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Relative Activity of Radium and Uranium
J. H. L. Johnstone and B. B. Boltwood, On the Relative Activity of Radium and Uranium. Phil. Mag. 40, p. 52, (1920).
According to Geiger’s law, the number of ions formed in a gas by $\alpha$-rays of different ranges is expressed as follows:
\[ J = k R^{2/3}, \]
where $R$ is the magnitude of the range of the $\alpha$-particle, and $k$ is a constant for all $\alpha$-rays.
If we have several members of one radioactive series emitting $\alpha$-particles, then each of them, in the case of radioactive equilibrium, emits an equal number of $\alpha$-particles in a given interval of time. Therefore the ratio of the activities (with respect to $\alpha$-rays) of two radioelements in a state of equilibrium is equal to the ratio of the ranges of their $\alpha$-rays raised to the power $2/3$.
If, in the uranium series, the successive disintegration of the elements proceeds without branching from uranium to radium, then the ratio of the activities of uranium to radium is calculated as follows. Uranium consists of a mixture of two isotopes, $U_I$ and $U_{II}$, giving $\alpha$-rays with ranges, respectively, of 2.37 and 2.75 cm. The range of the $\alpha$-rays of $Ra$ is equal to 3.13 cm. Therefore the ratio of the activities $U : Ra$ should be equal to
\[ \left(2.37^{2/3} + 2.75^{2/3}\right) : 3.13^{2/3} = 1.00 : 0.57 \]
If, however, branching of the main series occurs between uranium and radium, the ratio of the activities $Ra/U$ must be less than that calculated from Geiger’s formula.
Thus, an exact determination of the relative activity of radium and uranium is very important for establishing the correct scheme of transformations in the uranium series. The work under review had as its aim to verify the numbers found by Boltwood in 1908 expressing the ratio of the activities $Ra/U$ in equilibrium, as well as the ratio of the activities of uranium alone and uranium in equilibrium with all subsequent products.
The determination of the relative activity of uranium was carried out by the usual method using $\alpha$-rays. The starting material was uraninite.
The preparations compared were taken in very thin layers, in order to avoid absorption of $\alpha$-rays in the active layer itself. Corrections were introduced for the presence of thorium and for the loss of emanation.
The value obtained for the ratio of the activity of uranium in equilibrium with all products of disintegration to the activity of uranium alone, 4.73, is very close to the value 4.69 previously found by Boltwood1.
The relative activity of radium and uranium was determined in the same mineral. Radium was precipitated from the solution in the form of the sulphate and compared with uranium. The amount of radium was determined by emanation. All the corrections necessary in measurements of this kind were introduced very carefully. The resulting ratio of the activity of radium to uranium, 0.488, is likewise in satisfactory agreement with the value 0.45 found by Boltwood.
The experimentally obtained ratio of the activity of \(Ra\) to \(U\), 0.49, differs considerably from the value 0.57 calculated by Geiger’s formula. It is natural to attempt to explain the discrepancy by a branching of the uranium series, giving rise to the actinium series.
If the activity of uranium \((U_I + U_{II})\) is taken as unity and the relative activity of all members of the uranium series emitting \(\alpha\)-rays is calculated, beginning with ionium, on the assumption that beyond ionium there is no branching of the series, and if in this calculation one proceeds from the experimentally found value 0.49 for \(Ra\), then the sum obtained is 4.47. Comparing this with the experimentally found ratio of the activity of uranium in equilibrium with all its decay products to the activity of pure uranium, 4.73, we find a difference of 0.26.
This number comes exceedingly close to the value 0.28 found by Boltwood for the relative activity of the actinium series. The authors see in this a confirmation of the ratio of actinium to uranium found by Boltwood and calculate that the formation of the actinium series accounts for 8% of the disintegrating atoms of one of the members of the uranium series.
However, if one examines more carefully the transformation schemes of the uranium series proposed in recent times, a number of disagreements with experiment is obtained. The authors consider the two most probable schemes proposed by Soddy and Cranston\(^1\).
\[ \begin{array}{l} \text{(I)}\quad U_I\ (VI) \ \xrightarrow{\alpha}\ \begin{array}{c} 92\% \end{array} \ UX_1\ (IV) \ \xrightarrow{\beta}\ UX_2\ (V) \ \xrightarrow{\beta}\ U_{II}\ (VI) \ \xrightarrow{\alpha}\ Io \ \xrightarrow{\alpha}\ Ra \ \longrightarrow \\[1.0em] \hspace{5.8em} \begin{array}{c} 8\% \end{array} \searrow\ UY\ (IV) \ \xrightarrow{\beta}\ UZ\ (V) \ \xrightarrow{\alpha}\ Ac\ (III) \ \longrightarrow \end{array} \]
\[ \begin{array}{l} \text{(II)}\quad U_I\ (VI) \ \xrightarrow{\alpha}\ UX_1\ (IV) \ \xrightarrow{\beta}\ UX_2\ (V) \ \xrightarrow{\beta}\ U_{II}\ (VI) \ \begin{cases} \xrightarrow[\ 92\%\ ]{\alpha}\ Io\ (IV)\ \xrightarrow{\alpha}\ Ra\ (II)\ \longrightarrow,\\[0.8em] \xrightarrow[\ 8\%\ ]{\alpha}\ UY\ (VI)\ \xrightarrow{\beta}\ UZ\ (V)\ \xrightarrow{\alpha}\ Ac\ (III)\ \longrightarrow. \end{cases} \end{array} \]
If the branching into actinium is taken into account and the ratio of the activity of \(Ra\) to uranium is calculated by Geiger’s formula, then scheme \((I)\) gives 0.55, and scheme \((II)\) 0.53. The deviations from the experimentally found number 0.49 lie outside the limits of possible errors of determination. Thus both proposed schemes do not satisfy the experimental data.
To explain the disagreement the authors put forward two possible assumptions:
- The possible existence of a third isotope of uranium, emitting \(\alpha\)-rays
\(^1\) Proc. Roy. Soc. A. XCV p. 384, 1918.
and that of actinium, which is mixed into the side branch. However, the authors themselves consider this assumption to be rather improbable.
- It may be that the value of the range of the $\alpha$-particles of uranium is known to us incorrectly.
The works of Hahn and Meitner1 on the origin of actinium apparently were not known to the authors of the article under review. If the protactinium discovered by Hahn and Meitner is introduced into Boltwood’s calculations, then for the percentage of branching one obtains $6.5\%$ instead of $8\%$. Meanwhile Hahn and Meitner found that only $3\%$ goes into the side branch. Thus a considerable discrepancy is obtained. If the more precise value of Hahn and Meitner is accepted, an even greater disagreement is obtained between the calculated and the experimental activity of radium, namely $0.56$ and $0.49$.
Thus the question of the decay of uranium cannot be considered finally solved and requires further investigation.
V. Baranov.