Full Text
ISOTOPE SHIFT IN THE URANIUM SPECTRUM
It is known from Bohr’s theory that the frequency of the emitted lines depends, through the Rydberg constant, on the mass of the atomic nucleus, i.e., on the atomic weight. As a result, the lines of two isotopes of one and the same element are shifted relative to one another. The magnitude of this isotope shift for a one-electron system is inversely proportional to the square of the atomic weight, and the displacement of the lines of the heavier isotope should occur toward the short wavelengths. Thus, from Bohr’s theory it follows that the isotope shift can be clearly observed in relatively light elements; in elements of medium and large atomic weights it should be very small.
The magnitudes of the isotopic shifts of the deuterium lines relative to the lines of ordinary hydrogen almost exactly correspond to the values calculated on the basis of Bohr’s theory, with the shift indeed occurring toward shorter wavelengths. For light elements (Li, Mg, Ar) the isotopic shift of lines has an appreciable magnitude; for elements of medium atomic weights the isotopic shift is either very small or not observable at all.
In the case of heavy elements, contrary to Bohr’s theory, the isotopic shifts again turn out to be rather large. In most cases these shifts are proportional to the masses (Hg, Zn), although deviations from simple proportionality also occur (Sm). For heavy elements an inversion of the shifts is also observed, i.e., in contrast to hydrogen, the heavier isotopes give lines shifted into the long-wavelength region.
Although attempts have been made, a comprehensive theory of isotopic shift has not yet been developed. Apparently, in addition to mass, the dimensions of the nucleus also play an essential role, and perhaps other properties of it as well.
Found shift for characteristic lines
| U\(^{238}\) line, Å | U\(^{238}\) line, cm\(^{-1}\) | Shift U\(^{238}\)—U\(^{235}\), Å | Shift U\(^{238}\)—U\(^{235}\), cm\(^{-1}\) | Shift U\(^{235}\)—U\(^{233}\), Å | Shift U\(^{235}\)—U\(^{233}\), cm\(^{-1}\) | Shift U\(^{238}\)—U\(^{233}\), Å | Shift U\(^{238}\)—U\(^{233}\), cm\(^{-1}\) |
|---|---|---|---|---|---|---|---|
| 2565,406 | 38980,18 | 0,075 | 1,14 | 0,070 | 1,66 | 0,145 | 2,20 |
| 2802,157 | 35686,79 | 0,018 | 0,23 | 0,020 | 0,25 | 0,038 | 0,48 |
| 3313,94 | 30121,02 | 0,016 | 0,14 | 0,036 | 0,33 | 0,052 | 0,47 |
| 3634,29 | 27523,26 | 0,104 | 0,79 | 0,064 | 0,48 | 0,168 | 1,27 |
| 3670,072 | 27247,42 | 0,009 | 0,06 | 0,009 | 0,07 | 0,018 | 0,13 |
| 3890,364 | 25704,53 | 0,036 | 0,24 | 0,055 | 0,36 | 0,091 | 0,60 |
| 3944,130 | 25354,13 | 0,057 | 0,37 | 0,091 | 0,58 | 0,148 | 0,95 |
| 4244,372 | 23560,61 | 0,248 | 1,37 | 0,125 | 0,70 | 0,373 | 2,07 |
| 4252,426 | 23515,98 | 0,168 | 0,93 | 0,089 | 0,49 | 0,257 | 1,42 |
| 4365,553 | 22906,60 | 0,208 | 1,09 | 0,073 | 0,38 | 0,281 | 1,47 |
| 4609,864 | 21692,61 | 0,077 | 0,36 | 0,054 | 0,26 | 0,131 | 0,62 |
The isotopic shift in the spectrum of uranium was recently studied in detail by Bechert, Stuckenbroker, and Adams*).
The isotopic shift was observed by them directly in a spectrum obtained with the aid of a diffraction spectrograph with a grating of 15,000 lines per inch, used in the second order with a dispersion of 2.47 Å/mm. A direct-current arc and a spark were used as the excitation source. The sample for the arc consisted of a mixture of 100 mg of U\(_3\)O\(_8\) and 500 mg of powdered graphite. The sample for the spark was 500 mg of U\(_3\)O\(_8\), mixed with drops of a solution of acetylcellulose in acetone, then burned into the hollow of a copper electrode.
) Physical Review 75*, 83 (1949).
The authors found more than 900 lines in the region 2500–8300 Å showing an isotope shift. The table on p. 572 gives the most characteristic shifts for a number of lines.
The largest shift occurs for the line 4244.37 Å (see figure). It turned out that if this line in the spectra of U\(^{238}\) and U\(^{235}\) exhibits an isotope shift, then it also shifts in the spectrum of U\(^{233}\). The shift of U\(^{233}\) occurs in the same direction as that of U\(^{235}\), i.e. isotopes of smaller mass give a shift toward shorter wavelengths. However, if there is some relation between the mass difference and the direction of the shift, there is nevertheless no relation whatever between the mass difference and the magnitude of the shift. Indeed, the table shows that for the lines 2802.157, 3313.94, 3890.361, 3944.130 Å the shift between the spectra of U\(^{235}\) and U\(^{233}\) (mass difference 2) is greater than between U\(^{238}\) and U\(^{235}\) (mass difference 3), whereas in the case of other lines the largest shift is obtained between the isotope lines of U\(^{238}\) and U\(^{235}\).
The separation of spectral lines belonging to the three isotopes of uranium is so distinct that it becomes possible to analyze quantitatively the concentrations of individual components of mixtures of uranium isotopes. The authors present data from which it follows that the accuracy of quantitative analyses is determined by a relative error of ±5% in the content of one isotope in another. The lowest concentration of the isotope U\(^{235}\) in U\(^{238}\) that they determined quantitatively is 0.61%. Hence, in the natural state, the isotope U\(^{235}\) can be quantitatively analyzed by the spectrographic method.
A. S.