Magneto-Optical Method and Isotopes of Radioactive Elements

V. P. Rusakov, Smolensk

Introduction

The magneto-optical phenomenon, discovered by Faraday, is known to consist in the fact that polarized light, passing through isotropic bodies, undergoes rotation of the plane of polarization if these bodies are placed in a strong magnetic field and if the direction of the light is parallel to the direction of the magnetic lines of force; moreover, the direction of rotation of the plane of polarization of the light depends on whether the rays go from the north pole of the magnet to the south pole or in the opposite direction.^1 The angle \(\alpha\) through which the plane of polarization rotates is proportional to the magnetic-field strength \(H\), the path length \(l\) traversed by the ray inside the body, and is expressed by the formula:

\[ \alpha = VHl, \tag{1} \]

where the coefficient of proportionality \(V\) has received the name of the Verdet constant and denotes the angle through which the plane of polarization rotates when the ray passes inside the body a distance equal to \(1\) cm and when the field strength \(H\) is equal to 1 gauss. Its order of magnitude is several angular seconds.

Experiments carried out by Villari^1 showed that between the moment when the field arises and the moment when the rotation of the plane of polarization reaches its greatest value, although a small but quite definite time elapses. The experiments consisted of the following. A piece of heavy glass was rotated between the poles of a strong electromagnet; at the same time a decrease in the rotation of the plane of polarization was observed when the rotational speed of the piece of glass exceeded 100 rev/sec, and became practically equal to zero when it reached 200 revolutions. The time required for the rotation of the plane of polarization, after the creation of the magnetic field, to reach its greatest value received the name of the lag moment, or retardation moment. The order of magnitude of the lag moment is approximately \(10^{-8}\) sec. This, apparently, also explains why the subsequent experiments set up by Blondlot^2 and Lodge^3 to establish the lag moment led to negative results: the duration of the light flash was too short for it to be possible to take it accurately into account with the experimental technique that existed in their time.

Blondlot’s experiments consisted of the following. A Leyden jar was discharged through a spiral of insulated wire surrounding a tube filled with carbon disulfide (\(\mathrm{CS_2}\)). It was found that the plane of polarization rotated with each impulse of the oscillatory discharge, vibrating back and forth at a speed of approximately 70,000 times per second. The upper half of a narrow slit was illuminated by the light of the discharge spark, which fell on a rotating mirror. The lower part of the slit was illuminated by light passing through the tube with carbon disulfide and falling on the same mirror. The illuminated slit was seen in the mirror as a stretched, jagged band, and no discontinuities between the two halves were found. From this it was concluded that the Faraday effect is practically instantaneous.

MAGNETO-OPTICAL METHOD

DESCRIPTION OF THE APPARATUS

Very recently, the Faraday phenomenon and the basic idea of Blondlot’s apparatus were applied by F. Allison⁴ and his collaborators⁵ as a very precise method of chemical analysis, suitable for detecting isotopes and surpassing in its results the most sensitive of the methods known to us, the Aston mass spectrograph.⁷ Later, some of F. Allison’s experiments were repeated by F. Slack and V. Brazil⁶ and led, in the main, to the same results.

The experimental apparatus was as follows (Fig. 1). Between the crossed Nicol prisms \(N_1\) and \(N_2\) of a Lippich polarimeter there was placed a glass tube \(A\), about \(11.2\ \mathrm{cm}\) long and \(2.5\ \mathrm{cm}\) in diameter, to the ends of which transparent glass plates were fused. The tube was filled with the solution under investigation and inserted inside a coil \(L\), \(12\ \mathrm{cm}\) long and \(4.5\ \mathrm{cm}\) in diameter, consisting of 59 turns of insulated copper wire. The self-inductance of the coil was \(0.045\ \mathrm{mH}\). In parallel with coil \(L\) there was connected exactly the same auxiliary coil \(L'\). In the diagram \(T\) denotes a resonant spark transformer, rated at \(1\ \mathrm{kVA}\) and giving a maximum voltage of \(25{,}000\ \mathrm{V}\) in the secondary winding at \(110\ \mathrm{V}\) in the primary winding. The high-voltage current was rectified by means of a kenotron and charged the capacitor \(C\) every sixtieth of a second. The latter consisted of 20 glass plates, \(0.3\ \mathrm{cm}\) thick, covered with thin foil over an area of \(25\ \mathrm{cm}^2\), and gave a total capacitance of \(0.022\ \mathrm{mF}\). The capacitance could be varied by disconnecting capacitor plates.

Fig. 1.

The capacitor, on reaching a definite potential, discharged by means of the spark gap \(S\), which was arranged horizontally and had 1/3-inch magnesium electrodes standing \(0.25\) to \(0.30\ \mathrm{cm}\) from one another. The discharge current passed through the coil \(L\) or \(L'\), the ohmic resistance \(R\), and the inductive resistance \(L''\). The resistance \(R\) consisted of two wires stretched in parallel, which were placed above the apparatus. The resistance was varied by means of a contact that slid along these wires. The wires were made of chromel, having a resistance of \(6.85\ \Omega/\mathrm{m}\), and had a total length of about \(16\ \mathrm{m}\), although somewhat longer wires were sometimes also used. Coil \(L''\) had 325 turns of insulated copper wire and represented a self-inductance of \(0.66\ \mathrm{mH}\). There were several uninsulated points on it, thanks to which its self-inductance could be varied. Light from a spark passed through filter \(F\), consisting of two plates of Czech glass \((BG_4 + GG_3)\), transmitting chiefly the magnesium spark lines \(\lambda = 4481\ \text{Å}\) and, in small amount, the lines \(\lambda = 4703\), \(\lambda = 4391\), and \(\lambda = 3835\ \text{Å}\), and fell on the Lippich half-shadow polarimeter. Then the light passed through tube \(A\) and entered analyzer \(N_2\). During the time when the current passed through coil \(L\), the liquid contained in tube \(A\), under the action of the magnetic field, rotated the plane of polarization of the light beam; the magnitude of the rotation was measured by turning analyzer \(N_2\), and the reading of the rotation could be made with an accuracy of \(0.01^\circ\). The auxiliary coil \(L'\) was usually not used and was employed only in order to divert the current when coil \(L\) was switched off for setting up

of the zero position. Both the coil \(L''\) and the resistance \(R\) were usually switched in and used only when it was desired to change either the self-inductance or the ohmic resistance of the oscillatory circuit.

Sometimes the arrangement was modified. In this case the active coil \(L\) consisted of two completely identical parts \(L_1\) and \(L_2\), which were switched in either each separately, or in series, or in parallel with each other; in the latter two cases the switching was done so that the rotating fields either added or were opposite. With this arrangement two resistances \(R_1\) and \(R_2\) were used, connected in series with each of the coils. In Fig. 2 the circuit of the parallel connection of the coils \(L_1\) and \(L_2\) is given. The rest of the arrangement was the same as that shown in Fig. 1.

Before carrying out the experiments, the zero position of the analyzer was established, for which purpose a current was passed through the auxiliary coil \(L'\). Then the same pulsed current, arising as a result of the discharge of the capacitor, was passed through the coil \(L\), inside which a magnetic field was produced, acting on the substance placed in tube \(A\). The plane of polarization of the light rotated in accordance with the field, and an illumination of both fields of the polarimeter was observed, but the brightness of one of them was more sharply expressed. The position of the analyzer was selected so that both fields were illuminated equally, which was taken as the magnitude of the rotation. Such observations were made at different current strengths. The length of the spark gap and the primary voltage of the transformer were kept approximately constant; the latter was about 60 volts and was regulated by a rheostat.

Fig. 2.

The mechanism of the process causing the rotation may be explained as follows. The current in the circuit, owing to the self-inductance \(L\) and the ohmic resistance \(R\) introduced into it, is rapidly damped, as can be seen from the equation for a damped sinusoidal oscillation:

\[ i = \frac{E e^{-\frac{Rt}{2L}}} {L\left(\frac{1}{LC}-\frac{R^2}{4L^2}\right)^{1/2}} \sin \left[ \left(\frac{1}{LC}-\frac{R^2}{4L^2}\right)^{1/2} t \right], \]

where \(i\) is the current at some instant of time, and \(E\) is the initial voltage at which the capacitor was discharged.

Under the conditions of the experiment, the oscillations died out after several cycles, and observations showed that the number of cycles had little influence on the magnitude of the observed rotation. The latter was proportional to the difference between the first maximum of the current curve (positive) and the second maximum (negative). Suppose that the first cycle of the wave causes rotation in the clockwise direction, which, in turn, causes the greatest brightness on the right side of the field of the polarimeter, proportional to the first maximum of the current. The second maximum causes rotation opposite to clockwise, as a result of which there will be illumination of the left side of the field. But since the second peak is smaller than the first, the brightness of the left side of the field will not be as great as that of the right. Such cycles are repeated sixty times per second; the eye will not notice any flickering of light, and each field will appear uniformly illuminated. Rotating the analyzer until the brightness of the two fields becomes identical gives the magnitude of the rotation of the plane of polarization. The assumption that the magnitude of the rotation is proportional to the difference of the maxima was checked as follows. The maxima curves of the positive and negative parts of the current wave were calculated and plotted for various resistances \(R\), which are shown in Fig. 3 by dotted curves, respectively. Curve 3 represents the difference of the ordinates of the first two curves.

The experimental results are plotted as points, which agree very well with the theoretical curve. Since the greatest magnitude of the magnetic field produced in the coil can be expressed by the equation

\[ H = 0.4\pi ni, \tag{3} \]

where \(n\) is the number of turns of wire per centimeter of the coil, and \(i\) is the maximum current in amperes, the angle of rotation \(\alpha\), according to equation (1), will be expressed as follows:

\[ \alpha = 0.4\pi niV. \tag{4} \]

It should be noted that Sjak’s apparatus differed from Ellison’s only in that the former, instead of Lippich’s shadow polarimeter, used simply crossed Nicols.

3. Application of the Method to the Study of Isotopes

In studying the phenomenon of rotation of the plane of polarization, Ellison \(^{4}\) found that every chemical compound produces a minimum of light at positions characteristic of the given compound, and the position of the minimum represents a certain function of the chemical equivalent of the metallic element of the inorganic compound. Such a minimum remains noticeable as long as the concentration of the dissolved substance does not become less than \(10^{-10}\). At the same time it was discovered that every inorganic compound is characterized by either one or two or more minima, and the number of minima, with some exceptions, was the same as the number of known isotopes of the metallic element of the compound. Taking the concentration of the solution so weak that no minimum was noticeable, and gradually increasing it, it could be observed that the appearance of the first minimum is associated with the most abundant isotope. With a further increase in concentration, the next minimum “appeared,” associated with the isotope occupying, in its abundance in the given element, second place. In the same order the remaining minima appeared. This conclusion proved correct for every metal taken in the form of chloride, sulfate, nitrate, or hydroxide. In those cases where this was possible, the results were compared with Aston’s observations by means of the mass spectrograph and in all cases proved to agree.

Fig. 3.

Already in the first works \(^{6}\), isotopes were discovered for a whole series of elements whose existence had not previously been known. Thus, for gold 2 isotopes were found, for palladium—3, for rhodium—1, for ruthenium—2, for tantalum—3, for thallium—2, for thorium—3. Here it was also noted that the moment of cessation changes in direct dependence on the atomic weight of the isotope, i.e., with an increase in atomic weight the moment of cessation also increases.

The method proved to be very convenient and an extraordinarily sensitive means of physico-chemical analysis, and therefore a group of persons was organized, under Ellison’s direction, to study the isotopes of radioactive elements, a complex and rather confused question.

Each group worked on the isotopes of individual substances. We shall now proceed to a brief survey of the results of these works.

4. Isotopes of Radioactive Elements

1. Isotopes of lead. Lead was studied by E. Bishop, M. Laurens, and Dollens[^9]. To determine the number of lead isotopes, four different chemical compounds of this element were investigated: PbCl₂, Pb(NO₃)₂, PbSO₄, and Pb₃(PO₄)₂. Solutions of each compound were prepared, at least, from two different sources independent of one another. The investigation was carried out with different apparatus setups and by at least three different observers, working in different laboratories and even institutions. If the results of individual observations did not coincide, a new solution was prepared by adding to the previous one the necessary anion, either in the form of a nitrate solution or in the form of a chloride solution, the cation of which had been studied. For each of the compounds, sixteen isotopes were found, whose atomic weights varied only slightly from 201 to 216.

In 1927 Aston determined the main isotopes of lead, and in 1929 the isotopes of lead of radioactive origin, with which Piggot supplied him[^10]. His work showed that the accepted atomic weight of lead, 207.2, is the statistical mean of at least three isotopes, and that one of these principal isotopes has mass 207 and is, in all probability, the final product of the actinium series. In addition, he showed that lead of radioactive origin has an isotope composition different from ordinary lead. Whereas the latter consists, in order of abundance, of the isotopes 208, 206, 207, in lead of radioactive origin the order is 206, 207, 208. This made it necessary to study lead specimens that had been developed from geological and geographical origins and that were entirely free from possible contamination by ordinary lead.

Uranium and the leads associated with it were separated: 1) from uranium ore of Upper Katanga in the Belgian Congo, 2) from Canadian pitchblende ore taken near Great Bear Lake, 3) from Swedish coals (Kolm). The probable order of abundance of the lead isotopes, on the basis of the results obtained, is as follows:

Ordinary lead 208, 206, 207, 205, 212, 210, 204, 202, 203, 211, 201, 209, 216, 215, 214, 213.

Uranium salt 206, 210, 202, 214, 207, 208, 215, 203, 205, 204, 209, 211, 212, 213, 216, 201.

Thorium salt 208, 216, 204, 212, 206, 207, 202, 205, 214, 211, 209, 210, 203, 213, 215, 201.

At the beginning of the experiment it was expected that only the lead isotope Pb²⁰⁶ would be found in uranium salts, and Pb²⁰⁸ in thorium salts. As is evident from the results presented, all the salts contain the entire sixteen isotopes. These experiments are partly confirmed by the recent work of Aston[^11], who discovered the following lead isotopes—208, 206, 207, 204, 209, 210, 203, 205—and by the work of Schuler and Jones[^12], who spectroscopically confirmed the existence of Pb²⁰⁴, Pb²⁰⁸, and Pb²⁰⁵. It should be noted that leads of different origin have a comparatively different abundance of their isotopes, but it does not appear possible to dwell on this question in greater detail within the scope of this place.

2. Isotopes of bismuth. The isotopes of bismuth were studied by F. Ellison and E. Bishop[^13] by the same method that was described at the beginning and that was used in the study of the isotopes of lead. Three different compounds of bismuth were investigated—chloride, sulfate, and phosphate. Fourteen isotopes were found for each compound, the probable atomic masses of which, in order of abundance, are as follows: 211, 210, 209, 212, 215, 214, 213, 216, 207, 205, 206, 208, 219, 217.

The bismuth solution that was used in each individual case was tested for uranium; the presence of the latter was found to be approximately \(10^{-8}\) parts, which accounts for the presence of heavy short-lived isotopes.

3. Isotopes of radium. The isotopes of radium were studied by E. Bishop and S. Dollens[^14]. This question was successfully resolved thanks to C. Piggot, who, for the experiments undertaken, separated from a standard solution of radium the necessary—

...able quantity of this element and placed it at the disposal of the investigators. The solution was diluted to a concentration of \(10^{-11}\) g of radium per 1 g of water, and the desired compound was obtained by adding traces of hydrochloric acid, sodium sulfate, and sodium ammonium phosphate. In the polarimeter four minima were observed for each radium compound, which led to the conclusion that there are four isotopes of this element, with atomic weights, in order of abundance, 226, 228, 230, 232. Since the chemically found atomic weight of radium is equal to 225.97, the indicated contradiction is apparently explained by the fact that isotopes with atomic weights heavier than 226 probably have a short lifetime and decay during the time required for determining their atomic weight chemically.

1. Isotopes of uranium, thorium, and thallium. This question was studied by R. Goslin and F. Allison^[15]. Uranium was isolated from the same samples as lead, and each of the elements was investigated in at least three different compounds. The approximate order of abundance of the isotopes was determined from the concentrations at which the corresponding minima appeared; the number of isotopes from the number of minima, and relative atomic weights from the moment of lag. For all three elements eight isotopes were found. Thus, uranium was determined in four different compounds—\(\mathrm{UCl}_4\), \(\mathrm{UCl}_6\), \(\mathrm{U(SO_4)_2}\), \(\mathrm{U_3(PO_4)_4}\); thorium in three—\(\mathrm{ThCl}_4\), \(\mathrm{Th(CO_4)_2}\), \(\mathrm{Th_3(PO_4)_4}\); and thallium likewise in three—\(\mathrm{TlCl}\), \(\mathrm{Tl_2SO_4}\), \(\mathrm{Tl_3PO_4}\). The atomic weights of the isotopes of these elements, in order of their abundance, are as follows:

Uranium: 238, 239, 240, 234, 237, 235, 233, 236.
Thorium: 232, 230, 234, 235, 236, 229, 233, 231.
Thallium: 207, 205, 211, 203, 201, 209, 215, 213.

The discovery of new isotopes that had not been noted in previous investigations is explained exclusively by certain improvements in the experimental technique and the practice of observation.

LITERATURE

1. R. W. Wood, Physic. Optics, 496, 1924.
2. Blondlot, Comp. Rend., 1882.
3. Lodge, Phil. Mag., 1889.
4. F. Allison, “Phys. Rev.”, 30, 66, 1927; 31, 313, 1928.
5. F. Allison and E. Murphy, J. Am. Chem. Soc., 52, 3796, 1930.
6. F. Allison and E. Murphy, Phys. Rev., 36, 1097, 1930; F. Allison, Ind. Eng. Chem. (Anal. Ed.), 4, 9, 1932.
7. F. Aston, Isotopes, 45, 1923.
8. F. Slack a. W. Breazeale, Phys. Rev., 40, 1052, 1932; 42, 305, 1932.
9. E. Bishop, M. Lawrenz and C. Dollins, Phys. Rev., 43, 43, 1933.
10. F. Aston, Nature, 120, 224, 1927; 123, 313, 1929.
11. F. Aston, Nature, 129, 649, 1932.
12. Schüler u. Jones, Naturwiss., 20, 171, 1932.
13. F. Allison a. E. Bishop, Phys. Rev., 43, 47, 1933.
14. E. Bishop a. C. Dollins, Phys. Rev., 43, 48, 1933.
15. R. Goslin a. F. Allison, Phys. Rev., 43, 49, 1933.