The Isotope Effect in Band Spectra, II: The Spectrum of Boron Monoxide

Abstract

Band spectrum of boron monoxide.---Previous measurements of Jevons on the BO bands (ascribed by him to BN) have been extended, with the help of new spectrograms. Over $100\ensuremath{\beta}$ and about $200\ensuremath{\alpha}$ heads were measured or identified and are tabulated with their intensities. (1) Complete verification of the predicted vibrational isotope effect is found for both $\ensuremath{\alpha}$ and $\ensuremath{\beta}$ systems. Each is composed of two closely similar superposed systems, of which the weaker and larger scale one is due to the less abundant isotope ${\mathrm{B}}^{10}$O, the other to ${\mathrm{B}}^{11}$O. There was no indication of any other B isotopes than ${\mathrm{B}}^{10}$ and ${\mathrm{B}}^{11}$. The measured positions of all the heads can be represented by the equations: $\mathrm{B}^{10}\mathrm{O}: {\ensuremath{\nu}}_{\ensuremath{\alpha}}=\left\{{23,652.2;23,638.9;}{23,526.0;23,512.7}\right\}+1285.6{n}^{\ensuremath{'}}\ensuremath{-}11.7{n}^{\ensuremath{'}2}\ensuremath{-}1926.8{n}^{\ensuremath{'}\ensuremath{'}}+12.21{n}^{\ensuremath{'}\ensuremath{'}2}$ $\mathrm{B}^{11}\mathrm{O}: {\ensuremath{\nu}}_{\ensuremath{\alpha}}=\left\{{23,661.6;23,648.3;}{23,535.4;23,522.1}\right\}+1247.9{n}^{\ensuremath{'}}\ensuremath{-}10.6{n}^{\ensuremath{'}2}\ensuremath{-}1873.2{n}^{\ensuremath{'}\ensuremath{'}}+11.68{n}^{\ensuremath{'}\ensuremath{'}2}$ $\mathrm{B}^{10}\mathrm{O}: {\ensuremath{\nu}}_{\ensuremath{\beta}}=42,874.6\ensuremath{-}0.19{n}^{\ensuremath{'}}{n}^{\ensuremath{'}\ensuremath{'}}+1304.6{n}^{\ensuremath{'}}\ensuremath{-}10.43{n}^{\ensuremath{'}2}\ensuremath{-}1927.9{n}^{\ensuremath{'}\ensuremath{'}}+12.66{n}^{\ensuremath{'}\ensuremath{'}2}$ $\mathrm{B}^{11}\mathrm{O}: {\ensuremath{\nu}}_{\ensuremath{\beta}}=42,880.9\ensuremath{-}0.17{n}^{\ensuremath{'}}{n}^{\ensuremath{'}\ensuremath{'}}+1268.8{n}^{\ensuremath{'}}\ensuremath{-}9.98{n}^{\ensuremath{'}2}\ensuremath{-}1872.9{n}^{\ensuremath{'}\ensuremath{'}}+11.84{n}^{\ensuremath{'}\ensuremath{'}2}$For the linear terms in ${n}^{\ensuremath{'}}$ and ${n}^{\ensuremath{'}\ensuremath{'}}$ (the initial and final vibrational quantum numbers), the weighted mean ratio for corresponding coefficients of the two isotopes is 1.0291\ifmmode\pm\else\textpm\fi{}0.0003; for the quadratic terms, 1.062\ifmmode\pm\else\textpm\fi{}0.008. The theoretical values are 1.0292 and 1.059 for BO, 1.0276 and 1.056 for BN. The complete agreement with theory for BO, but not for BN, in the absence of contradiction from more direct experimental evidence, makes practically certain the BO origin of the bands, and at the same time quantitatively confirms the predicted vibrational isotope effect and gives powerful new support to the quantum theory of band spectra. Further evidence supporting the assignment of the bands to BO is presented. A comparative energy-level diagram for both isotopes is given, showing also the existing transitions with their intensities. The $\ensuremath{\alpha}$ and $\ensuremath{\beta}$ systems correspond to the same final state of the BO molecule, which is in all probability its normal state. (2) The inequality of the constant terms for the two isotopes in the above equations indicates an electronic isotope effect of wholly unprecedented magnitude. This vanishes, however, if one makes the assumption that the minimum values of ${n}^{\ensuremath{'}}$ and ${n}^{\ensuremath{'}\ensuremath{'}}$ are not zero, but \textonehalf{}. This result makes probable the existence of half-integral vibrational quantum numbers in BO, and of a null-point vibrational energy of \textonehalf{} quantum for BO (and doubtless for other molecules). (3) Measurements on the structure lines of three $\ensuremath{\beta}$ bands gave an approximate confirmation of the rotational isotope effect. (4) They also permitted a partial analysis of the band structure, so that approximate equations for the origins of the $\ensuremath{\alpha}$ and $\ensuremath{\beta}$ bands were obtained, as well as values for the internuclear distance for BO. (5) Measurements are given on a new system of BO bands of low intensity lying in the visible, and corresponding to a transition from the $\ensuremath{\beta}$ initial state to two (probably the first and third) of the four $\ensuremath{\alpha}$ initial states. The agreement with calculation is very close for both isotopes (on the assumption that the new bands consist of Q branches). This result confirms the preceding analyses of the $\ensuremath{\alpha}$ and $\ensuremath{\beta}$ systems. The grouping of the new bands is of an unusual type, due to the values of the constants involved. (6) Comparison of the arc and active nitrogen spectra of BO. The $\ensuremath{\beta}$ bands, when generated in active nitrogen, appear to consist usually of an isolated positive branch. A negative branch appears to be weakly present in a few cases. In the arc, doublets appear in place of the single positive branch lines, a new component being added. The intensity distribution of the BO bands in active nitrogen among various ${n}^{\ensuremath{'}}$ and $\ensuremath{\Delta}n$ values is discussed. The ${n}^{\ensuremath{'}}$ distribution, unlike the ${m}^{\ensuremath{'}}$ distribution, corresponds to a high effective temperature.Possible analogy of BO and CN to the Na atom.---If the $\ensuremath{\alpha}$ and $\ensuremath{\beta}$ systems of BO, and the red and violet CN bands, are respectively analogous to the first two members of the principal series of Na, the electronic resonance potentials of BO at 2.9 and 5.3 volts (calculated from the constant terms of the above equations), and of CN at 1.8 and 3.2 v, may be compared with the values 2.10 and 3.74 for Na. The weakness of the transition $\ensuremath{\beta}\ensuremath{\rightarrow}\ensuremath{\alpha}$ in BO is then analogous to that of the "forbidden" transition $2p\ensuremath{-}3p$ in Na. BO and CN, like Na, have nine outer electrons (outside the nucleus and K electrons) of which the first eight possibly form an octet somewhat as in Na, leaving the ninth in a loosely bound orbit. If the preceding analogy is correct, BO and CN should have ionizing potentials at about 7.0 and 4.4 volts, respectively (Na ionizes at 5.1 v). If this is true the alternation from higher to lower ionization potentials observed in the case of atoms, according as the number of electrons is even or odd, also holds for the series of molecules BO, CN, ${\mathrm{N}}_{2}^{+}$; CO, ${\mathrm{N}}_{2}$; NO; ${\mathrm{O}}_{2}$, with 9, 10, 11, and 12 outer electrons, respectively.