and other active products, and can be expressed by the equation
$$ \frac {I_t} {I₀} = 1 − e^{–λt} $$,
where I₀ is the maximum activity. The activity reaches half its final value in about six days, and the value of λ is equal to ·115 (day)⁻¹. We have shown in section 203 that a rising curve of this character indicates that the β ray activity arises from a product which is supplied at a constant rate from a primary source. Before discussing in detail the explanation of these curves, showing the rise with time of the α and β ray activity, further experimental results will be considered.
=232. Effect of temperature on the activity.= A platinum plate, made active in the manner described, was exposed to varying temperatures in an electric furnace, and the activity tested at atmospheric temperature after exposure. Four minutes’ exposure in the furnace, at first at 430° C., and afterwards at 800° C., had little, if any, effect on the activity. After four minutes at about 1000° C. the activity decreased about 20 per cent., and a further exposure of eight minutes at a temperature of about 1050° C. almost completely removed the α ray activity. On the other hand, the β ray activity, when measured immediately after removal, was not altered by the heating, but exposure to a still higher temperature caused it to decrease. These results show that the active matter consists of two kinds. The part which emits β rays is not volatile at 1000° C., but the other part, which emits α rays, is almost completely volatilized at that temperature.
It was found, however, that the β ray activity after heating to about 1000° was not permanent, but decayed according to an exponential law with the time, the activity decreasing to half value in about 4·5 days. From the recovery curve of the β ray activity already considered, it was to be expected that the activity would decay to half value in six days. This difference in the periods is possibly due to an effect of the high temperature in altering the rate of decay of radium E. The period of six days is more probably correct. The results obtained on the rise and decay of the β rays, taken together, show:—
(1) That the product giving β rays is supplied at a constant rate from some parent matter of very slow rate of change.
(2) That this parent matter is volatilized at or below 1000° C., and the β ray product is left behind. Since the parent matter is removed, the product immediately begins to lose its activity at its characteristic rate, viz. the activity falls to half value in about six days.
=233. Separation of the constituents by means of a bismuth plate.= The active matter of slow decay was obtained in solution by introducing dilute sulphuric acid into a glass tube in which the emanation from 30 milligrams of radium bromide had been stored for a month. The solution showed strong activity and gave out both α and β rays, the latter, as in other cases, being present in an unusually large proportion.
When a polished bismuth disk was kept for some hours in the solution, it became strongly active. The active matter deposited on the bismuth gave out α rays, but no trace of β rays. After several bismuth disks had been successively left in the solution, the active matter, which emits α rays, was almost completely removed. This was shown by evaporating down the solution after treatment. The β ray activity remained unchanged, but that of the α rays had been reduced to about 10 per cent. of its original value. Three bismuth disks, made active in this way, were set aside and their activity measured at regular intervals. The activity fell off according to an exponential law with the time during the 200 days since their removal, while that of each fell to half value on an average in about 143 days.
At the same time it was observed that the solution, from which the α ray activity was removed, gradually regained its activity, showing that the active substance which gave out α rays was continuously produced from the matter left behind in the solution.
=234. Explanation of the results.= We have seen that a close examination of the active deposit of slow change has disclosed,
(1) the presence of a β ray product which loses half of its activity in about six days;
(2) the presence of an α ray product, which is deposited on bismuth and is volatilized at 1000° C. This product loses half of its activity in 143 days;
(3) the presence of a parent substance, which produces the β ray product at a constant rate.
This parent product must be transformed very slowly since the β ray product, which arises from it, soon reaches an equilibrium value, which does not change appreciably over a period of more than one year. The experimental evidence points to the conclusion that the parent product does not give rise to β rays, but that the β rays arise entirely from the next product. This parent product cannot give rise to α rays, for we have seen that the initial α ray activity is at first extremely small, but increases steadily with the time for a period of at least eighteen months. Thus the parent product does not give rise to either α or β rays, and must be a “rayless” product.
The first three transition products of the radium emanation, viz. radium A, B and C, have already been analysed, and shown to be consecutive. It thus seems probable that the active deposit of slow change must arise from the successive transformations of the last product radium C. The results already obtained can be completely explained if it is supposed that three transition products, viz. radium D, E and F, are present in the active deposit of slow rate of change. The properties of these products are summarized below.
Radium D is a rayless product of very slow rate of change. It will be shown later that it is half transformed in about 40 years. It is volatile below 1000° C. and is soluble in strong acids.
Radium E is produced from radium D. In breaking up, it emits β (and probably γ) rays but no α rays. It is half transformed in about 6 days and is not so volatile as radium D and F.
Radium F is produced from radium E. It emits only α rays and is half transformed in 143 days. This substance in solution attaches itself to bismuth. It is volatile at about 1000° C.
Apart from their value and interest in showing the stages of transformation of the radium atom, the results of this analysis have an important bearing upon the origin of some of the well-known radio-active substances separated from pitchblende; for it will be shown later that the product radium F is the radio-active substance present in radio-tellurium and probably also in polonium. In addition, there is very strong evidence that the radio-active lead obtained by Hofmann contains the three products radium D, E and F together.
The changes of radium as far as they are at present known, are shown diagrammatically in Fig. 95. It is possible that further investigation will show that the transformation does not end with radium F.
While we have shown that radium D is the parent of E, we have not given any conclusive evidence that E is the parent of F. This evidence is, however, supplied by the following experiment. A platinum plate, made active in the manner already described, was placed in an electric furnace and heated for four minutes at about 1000° C. Most of the products D and F were volatilized, but E was left behind. Since the parent matter D was removed, E at once commenced to lose its β ray activity. At the same time it was observed that the small α ray activity, left behind on the platinum plate, increased rapidly at first and then more slowly, as the activity of E became smaller and smaller. This experiment shows conclusively that E was the parent of F, the α ray product.
=235. Rate of transformation of radium D.= It has been observed experimentally that each of the products of radium, which emit α rays, supplies about an equal proportion of the activity of radium when in radio-active equilibrium. Since, when equilibrium is reached, the same number of particles of each of the successive products must break up per second, this is an expression of the fact that every atom of each product breaks up with the expulsion of an equal number (probably one) of α particles. Now radium D is directly derived from radium C, and, since the rate of change of D is very slow compared with that of C, the number of particles of D initially present must be very nearly equal to the number of particles of radium C which break up during the time that radium D is being formed. Now D does not itself give out rays, but the succeeding product E does. The products D and E are practically in radio-active equilibrium one month after D is set aside, and the variation of the β ray activity of E then serves as a measure of the variation of the parent product D. Suppose that a vessel is filled with a large quantity of radium emanation. After several hours, the product radium C, which emits β rays, reaches a maximum value, and then decreases at the same rate as the emanation loses its activity, i.e. it falls to half value in 3·8 days. If N₁ is the number of β particles expelled from radium C at its maximum value, the total number Q₁ of β particles expelled during the life of the emanation is given approximately by
$$ Q_1 = \int₀^{\infty} N_1 e^{–λ_1 t} dt = \frac {N_1} {λ_1} $$,
where λ₁ is the constant of change of the emanation.
After the emanation has disappeared, and the final products D + E are in radio-active equilibrium, suppose that the number of β particles N₂ expelled per second by radium E is determined. If Q₂ is the total number of particles expelled during the life of D + E, then Q₂ as before is approximately given by Q₂ = N₂/λ₂ where λ₂ is the constant of change of radium D. Now we have seen that if each particle of C and of E gives rise to one β particle, it is to be expected that
Q₁ = Q₂,
or
λ₂ N₂ ---- = ---- . λ₁ N₁
The ratio N₂/N₁ was determined by measuring the activity due to the β rays from C and E in the same testing-vessel. Then, since N₂/N₁ is known, and also the value of λ₁, the value of the constant of change, λ₂, of radium D is obtained. In this way it was calculated that D is half transformed in about 40 years.
In the above calculations it is assumed, as a first approximation, that the β rays from C and E have the same average velocity. This is probably not accurately the case, but the above number certainly serves to fix the order of magnitude of the period of the product D. This calculation is confirmed by observations to be given later on the amount of D and E in old radium.
It may be of interest to mention that the writer calculated the period of radium F by a similar method, before its value was experimentally determined, and found that F should be half transformed in about one year. This is not very different from the experimental value of 143 days found later. In addition, it was assumed in the calculation that the α particles from C and F were projected with the same velocity, and in consequence produced the same amount of ionization. In practice, however, it is found that the α particle of F is absorbed in about half the distance of the α particles of C, and in consequence produces only about half of the ionization of the latter. If this correction were made, the calculated period for half transformation would be six months instead of one year.
A table of the transformation products of radium, together with some of their physical and chemical properties, is given below.
Transformation Time to be Rays Chemical and Products half Physical transformed Properties
Radium 1200 years α rays —
Emanation 3·8 days α rays Chemically inert gas; condenses at −150° C.
Radium A 3 mins. α rays Behaves as (active deposit solid; of rapid deposited on change) the surface of bodies; concentrated on cathode in electric field. Soluble in strong acids; volatile at a white heat. B is more volatile than A or C.
:: B (same) 21 mins. no rays Same
:: C (same) 28 mins. α, β, γ rays Same
:: D (active about 40 no rays Soluble in deposit of slow years strong acids change) and volatized below 1000° C.
:: E (same) 6 days β (and γ) Non-volatile at 1000°C.
:: F (same) 143 days α rays Volatile at 1000° C; deposited from solution on to bismuth plate.
? — — —
=236. Variation of the activity over long periods of time.= We are now in a position to calculate the variation of the α and β ray activity of the active deposit over long periods of time. If it is supposed that the matter initially deposited consists only of D, the amounts P, Q and R of radium D, E and F existing at any later time are given by the equations 3, 4, 5, section 197.
Since, however, the intermediate product E has a much more rapid rate of change than D or F, the equations can be simplified, without much loss of accuracy, by disregarding the change E, and by supposing that D gives out β rays and changes directly into the α ray product F.
Let λ₁, λ₂ be the constants of change D and F respectively. Let n₀ be the number of particles of D present initially. Then using the notation of section 197, the amount P of radium D at any time t is given by
$$ P = n₀ e^{–λ_1 t} $$ .
The amount Q of radium F is given by
$$ Q = \frac {n₀ λ_1} {λ_1 − λ_2} (e^{–λ_2 t} - e^{–λ_1 t}) $$ .
The number of β particles emitted by D + E per second, some months afterwards, is
$$ λ_1 n₀ e^{–λ_1 t} $$,
and the number of α particles emitted by radium F is
$$ \frac {λ_1 λ_2 n₀} {λ_1 − λ_2} (e^{–λ_2 t} − e^{–λ_1 t} ) $$ .
The results are shown graphically in Fig. 96, by the curves EE and FF, in which the ordinates represent the number of β and α particles expelled per second by the products D and F respectively. The complete calculation for three changes shows that the number of β particles soon reaches a practical maximum, and then decays nearly exponentially with the time, falling to half value in 40 years. The number of α particles expelled per second increases for several years, but reaches a maximum after 2·6 years and then diminishes, finally falling off exponentially with the time to half value in 40 years.
The experimental curve of the rise of α ray activity, shown in Fig. 93, as far as it has been determined, lies accurately on this curve, if the maximum is calculated from the above theory. The observed activity after a period of 250 days is marked by the point X on the curve.
=237. Experiments with old radium.= Since the substance radium D is produced from radium at a constant rate, the amount present mixed with the radium will increase with its age. The writer had in his possession a small quantity of impure radium chloride, kindly presented by Professors Elster and Geitel four years before. The amount of radium D present in it was tested in the following way:—The substance was dissolved in water and kept continuously boiling for a period of about six hours. Under these conditions the emanation is removed as rapidly as it is formed, and the β rays from the radium, due to the product radium C, practically disappear. A newly prepared specimen of radium bromide under these conditions retains only a fraction of 1 per cent. of its original β radiation. The old radium, however, showed (immediately after this treatment) an activity measured by the β rays of about 8 per cent. of its original amount. The activity could not be reduced any lower by further boiling or aspiration of air through the solution. This residual β ray activity was due to the product radium E stored up in the radium. The β ray activity due to radium E was thus about 9 per cent. of that due to radium C. Disregarding the differences in the absorption of the β rays, when the activity of the product E in radium reaches a maximum value, the β ray activity due to it should be the same as that due to C. Since the parent product D is half transformed in forty years, the amount present in the radium after four years should be about 7 per cent. of the maximum amount; i.e. it should show a β ray activity of about 7 per cent. of that due to radium C. The observed and calculated values (7 and 9 per cent. respectively) are thus of the same order of magnitude. The amount of β rays from radium E present in pure radium bromide about one year old was about 2 per cent. of the total.
The amount of radium F present in old radium was measured by observations of the activity imparted to a bismuth disk left for several days in the solution, and was found to be of the same order as the theoretical value. Radium F is not deposited to an appreciable extent on the bismuth from a water solution of radium bromide. If, however, a trace of sulphuric acid is added to the solution, the radium F is readily deposited on the bismuth. The addition of sulphuric acid to the radium solution practically effected a separation of radium D, E and F from the radium proper; for the latter was precipitated as sulphate and the products D, E and F remained in solution. After filtering, the solution contained the greater proportion of the products D, E, and F and very little radium.
=238. Variation of the activity of radium with time.= It has been shown that the activity of freshly prepared radium increases at first with the time and practically reaches a maximum value after an interval of about one month. The results already considered show that there is a still further slow increase of activity with the time. This is the case whether the activity is measured by the α or β rays. It will be shown later that radium is probably half transformed in about 1000 years. From this it can readily be calculated that after a lapse of about 200 years the amount of the products radium D, E and F will have reached a maximum value. The same number of atoms of each of the products C and E will then break up per second. If each atom of these products in disintegrating throws off an equal number (probably one) of β particles, the number of β particles thrown off per second will be twice as great as from radium a few months old. The number will increase at first at the rate of about 2 per cent. a year.
Similar considerations apply to the α ray activity. Since, however, there are four other products of radium besides radium itself which expel α particles, the number of α particles emitted per second from old radium will not be more than 25 per cent. greater than the number from radium a few months old. The activity measured by the α rays will thus not increase more than 25 per cent., and probably still less, as the α particles from radium F produce less ionization than the α particles expelled from the other radium products. The activity of radium will consequently rise to a maximum after 200 years and then slowly die away with the time.
=239. Presence of these products in pitchblende.= The products radium D, E and F must be present in pitchblende in amounts proportional to the quantity of radium present, and should be capable of separation from the mineral by suitable chemical methods. The radio-active properties of these substances, if obtained in the pure state, are summarized below.
Radium D when first separated, should give out very little α or β radiation. The β ray activity will rapidly increase, reaching half its maximum value in 6 days. The α ray activity will at first increase nearly proportionately with the time, and will reach a maximum value after an interval of about 3 years. The α and β ray activity, after reaching a maximum, will finally decay, the activity falling to half value in about 40 years. Since radium D is half transformed in 40 years, and radium in 1200 years, the maximum β ray activity of radium D, weight for weight, will be about 300 times that of radium.
The α ray activity, at any time, will be removed by placing a bismuth disk in the solution.
Radium F, after separation, will give out only α rays. Its activity, after separation, will decrease according to an exponential law, falling to half value in 143 days. Since radium in radio-active equilibrium contains four products which emit α rays, the number of α particles expelled per second from radium F will, weight for weight, be about 800 times as numerous as from new radium in radio-active equilibrium. Since the α particles from radium F produce only about half as much ionization as the α particles from the other radium products, the activity of radium F, measured by the electric method, will be about 400 times that of radium.
=240. Origin of radio-tellurium and polonium.= It is now necessary to consider whether these products of radium have been previously separated from pitchblende, and known by other names.
We shall first consider the α ray product, radium F. The radio-tellurium of Marckwald and the polonium of Mme Curie both resemble radium F in giving out only α rays, and in being deposited on a bismuth disk from a solution. If the active constituent present in radio-tellurium is the same as radium F, its activity should decay at the same rate as the latter. The writer[320] has carefully compared the rates of decay of the activity of radium F and of the radio-tellurium of Marckwald and found them to be the same within the limits of experimental error. Both lose half of their activity in about 143 days[321]. A similar value of the rate of decay of radio-tellurium has been obtained by Meyer and Schweidler[322].
The experiments on radio-tellurium were made upon the active bismuth plates supplied by Dr Sthamer of Hamburg, which were prepared under Marckwald’s directions.
An additional proof[323] of the identity of these two products was obtained by comparing the absorption of the α rays by aluminium foil. The α rays from different products are projected with different velocities, and, in consequence, are unequally absorbed by matter. The absorption of the rays from the two products by aluminium foil agreed very closely, indicating the probable identity of the substances from which they were emitted.
There can thus be no doubt that the active constituent present in the radio-tellurium of Marckwald is identical with the product radium F. This is a very interesting result, and shows how the close examination of the successive transformations of the radio-active bodies may throw light on the origin of the various substances found in pitchblende.
We have already seen (section 21) that Marckwald, by special chemical methods, was able to obtain a few milligrams of very active substance by working over 2 tons of pitchblende. We have already seen (section 239) that this substance, if obtained in the pure state, should be about 400 times as active as radium. Comparative measurements of the activity of this substance with radium will thus indicate the amount of impurity that is present with the former. This method should be of value in purifying radium F for the purpose of determining its spectrum, which has not yet been observed.
=241. Polonium.= Since the separation of the active substance by Marckwald, called by him radio-tellurium, there has been some discussion as to whether the active constituent is the same as that present in the polonium of Mme Curie. Both of these substances have similar radio-active and chemical properties, but the main objection to the view that the active constituents were identical has rested on an early statement of Marckwald that the activity of one of his very active preparations did not decay appreciably in the course of six months. This objection is now removed, for we have seen that the activity of radio-tellurium does decay fairly rapidly. It was early recognised that the activity of the polonium, separated from pitchblende by the methods of Mme Curie, was not permanent, but decayed with the time. Observations on the rate of decay have not been very precise, but Mme Curie states that some of her preparations lost half of their activity in about six months but in others the rate of decay was somewhat smaller. It is possible that the initial differences observed in the rates of decay of different specimens of polonium may be due to the presence of some radium D with the polonium. The polonium in my possession lost its activity fairly rapidly, and was reduced to a small portion of its value in the course of about four years. Rough observations of its activity, made from time to time, showed that its activity diminished to half value in about six months. If it is identical with radio-tellurium, the activity should decay to half value in 143 days, and I think there is little doubt that more accurate measurement will prove this to be the case.
While the proof of the identity of the active constituent in polonium is not so definite as for radio-tellurium, I think there can be no reasonable doubt that these substances both contain the same active substance, which is the seventh transformation product of radium. Marckwald has noticed some chemical differences in the behaviour of polonium and radio-tellurium, but little weight can be attached to such observations, for it must be remembered that the active constituent in both cases is present in minute quantity in the material under examination, and that the apparent chemical properties of the active substance are much influenced by the presence of impurities. The most important and trustworthy test rests upon the identity of the radiations and the period of decay.
=241 A. Origin of radio-active lead.= Some experiments will now be discussed which show that the radio-lead first separated from pitchblende by Hofmann (section 22) contains the products radium D, E and F. Hofmann has observed that the activity of this substance did not appreciably decay in the course of several years. In some recent experiments, Hofmann, Gonder and Wölfl[324] have made a close chemical examination of the radio-active lead, and have shown the presence of two radio-active constituents, which are probably identical with the products radium E and F. The radio-active measurements were unfortunately not very precise, and the periods of change of the separated products have not been examined very closely.
Experiments were made on the effect of adding substances to a solution of radio-lead, and then removing them by precipitation. Small quantities of iridium, rhodium, palladium, and platinum, in the form of chlorides, were left in the solution for three weeks, and then precipitated by formalin or hydroxylamine. All of these substances were found to give out both α and β rays, the activity being greatest for rhodium and least for platinum. A large proportion of the β ray activity disappeared in the course of six weeks, and of the α ray activity in one year. It is probable that the two products radium E and F were in part removed with the metals from the radio-lead. We have seen that radium E gives out β rays and loses half of its activity in about six days, while radium F gives out only α rays and its activity falls to half value in 143 days. This conclusion is further confirmed by experiments on the effect of heat on the activity of these substances. By heating to a full red heat, the α ray activity was lost in a few seconds. This is in agreement with the results (section 232) where we have seen that radium F is volatilized at about 1000° C. and radium E is left behind.
Salts of gold, silver and mercury added to the radio-lead were found to show only α ray activity on removal. This is in accordance with the view that radium F alone is removed with these substances. Bismuth salts on the other hand showed initially α and β ray activity, but the latter rapidly died away. The presence of β rays in freshly prepared polonium was early observed by Mme Curie. The α and β ray activity of the radio-lead is much reduced by the precipitation of bismuth added to the solution. The α and β ray activity of the radio-lead, however, recovers itself again. This result is exactly what is to be expected if radio-lead contains radium D, E and F. Radium E and F are removed with the bismuth, but the parent substance, radium D, is left behind, and, in consequence, a fresh supply of radium E and F is produced.
While further experiments are required to settle definitely whether the products separated from radio-lead are identical with radium E and F, there can be little doubt that such is the case. This conclusion is strengthened by some experiments which I have made on a specimen of radio-lead, which was kindly forwarded to me by Mr Boltwood of New Haven. This active lead gave out α and β rays, the latter being in unusually large proportion. The active lead was four months old when first tested. The β ray activity in the following six months has remained sensibly constant, but the α ray activity has steadily increased. These results are to be expected if the radio-lead contains radium D. Radium E will reach a practical maximum about 40 days after separation of the product radium D with the lead. The α ray activity due to radium F should increase to a maximum in about 2·6 years (see section 236).
Further experiments are required to settle whether the lead immediately after separation from pitchblende contains only radium D, or whether radium E also appears with it. It seems likely, however, that the bismuth, which is initially present in solution at the time of separation of the lead, will retain both radium E and F, and that the presence of these products in radio-lead is due to their production, after separation, by the parent substance, radium D.
It would be of scientific value to separate radium D from pitchblende and obtain it in the pure state, for, a month after removal, the β ray activity from it would be about 300 times as great as from an equal weight of radium. By placing a bismuth plate in a solution of this substance, radium F (polonium) should be separated, and, provided a sufficient interval is allowed to elapse, a fresh supply of radium F can at any time be obtained.
The rate of transformation of radium D (half transformed in 40 years) is sufficiently slow not to interfere seriously with its utility in most experiments.
The results of the comparison of the products of radium with those contained in polonium, radio-tellurium and radio-lead are summarized below.
Radium D = product in new radio-lead, no rays. Half transformed in 40 years.
Radium E gives out β rays, separated with bismuth, iridium and platinum. Half transformed in 6 days.
Radium F = product in polonium and radio-tellurium. Gives out only α rays. Half transformed in 143 days.
=242. Temporary activity of inactive matter separated from radio-active substances.= We have seen in the last section that the platinum metals and bismuth acquire temporary activity by their admixture with a solution of radio-lead, and that these effects are very satisfactorily explained on the view that some of the products of change of radio-lead are removed with the inactive substances. Very similar effects have been observed by Pegram and von Lerch (section 186), when inactive substances were added to solutions of thorium and of the active deposit of thorium. These results, too, are almost certainly due to the removal of one or more of the products of thorium with the inactive matter. Examples of this character may readily be multiplied, and some of the more interesting and important of these will be briefly discussed later.
There have been two general points of view regarding the character of this activity which is temporarily acquired by inactive matter. Some people have supposed that the inactive molecules of the substance, mixed with the solution, acquire by “radio-active induction” temporary activity, the underlying idea being that the close admixture of an inactive and an active substance has communicated the property of radiating to some of the molecules of the former. According to the disintegration theory of radio-activity, on the other hand, the temporary activity of originally inactive matter is not due to any alteration of the inactive substance itself, but to an admixture with it of one or more of the numerous radio-active products. The idea of “radio-active induction” has no definite experimental evidence in support of it, while there is much indirect evidence against it.
We shall now consider how these facts are interpreted according to the disintegration theory. In a specimen of old radium, for example, there are present, besides radium itself, the seven successive products which arise from it. Each of these differs in chemical and physical properties from the others. If now, for example, a bismuth rod is introduced into the solution, one or more of these products are deposited on the bismuth. This action is most probably electrolytic in nature, and will depend upon the electro-chemical behaviour of the bismuth compared with that of the products in solution. An electro-negative substance will tend to remove the product or products which are strongly electro-positive. This point of view serves to explain why different metals are made active to different degrees, depending upon their position in the electro-chemical series.
It seems probable that the activity communicated to inactive matter by precipitation from an active solution occurs only during the precipitation. The correctness of this view could readily be tested by observing whether the time that the inactive substance is present in solution has any effect on the magnitude of the activity imparted to it.
When it is remembered that in pitchblende there are present the radio-elements uranium, thorium, radium and actinium and their numerous family of products, it is not surprising that many of the inactive substances separated from it may show very considerable activity due to the mixture of products which may be removed with them. In carrying out experiments on the separation of radium from pitchblende, M. and Mme Curie observed that the separation of the active substance is fairly complete if the stage of purification is not far advanced. Copper, antimony and arsenic can be separated only slightly active, but other substances like lead and iron always show activity. When the stage of precipitation is more advanced, every substance separated from the active solution shows activity.
One of the earliest observations in this direction was made by Debierne, who found that barium could be made active by solution with actinium. The active barium removed from the actinium still preserved its activity after chemical treatment, and, in this way, barium chloride was obtained whose activity was 6000 times that of uranium. Although the activity of the barium chloride could be concentrated in the same way as the activity of radiferous barium chloride, it did not show any of the spectroscopic lines of radium, and could not have been due to the admixture of that element with the barium. The activity of the barium was not permanent, and Debierne states that the activity fell to about one-third of its value in three months. It seems probable that the precipitated barium carried down with it the product actinium X, and also some of the actinium itself, and that the decay observed was due to the transformation of actinium X. It is interesting to note that barium is capable of removing a large number of products of the different radio-elements. This effect is probably connected with its position in the electro-chemical series, for barium is highly electro-positive.
Giesel showed in 1900 that bismuth could be made active by placing it in a radium solution, and considered that polonium was in reality bismuth made active by the process of induction. In later experiments, he found that the bismuth plate gave out only α rays, and that the activity of the bismuth could not be ascribed to radium, since no β rays were present. We have seen that this activity of the bismuth is due to the product radium F deposited on its surface.
Mme Curie also found that bismuth was made active by solution with a radium compound, and succeeded in fractionating the above bismuth in the same way as polonium. In this way bismuth was obtained 2000 times as active as uranium, but the activity, like that of polonium separated from pitchblende, decreased with the time. In the light of the experiments on the transformation products of radium, it is seen that these early experiments of Mme Curie add additional confirmation to the view that the product (radium F) separated from radium itself is identical with the polonium obtained directly from pitchblende.
Footnote 314:
Rutherford and Soddy, Phil. Mag. April, 1903.
Footnote 315:
Rutherford, Phil. Trans. A. p. 169, 1904. Curie and Danne, C. R. p. 748, 1904.
Footnote 316:
P. Curie and Danne, Comptes Rendus, 138, p. 748, 1904.
Footnote 317:
Miss Gates, Phys. Rev. p. 300, 1903.
Footnote 318:
Miss Brooks, Nature, July 21, 1904.
Footnote 319:
Rutherford, Phil. Mag. Nov. 1904. Nature, p. 341, Feb. 9, 1905.
Footnote 320:
Rutherford, Nature, p. 341, Feb. 9, 1905.
Footnote 321:
Marckwald (Ber. d. D. Chem. Ges. p. 591, 1905) has recently found that the activity of his radio-tellurium falls to half value in 139 days.
Footnote 322:
Meyer and Schweidler, Wien Ber. Dec. 1, 1904.
Footnote 323:
Rutherford, Phil. Trans. A. p. 169, 1904.
Footnote 324:
Hofmann, Gonder and Wölfl, Annal. d. Phys. 15, p. 615, 1904.
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[325] 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[326] 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 ⅙ 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 ⅙ 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[327] 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[328] 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.
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[329]. 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.
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.
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
$$ \frac {Q_t} {Q_{max}} = e^{–λt} $$
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
$$ \frac {Q_t} {Q_{max}} = \cdot25 + \cdot75 (1 − e^{–λt}) $$,
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.
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.
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 31 „ „ rays
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[330], 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[331] 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 × 10¹¹ α particles per second. The corresponding number for 1 gram of radium (Ra = 225) is 2·5 × 10¹¹. 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 × 10⁶ 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
$$ \int₀^{\infty} 75 e^{–λt} dt = \frac {75} {λ} $$
= 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 10⁷ 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 × 10⁶ 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 10⁹ 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[332]. 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-constantan 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 × 10¹⁹ molecules in one cubic centimetre of hydrogen, it can easily be calculated that there are about 3·6 × 10²¹ 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 × 10¹⁶ ergs or 8 × 10⁸ 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 × 10⁹ 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 10¹¹ 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 × 10⁶. 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 × 10¹¹. 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 × 10¹⁰ and 7·0 × 10¹⁰ 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 × 10¹⁰.
The total number of α particles expelled from one gram of radium at its minimum activity has been shown to be 6·2 × 10¹⁰ (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.
Footnote 325:
Phil. Trans. A. p. 25, 1901.
Footnote 326:
P. Curie and Laborde, C. R. 136, p. 673, 1903.
Footnote 327:
Runge and Precht, Sitz. Ak. Wiss. Berlin, No. 38, 1903.
Footnote 328:
P. Curie, Société de Physique, 1903.
Footnote 329:
Rutherford and Barnes, Nature, Oct. 29, 1903. Phil. Mag. Feb. 1904.
Footnote 330:
Paschen, Phys. Zeit. Sept. 15, 1904.
Footnote 331:
Rutherford and Barnes, Nature, Dec. 18, 1904; Phil. Mag. May, 1905.
Footnote 332:
Pegram, Science, May 27, 1904.