Aston 1922/Chapter 10

(Chapter X - The Spectra of Isotopes

108. The Spectra of isotopes

As has already been stated^[1] the first experimental work on the spectra of isotopes was that of Russell and Rossi in 1912 who failed to distinguish any difference between the spectrum of thorium and that of a mixture of thorium and ionium containing a considerable percentage of the latter. The same negative result was obtained by Exner and Haschek.^[2] During the fractional diffusion of neon^[3] no spectroscopic difference was detected between the heaviest and the lightest fraction, though as the separation was small this negative evidence was not very strong. In 1914 Soddy and Hyman showed that the spectrum of lead derived from thorium was identical with that of ordinary lead.^[4] Furthermore in the same year the experiments of Richards and Lembert,^[5] Honigschmidt and Horowitz,^[6] and Merton^[7] proved the same result. Merton concluded from his 1914 experiments that the difference in wave-length for the λ 4058 line must be less than 0.003 Å. Before going on to consider the more recent results it will be as well to discuss the magnitude of the difference to be expected from theory.

109. The magnitude of the Gravitational effect

In the Bohr theory of spectra the planetary electrons of the atom rotate round the central positively charged nucleus in various stable orbits. The frequencies of the spectral lines emitted by the element are associated in an absolutely definite manner with the rotational frequencies of these orbits which are calculated by what is known as a "quantum "relation. Without going further into the theory it will be seen at once that if we alter the force acting between the central nucleus and its planetary electrons these orbits will change and with them the frequency of the light emitted. It is therefore of interest to examine the magnitude of the change, to be expected from this theory, when we alter the mass of the nucleus without changing its charge, and so pass from one isotope to another.

The difference in the system which will first occur to one is that although the electrical force remains the same the gravitational force must be altered. The order of magnitude of the change expected in the total force will clearly be given by considering the ratio between the electrical and gravitational forces acting, to take the simplest case, between the proton and the electron in a neutral hydrogen atom.

Assuming the law of force to be the same in both cases, this ratio is simply $\frac{e^{2}}{G M m}$ ; where e is the electronic charge 4.77 X 10^-10, G the universal gravitational constant 6.6 x 10^-8, M the mass of the proton 1.66 x lO^-24 and m the mass of the electron 9.0 x 10^-24. Putting in these numerical values we obtain the prodigious ratio 2.3 x 10^-39. In other words the effect of doubling the mass of the nucleus without altering its charge would give the same percentage increase in the total pull on the planetary electron, as would be produced in the pull between the earth and the moon by a quantity of meteoric dust weighing less than one million millionth of a gramme falling upon the surface of the former body. The gravitational effect may therefore be dismissed as entirely negligible.

110. Deviation of the Bohr orbits due to change in the position of the centre of gravity of the rotating system

Although we may neglect the gravitational effect there is another, of quite a different order, which arises in the following manner. The mass of the electron compared with that of the nucleus is small but not absolutely negligible, hence it will not rotate about the nucleus as though that were a fixed point, but both will rotate about their common centre of gravity. The position of this centre of gravity will be shifted by any alteration in the mass of the nucleus. If E, M and e, m are the respective charge and mass of the nucleus and the rotating electron, the equation of motion is

m \times \frac{r M}{M + m} ω^{2} = \frac{E e}{r^{2}}

where r is the distance between the two charges and ω the angular velocity. Bohr^[8] introduced this effect of the mass of the nucleus in order to account for the results obtained by Fowler.^[9] The Bohr expression for the frequency then becomes

ν = \frac{2 π^{2} e^{2} E^{2} m M}{h^{3} (M + m)} (\frac{1}{n_{1}^{2}} - \frac{1}{n_{2}^{2}})

where e, E and m, M are the charges and masses of the electron and nucleus respectively. If we suppose that the atomic weight of lead from radium to be one unit less than that of ordinary lead, this theory predicts a difference in wave-length, for the principle line, of 0.00005 Å between the two, a quantity beyond the reach of the most delicate methods of spectrum analysis used up to the present.

111. Later experiments of Aronberg and Merton

In 1917 Aronberg, applying the extremely high dispersion derived from the spectrum of the sixth order of a Michelson 10-inch grating to the line A 4058 emitted from a specimen of radio-lead of atomic weight 206-318, observed a difiference of 0.0044 Å between this and ordinary lead, of atomic weight 207.20. This remarkable result has been since confirmed by Merton of Oxford^[10] who gives the difference of wave-length between radio-lead from pitchblende and ordinary lead as 0.00502 ±0.0007, Merton made use of a totally different optical system, namely a Fabry and Perot etalon, so that the agreement is very striking.

It is to be noticed that the effect observed was not a mere broadening of the line but a definite shift, and that, though of the same sign, it is about one hundred times greater than that predicted by the Bohr theory, Merton also found a shift of 0.0022 ±0.0008 A between the wave-length of thorite-lead and ordinary lead, differing in atomic weight by about 0.6. The heavier atom shows the higher frequency in all cases. This remarkable discrepancy between the shift predicted by theory and that actually observed has been discussed by Harkins and Aronberg.^[11]

At a recent discussion on isotopes at the Royal Society^[12] Merton commented upon the line 6708 Å emitted by the element lithium, which consists of two components 0.151 Å apart. If lithium is accepted as a mixture of isotopes 6 and 7,^[13] he calculated that each of these components should be accompanied by a satellite, some sixteen times as faint, displaced by 0.087 Å. So far he had not been able to observe such satellites. Previous experiments of Merton and Lindemann^[14] on the expected doubling in the case of neon had given no conclusive results on account of the physical width of the lines. It was hoped that this difficulty could be overcome by the use of liquid hydrogen temperatures.

Still more recently Merton^[15] has repeated his experiments on lead, using a very pure sample of uranium lead from Australian Carnotite. His final results are indicated in the following table:

It will be noticed that the shift for the line λ 4058 is rather more than twice that obtained before. Merton suggests that the most probable explanation of this difference is evidently that the Carnotite lead used is a purer sample of uranium lead than that obtained from the pitchblende residues. It is also apparent that the differences are not the same for different lines, an interesting and somewhat surprising result.

112. "Isotope" effect on the Infra-red spectrum of molecules

The extreme smallness of the isotope "shift " described above in the case of line spectra emitted by atoms is due to the fact that one of the particles concerned in the vibration is the electron itself, whose mass is minute compared with that of the nucleus. Very much larger effects should be expected for any vibration in which two atoms or nuclei are concerned, instead of one atom and an electron. Such a vibration would be in the infra-red region of the spectrum.

This effect was first observed by Imes^[16] when mapping the fine structure of the infra-red absorption bands of the halogen acids. In the case of the HCl "Harmonic "band at 1.76 μ, mapped with a 20,000 line grating, the maxima were noticed to be attended by satellites. Imes remarks:

"The apparent tendency of some of the maxima to resolve into doublets in the case of the HCl harmonic may be due to errors of observation, but it seems significant that the small secondary maxima are all on the long-wave side of the principal maxima they accompany. It is, of course, possible that still higher dispersion applied to the problem may show even the present curves to be composite."

Loomis{ref>Loomis, Nature, Oct. 7, 179, 1920.[8]</ref> pointed out that these satellites could be attributed to the recently discovered isotopes of chlorine. In a later paper he has shown that, if m₁ is the mass of the hydrogen nucleus, and m₂ the mass of the charged halogen atom, the difference should be expressed by the quanity $\frac{m_{1} m_{2}}{m_{1} + m_{2}}$ the square root of which occurs in the denominator of the expression for frequency.

"Consequently the net difference between the spectra of isotopes will be that the wave-lengths of lines in the spectrum of the heavier isotope will be longer than the corresponding lines for the lighter isotope in the ratio 1 + 1/1330: 1 for chlorine and 1 + 1/6478: 1 for bromine. Since the average atomic weight of chlorine is 35.46 the amounts of Cl³⁵ and Cl³⁷ present in ordinary chlorine must be as 1.54:0.46 or as 3.35:1 and, if the lines were absolutely sharp and perfectly resolved, the absorption spectrum of ordinary HCl should consist of pairs of lines separated by 1/1330 of their frequency and the one of shorter wave-length should have about 3.35 the intensity of the other. The average atomic weight of bromine is 79.92, hence the two isotopes are present in nearly equal proportions and the absorption spectrum of HBr should consist of lines of nearly equal intensity separated by 1/6478 of their frequency."

The latter will be too close to be observed with the dispersion employed. In the case of the HCl band at 1.76 μ the difference of wave number on this view should be 4.3. The mean difference of wave number given by Loomis' measurements of 13 lines on Imes' original curves for this band is 4.5 ±0.4 corresponding to 14 Å in wave-length.

The spectroscopic confirmation of the isotopes of chlorine has also been discussed by Kratzer,^[17] who considers that the oscillation-rotation bands of hydrogen chloride due to Imes^[18] are in complete accordance with the theory.