The Extension of the X-ray-Doublet Laws into the Field of Optics

Application of relativity formulas for x-ray doublets to ultra-violet spectra.— Evidence has been presented which indicates that many of the strongest lines in hot spark spectra are due to atoms stripped of all valence electrons excepting the one which in jumping between energy levels emits the radiation. For the L doublets due to atoms with but one $L$ electron, Li(+), Be(2+), B(3+), C(4+), it is found that the frequency difference varies with atomic number $Z$ in accordance with the relativity formula for x-ray doublets $\Delta \nu =K{\mathrm{}(Z-s)\mathrm{}}^4$, the constant $K$ being.365 for the regular L series, and the screening constant $s$ decreasing from 2.02 for Li(+) to 1.86 for C(4+). Other L doublets are attributed to atoms stripped of all but three $L$ electrons, the same formula holding but giving values of $s$ about 20 per cent greater. In the case of triplets, the frequency differences of the widest pairs give values of $s$ for atoms stripped of all but two or four L electrons which agree well with values for only one, three or five L electrons, though tending to be somewhat greater. Similarly from M doublets and triplets ($K=.\mathrm{}108\mathrm{}$) of C and N, values of $s$ were obtained for atoms with from one to three L electrons slightly greater than from the corresponding L lines. In the case of atoms with only one $M$ electron, the values of $s$ decrease from 7.45 for Na(+) to 5.74 for P(5+), corresponding values of $s$ from N, O and P series of doublets being slightly larger; for atoms with only two $M$ electrons (widest pair of triplets) and with only three $M$ electrons (doublets) the values of $s$ vary up to about 9. For doublets corresponding to outer transitions $3d_2-3\mathrm{}{d}_1$, $4d_2-4\mathrm{}{d}_1$ and $4f_2-4\mathrm{}{f}_1$ the values of $s$ come out close to 10. In the case of irregular $L$ and $M$ doublets corresponding to transitions from the $2s$ and $3s$ levels, the law for corresponding x-ray doublets also holds, the differences ($\sqrt{{\nu }_s}-\sqrt{{\nu }_p}$) increasing regularly and not very greatly with $Z$. All these facts are shown to agree well with what should be expected according to the Bohr-Sommerfeld theory; and the values of $s$ give quantitatively the influence upon the effective nuclear charge of the addition of electrons in the valence shells. New series terms. The above relations enable the value of $s$ for a given series for a given ionized atom to be predicted, and led to the discovery of an L doublet at $\lambda 1240$ due to N(5+), and to the assignment of the following L doublets: $\lambda 990$ to N(3+), $\lambda 1493$ and 1744 to N(+), $\lambda 789$ and $\lambda 658$ to O(4+), and $\lambda 922$ to O(2+). These results give us a new method of predicting spectra and of determining the state of ionization of atoms emitting certain lines.