Aston 1922/Chapter 11

Chapter XI - The Separation of Isotopes

Francis William Aston (1922), Isotopes, ISBN 978-1016732383, Internet Archive.

• Preface

• Chapter I - Introduction

• Chapter II - The Radioactive Isotopes

• Chapter III - Positive Rays

• Chapter IV - Neon

• Chapter V - The Mass-Spectrograph

• Chapter VI - Analysis of the Elements

• Chapter VII - Analysis of the Elements (Continued)

• Chapter VIII - The Electrical Theory of Matter

• Chapter IX - Isotopes and Atomic Numbers

• Chapter X - The Spectra of Isotopes

• Chapter XI - The Separation of Isotopes

• Appendices

113. The Separation of Isotopes

The importance, from purely practical and technical points of view, of the theory of isotopes would have been insignificant had its application been confined to the radioactive elements and their products, which are only present in infinitesimal quantities on the Earth. But now that the isotopic nature of many elements in everyday use has been demonstrated, the possibility of their separation, to any reasonable extent, raises questions of the most profound importance to applied science. In physics all constants involving, e.g., the density of mercury or the atomic weight of silver may have to be redefined, while in chemistry the most wholesale reconstruction may be necessary for that part of the science the numerical foundations of which have hitherto rested securely upon the constancy of atomic weights.

It is therefore of great interest to consider in turn the various methods of separation proposed and examine how far they have been successful in practice.

114. Separation by Diffusion

The subject of the separation of a mixture of two gases by the method of Atmolysis or has been thoroughly investigated by the late Lord Rayleigh. The diffusion is supposed to take place through porous material. The conditions under which maximum separation is to be obtained are that "mixing" is perfect, so that there can be no accumulation of the less diffusible gas at the surface of the porous material, and that the apertures in the material through which the gases must pass are very small compared with the mean free path of the molecules. If these conditions are satisfied he obtains as an expression for the effect of a single operation :

$\frac{x+y}{X+Y}=\frac{X}{X+Y}r\frac{\nu }{\nu -\mu }+\frac{Y}{X+Y}r\frac{\nu }{\nu -\mu }$

where (X Y) {x, y) are the initial and final volumes of the gases, μ, ν, the velocities of diffusion, and r the enrichment of the residue as regards the second constituent.

The velocity of diffusion of a gas is proportional to the square root of the mass of its molecules, so that if a mixture of two isotopes is allowed to diffuse a change in composition must be brought about. Now no known isotopes differ from each other much in mass, so the difference between their rates of diffusion will also be small, hence the above equation may be written in the approximate form

$\frac{x+y}{X+Y}=r^{\frac{1}{k}}$

where

$k=\frac{\nu -\mu }{\mu }$

and, finally, the enrichment by diffusion of the residue as regards the heavier constituent may be expressed with sufficient accuracy by the expression

$r=\sqrt[\frac{m_1+m_2}{m_1-m_2}]{\frac{Initialvolume}{Finalvolume}}$

where m₁, m₂ are the molecular masses of the lighter and heavier isotope respectively. In the most favourable case known at present, that of the isotopes of neon, the number over the root is 21 so that the change in composition obtainable in a single operation will in practice be very small.

If we take the density of the original mixture as unity, the increase in density of the residual gas to be expected from the operation of diffusion will be approximately

$(r-1)\times \frac{Y}{X}\times 2\frac{m_2-m_1}{m_2-m_1}$

Now neon consists of monatomic molecules differing between each other in mass by 10 per cent, and the heavier is present to the extent of 10 per cent. In the diffusion experiments described on p. 39 the effective ratio of the initial volume to the final volume was estimated as certainly greater than 500 and probably less than 10,000, so that r lies between 1.3 and 1.5. Hence the increase of density of the heavier residue should have been between .003 and .005. It was actually .004.

115. The separation of the isotopes of chlorine by the diffusion of HCl

In the case of other isotopic gaseous mixtures the numerical obstacles in the way of practical separation will be correspondingly greater. Thus in the case of HCl the 36th root is involved, and in that of HBr the 80th root. The only way by which measurable increase in density may be hoped for will clearly be by increasing the effective ratio of the initial to final volumes to an heroic degree. This can be done by experiments on a huge scale or by a vast number of mechanical repetitions.

Harkins started to attack the HCl problem in 1916 using the first of these two alternatives. In 1920 he mentions a quantity of 19,000 litres of HCl as having been dealt with in these experiments. In the following year he published numerical results indicating that a change in atomic weight of 0.055 of a unit had been achieved.

At the recent discussion on isotopes Sir J. J. Thomson pointed out that a change in the molecular weight of HCl should be caused by allowing a stream of the gas to flow over the surface of a material which absorbed it. The higher diffusion coefficient of the lighter isotope would result in it being absorbed more rapidly than the heavier one, so that the residue of unabsorbed gas should give a higher molecular weight. This "free diffusion" without the interposition of porous material has been recently tried in the Cavendish Laboratory by E. B. Ludlam, but no measurable difference has so far been detected.

116. Separation by Thermal Diffusion

It has been shown on theoretical grounds independently by Enskog and Chapman that if a mixture of two gases of different molecular weights is allowed to diffuse freely, in a vessel of which the ends are maintained at two different temperatures T, T', until equilibrium conditions are reached, there will be a slight excess of the heavier gas at the cold end, and of the lighter gas at the hot end. The separation attained depends on the law of force between the molecules and is a maximum if they behave as elastic spheres. The effect was experimentally verified for a mixture of CO₂ and H₂ by Chapman and Dootson, and recently Ibbs has demonstrated that the separation can be carried out continuously and that the time for equilibrium to be established is quite short.

Chapman has suggested that thermal diffusion might be used to separate isotopes. He shows that the separating power depends on a constant k_T. And when the difference between the molecular masses m₁, m₂ is small the value of this is approximately given by

$k_T=\frac{17}{3}\frac{m_2-m_1}{m_2+m_1}\frac{{\lambda }_1{\lambda }_2}{9.15-8.25{\lambda }_1{\lambda }_2}$

where λ₁, λ₂ denote the proportions by volume of each gas in the mixture; thus λ₁ + λ₂ =1. The actual separation is given by

${\lambda }_1-{\lambda }_1^{\prime }=-({\lambda }_1-{\lambda }_2^{\prime })=k_{T}log\frac{T^{\prime }}{T}$

He gives the following numerical example :

"Suppose that it is desired to separate a mixture of equal parts of Ne²⁰ and Ne²², then,

writing m₁ = 20, m₂ = 22, λ₁ = λ₁ = ½, we find that k_T 0.0095.

Suppose that the mixture is placed in a vessel consisting of two bulbs joined by a tube, and one bulb is maintained at 80° absolute by liquid air, while the other is heated to 80080° absolute (or 52780° C. When the steady state has been attained the difference of relative concentration between the two bulbs is given by the equation

${\lambda }_1-{\lambda }_1^{\prime }=-({\lambda }_1-{\lambda }_2^{\prime })=0.0095lo{g}_{e}800/80=0.022$

or 2.2 per cent. Thus the cold bulb would contain 48.9 per cent. Ne²⁰ to 51.1 per cent. Ne²², and vice versa in the hot bulb. By drawing off the contents of each bulb separately, and by repeating the process with each portion of the gas, the difference of relative concentrations can be much increased. But as the proportions of the two gases become more unequal, the separation effected at each operation slowly decreases. For instance, when the proportions are as 3:1, the variation at each operation falls to 1.8 per cent.; while if they are as 10:1 the value is 1.2 per cent. This assumes that the molecules behave like elastic spheres: if they behave like point centres of force varying as the inverse nth. power of the distance, the separation is rather less; e.g., n=9, it is just over half the above quantities."

Chapman points out that for equal values of log p/p and log T/T pressure diffusion (centrifuging) is about three times as powerful as thermal diffusion but suggests that it may be more convenient to maintain large differences of temperature than of pressure.

117. Separation by Gravitation or "Pressure Diffusion"

When a heterogeneous fluid is subjected to a gravitational field its heavier particles tend to concentrate in the direction of the field, and if there is no mixing to counteract this a certain amount of separation must take place. If therefore we have a mixture of isotopes in a gaseous or liquid state partial separation should be possible by gravity or centrifuging.

The simplest case to consider is that of the isotopes of neon in the atmosphere and, before the matter had been settled by the mass-spectrograph, analysis of the neon in the air at very great heights was suggested as a possible means of proving its isotopic constitution. The reasoning is as follows: =E2=80=94

If M be the atomic weight, g the gravitational constant, p the pressure, and p the density, then if no mixing takes place dp =3D gpdh, h being the height. In the isothermal layer convection is small. If it is small compared with diffusion the gases will separate to a certain extent. Since T is constant

$p=\frac{RT\rho }{M}$ and $\frac{\mathrm{d}\rho }{\rho }=\frac{MP}{RT}dh$

whence

$\rho ={\rho }_0{e}^{-\frac{Mg}{RT}\mathrm{\Delta }H}$

ρ₀ being the density at the height h₀ at which mixing by convection ceases, about 10 kilometres, and Δh the height above this level. If two isotopes are present in the ratio 1 to K₀, so that the density of one is ρ₀ and of the other K₀ ρ₀ at height h₀, then their relative density at height K₀ + Δh is given by

$K=K_0{e}^{-\frac{g\mathrm{\Delta }h}{RT}(M_1-M_2)}$

Putting T = 220 as is approximately true in England,

$\frac{K}{K_0}=e^{-5.38\times 10^{-3}\mathrm{\Delta }h(M_1-M_2)}$,

Δh being measured in kilometres. If M₁ - M₂ = 2, therefore

$\frac{K_0}{K}=e^{-1.075\times 10^{-2}}\mathrm{\Delta }h$,

It might be possible to design a balloon which would rise to 100,000 feet and there fill itself with air. In this case the relative quantity of the heavier constituent would be reduced from 10 per cent, to about 8.15, so that the atomic weight of neon from this height should be 20.163 instead of 20.2. If one could get air from 200,000 feet, e.g. by means of a long range gun firing vertically upwards, the atomic weight of the neon should be 20.12.

A more practicable method is to make use of the enormous gravitational fields produced by a high speed centrifuge.

In this case the same equation holds as above except that g varies from the centre to the edge. In a gas therefore

$\frac{\mathrm{d}\rho }{\rho }=-\frac{M{v}^2}{RT}\frac{\mathrm{d}r}{r}=-\frac{M{\omega }^2}{RT}r\mathrm{d}r$,

whence

$\rho ={\rho }_0{e}^{-\frac{m{v}_0^2}{2RT}}$,

ν₀ being the peripheral velocity. Here again, if K₀ is the ratio of the quantities present at the centre, the ratio at the edge will be

$K_0{e}^{-\frac{v_0^2}{2RT}(M_1-M_2)}$.

A peripheral velocity of 10⁵ cm,/s. or perhaps even 1.3 x 10⁵ cm./s. might probably be attained in a specially designed centrifuge, so that $\frac{K}{K_0}$ might be made as great as $e^{-0.205(M_1-M_2)}$ or even $e^{-0.37(M_1-M_2)}$.

If M₁ - M₂ is taken as 2 a single operation would therefore give fractions with a change of K of 0.65. In the case of neon the apparent atomic weight of gas from the edge would be about 0.65 per cent, greater than that of gas from the centre, i.e. a separation as great as the best yet achieved in practice by any method could be achieved in one operation. By centrifuging several times or by operating at a lower temperature the enrichment might be increased exponentially.

Centrifuging a liquid, e.g. liquid lead, would not appear so favourable, though it is difficult to form an accurate idea of the quantities without a knowledge of the equation of state. If compression is neglected and the one lead treated as a solution in the other, a similar formula to that given above holds. On assumptions similar to these Poole has calculated that a centrifuge working with a peripheral velocity of about 10⁴ cm. /sec should separate the isotopes of mercury to an extent corresponding to a change of density of 0.000015.

The only experiments on the separation of isotopes by the use of a centrifuge, so far described, are those of Joly and Poole who attempted to separate the hypothetical isotopic constituents of ordinary lead by this means. No positive results were obtained and the check experiments made with definite alloys of lighter metals with lead were by no means encouraging.

118. Separation by Chemical Action or Ordinary Fractional Distillation

The possibility of separating isotopes by means of the difference between their chemical affinities or vapour pressures has been investigated very fully from the theoretical standpoint by Lindemann. The thermodynamical considerations involved are the same in both cases. The reader is referred to the original papers for the details of the reasoning by which the following conclusion is reached:

"Isotopes must in principle be separable both by fractionation and by chemical means. The amount of separation to be expected depends upon the way the chemical constant is calculated and upon whether 'Nullpunktsenergie' is assumed. At temperatures large compared with βν, which are the only practicable temperatures as far as lead is concerned, the difference of the vapour pressure and the constant of the law of mass action may be expanded in powers of $\frac{\beta \nu }{T}$. The most important term of the type log$\frac{\beta \nu }{T}$ is cancelled by the chemical constant if this is calculated by what seems the only reasonable way. The next term in is cancelled by the 'Nullpunktsenergie' if this exists. All that remains are terms containing the higher powers of $\frac{\beta \nu }{T}$. In practice therefore fractionation does not appear to hold out prospects of success unless one of the above assumptions is wrong. If the first is wrong a difference of as much as 3 per cent, should occur at 1200 and a difference of electromotive force of one millivolt might be expected. Negative results would seem to indicate that both assumptions are right."

As regards experimental evidence it has already been pointed out that the most careful chemical analysis, assisted by radioactive methods of extraordinary delicacy, was unable to achieve the slightest separation of the radioactive isotopes. The laborious efforts to separate the isotopes of neon by a difference of vapour pressure over charcoal cooled in liquid air also gave a completely negative result.

119. Separation by evaporation at very low pressure

If a liquid consisting of isotopes of different mass is allowed to evaporate it can be shown that the number of Hght atoms escaping from the surface in a given time will be greater than the number of heavier atoms in inverse proportion to the square roots of their weights. If the pressure above the surface is kept so low that none of these atoms return the concentration of the heavier atoms in the residue will steadily increase. This method has been used for the separation of isotopes by Bronsted and Hevesy, who applied it first to the element mercury.

The mercury was allowed to evaporate at temperatures from 40 °C to 60 °C. in the highest vacuum attainable. The evaporating and condensing surfaces were only 1 to 2 cms. apart, the latter was cooled in liquid air so that all atoms escaping reached it without collision and there condensed in the sohd form.

It will be seen that the liquid surface acts exactly like the porous diaphragm in the diffusion of gases. The diffusion rate of mercury can be obtained approximately from the diffusion rate of lead in mercury and is such that the mean displacement of the mercury molecule in liquid mercury is about 5 X 10^-3 cm. sec.^-1 It follows that if not more than 5 x 10^-3 c.cm. per cm.² surface evaporate during one second no disturbing accumulation of the heavier isotope in the surface layer takes place.

The separation was measured by density determination. Mercury is particularly well suited for this and a notable feature of this work was the amazing dellcacy with which it could be performed. With a 5 c.cm. pyknometer an accuracy of one part in two millions is claimed. The first figures published were:

Condensed mercury . . . . 0.999981

Residual mercury . . . . . 1.000031

The densities being referred to ordinary mercury as unity.

The later work was on a larger scale. 2700 c.cm. of mercury were employed and fractionated systematically to about 1/100,000 of its original volume in each direction. The final figures were :

Lightest fraction vol. 0.2 c.c. . . 0.99974

Heaviest fraction vol. 0.3 c.c. . . 1.00023

Mercury behaves as though it was a mixture of equal parts of two isotopes with atomic weights 202.0, 199.2 in equal parts or of isotopes 201.3, 199.8 when the former is four times as strong as the latter, and so on.

120. Separation of the isotopes of chlorine by free evaporation

The same two investigators were able to announce the first separation of the isotopes of chlorine by applying the above method to a solution of HCl in water. This was allowed to evaporate at a temperature of 50 °C. and condense on a surface cooled in liquid air. Starting with 1 litre 8.6 mol. solution of HCl 100 c.c. each of the lightest and heaviest fraction were obtained.

The degree of separation achieved was tested by two differerent methods. In the first the density of a saturated solution of NaCl made from the distillate and the residue respectively was determined with the following results :

Density (salt from distillate) = 1.20222

Density (salt from residue) = 1.20235

These figures correspond to a change in atomic weight of 0.024 of a unit.

In the second method exactly equal weights of the isotopic NaCls were taken and each precipitated with accurately the same volume of AgNO₃ solution, in slight excess. After precipitation and dilution to 2,000 c.c. the approximate concentration of the filtrate was determined by titration, also the ratio of Ag concentration of the two solutions was measured in a concentration cell. Calculation showed that the difference in atomic weight of the two samples was 0.021 in good agreement with the density result.

121. Separation by Positive Rays

The only method which seems to offer any hope of separating isotopes completely, and so obtaining pure specimens of the constituents of a complex element, is by analysing a beam of positive rays and trapping the particles so sorted out in different vessels. It is therefore worth while inquiring into the quantities obtainable by this means.

Taking the case of neon and using the parabola method of analysis with long parabolic slits as collecting vessels we find that the maximum separation of the parabolas corresponding to masses 20 and 22 (obtained when electric deflexion θ is half the magnetic) is approximately

$2\frac{1}{\sqrt{2}}\frac{M_1-M_2}{M_1}\theta =\frac{\theta }{28}$ .

Taking a reasonable value of θ as .3 the maximum angular width of the beam for complete separation = 0.01. If the canal-ray tube is made in the form of a slit at 45° to axes, i.e. parallel to the curves, the maximum angular length of the beam might be say 5 times as great, which would collect the positive rays contained in a solid angle of .0005 sq. radian.

The concentration of the discharge at the axis of the positive ray bulb is considerable, and may be roughly estimated to correspond to a uniform distribution of the entire current over a ¼ sq. radian. One may probably assume that half the current is carried by the positive rays, and that at least half the positive rays consist of the gases desired. If neon is analysed by this method therefore the total current carried by the positive rays of mass 20 is

$-0005\times 4\times \frac{1}{2}\times \frac{1}{2}\times i=.0005i$ .

If i is as large as 5 milliamperes this = 1.5 x 10⁴ E.S.U.

or $\frac{1.5\times 10^4}{2.7\times 10^{19}\times 4.77\times 10^{-10}}=1.2\times 10^{-6}$ c.c./sec.,

i.e. one might obtain about one-tenth of a cubic millimetre of Ne²⁰ and 1/100 cubic millimetre of Ne²² per 100 seconds run. It is obvious that even if the difficulties of trapping the rays were overcome, the quantities produced, under the most favourable estimates, are hopelessly small.

122. Separation by photochemical methods

A remarkably beautiful method of separating the isotopes of chlorine has been suggested by Merton and Hartley which depends upon the following photochemical considerations. Light falling on a mixture of chlorine and hydrogen causes these gases to combine to form hydrochloric acid. This must be due to the activation of the atoms of hydrogen or those of chlorine. Supposing it to be the latter it is conceivable that the radiation frequency necessary to activate the atoms of Cl³⁵ will not be quite the same as that necessary to activate those of Cl³⁷. Calling these frequencies ν₃₅ and ν₃₇ respectively it would seem possible, by excluding one of these frequencies entirely from the activating beam, to cause only one type of chlorine to combine and so to produce pure HCl³⁵ or HCl³⁷. Now ordinary chlorine contains about three times as much Cl³⁵ as Cl³⁷ and these isotopes must absorb their own activating radiation selectively. In this gas therefore light of frequency ν₃₅ will be absorbed much more rapidly than that of frequency ν₃₇, so that if we allow the activating beam to pass through the right amount of chlorine gas ν₃₅ might be completely absorbed but sufficient ν₃₇ radiation transmitted to cause reaction. On certain theories of photo-chemistry light containing ν₃₇ but no V35 would cause only atoms of CP ⁿ to combine so that a pure preparation of HCP ⁿ would result. Pure CP' ⁿ made from this product could now be used as a filter for the preparation of pure HCP ⁿ, and this in its turn would yield pure CP ⁿ which could then be used as a more efficient filter for the formation of more HCP ⁿ

Had this very elegant scheme been possible in practice it would have resulted in a separation of a very different order to those previously described and the preparation of unlimited quantities of pure isotopes of at least one complex element. There is however little hope of this, for so far the results of experiments on this method have been entirely negative.

123. Other methods of separation and general conclusions

The following methods have also been suggested. By the electron impact in a discharge tube, in the case of the inert gases, the llghter atoms being more strongly urged towards the anode; by the migration velocity of ions in gelatine; by the action of light on metallic chlorides,

A survey of the separations actually achieved so far shows that from the practical point of view they are very small. In cases where the method can deal with fair quantities of the substance the order of separation is small, while in the case of complete separation (positive rays) the quantities produced are quite insignificant. We can form some idea by considering the quantity

Q = (difference in atomic weight achieved) x (average quantity of two fractions produced in grammes). As regards the first of these factors the highest figure so far was 0.13 obtained by the writer in the original diffusion experiments on neon, but as the quantities produced were only a few milligrams Q is negligibly small. The highest values of Q have been obtained by Bronsted and Hevesy by their evaporation method. It is 0.5 in the case of Hydrochloric Acid, 0.34 in that of Mercury.

When we consider the enormous labour and difficulty of obtaining this result it appears that unless new methods are discovered the constants of chemical combination are not likely to be seriously upset for some considerable time to come.

References

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Francis William Aston (1922), Isotopes, ISBN 978-1016732383, Internet Archive.

• Preface

• Chapter I - Introduction

• Chapter II - The Radioactive Isotopes

• Chapter III - Positive Rays

• Chapter IV - Neon

• Chapter V - The Mass-Spectrograph

• Chapter VI - Analysis of the Elements

• Chapter VII - Analysis of the Elements (Continued)

• Chapter VIII - The Electrical Theory of Matter

• Chapter IX - Isotopes and Atomic Numbers

• Chapter X - The Spectra of Isotopes

• Chapter XI - The Separation of Isotopes

• Appendices