CHAPTER 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