Total Quantum Number Research Articles

The Series Spectra of Two-Valence-Electron Atoms of Phosphorus (PIV), Sulphur (SV), and Chlorine (ClVI)

Series spectra of two-valence-electron atoms of P, S, and Cl.—In a previous Paper(1), the regular and irregular x-ray doublet laws were used to predict the spectra of stripped atoms, that is, atoms having only one valence electron. The method has now been applied to the spectra of two-electron atoms, since, although these spectra consist of triplets or singlets instead of doublets, the same laws apply to them. In this way 23 lines of PIV have been identified, 17 lines of SV and 6 lines of ClVI. With the help of the Ritz equation, 12 term values of PIV and 8 of SV were also determined. In a table are collected all known term values for two-electron atoms of Mg, Al, Si, P and S. Physical significance of the x-ray irregular doublet law.—Spectral lines which give parallel curves on a Moseley diagram sqrt[ν/R] plotted as a function of atomic number) and which therefore follow this law, are produced by jumps between orbits of the same total quantum number but with different screening constants.

The Series Spectra of Three-Valence-Electron Atoms of Phosphorus (PIII), Sulphur (SIV), and Chlorine (ClV)

Series spectra of two-valence-electron atoms of P, S, and Cl.—In a previous Paper(1), the regular and irregular x-ray doublet laws were used to predict the spectra of stripped atoms, that is, atoms having only one valence electron. The method has now been applied to the spectra of two-electron atoms, since, although these spectra consist of triplets or singlets instead of doublets, the same laws apply to them. In this way 23 lines of PIV have been identified, 17 lines of SV and 6 lines of ClVI. With the help of the Ritz equation, 12 term values of PIV and 8 of SV were also determined. In a table are collected all known term values for two-electron atoms of Mg, Al, Si, P and S. Physical significance of the x-ray irregular doublet law.—Spectral lines which give parallel curves on a Moseley diagram sqrt[ν/R] plotted as a function of atomic number) and which therefore follow this law, are produced by jumps between orbits of the same total quantum number but with different screening constants.

The constants of the Rydberg - Ritz equation

If the terms of the hydrogen spectrum to which certain quantum numbers have been assigned are compared with corresponding terms in the spectra of other elements, the latter will be found to be greater. While all writers agree that this is due to the presence of other orbital electrons, the structural reasons for this discrepancy are still a matter about which there is considerable difference of opinion. The present paper is an effort to consider this subject from a slightly new point of view. We may call such spectra hydrogen-like as arise from the radiation of the valence electron when it is alone in the outer shell. The alkali metals have such spectra normally and other elements give it in higher states of ionization. In all the cases to be considered, the valence electron moves about an atomic kernel, consisting of the nucleus and a number of electrons which move in orbits much smaller than those of the valence electron. The kernel is probably a structure geometrically similar to the atoms of the inert gases, but somewhat smaller, due to the contracting influence of the greater nuclear charge; and, unlike the inert gas atoms, the atomic kernel has a net positive electric charge. There was formerly some doubt about the total quantum numbers to be assigned to the valence orbit of the elements, but the correlations of X-ray and visible spectroscopy by Bohr and others have settled upon 3 as the total quantum number of the normal orbit in the sodium group, 4 in the potassium group, and so on.

Duration of Molecules in Upper Quantum States

Values of rate of decay and mean life of atoms and molecules in upper quantum states calculated from data on the intensity of absorption lines.---By combining F\"uchtbauer's method of determining from the intensity of absorption lines the probability that a molecule will absorb a quantum of energy, with Einstein's views as to the mechanism of light absorption and emission, the following equation is derived for calculating the rate at which molecules jump from upper to lower quantum states: ${A}_{21}=\left(\frac{8\ensuremath{\pi}{\ensuremath{\nu}}^{2}}{{c}^{2}{N}_{1}}\right)\left(\frac{{p}_{1}}{{p}_{2}}\right)\ensuremath{\int}{0}^{\ensuremath{\infty}}\ensuremath{\alpha}d\ensuremath{\nu}$ where ${A}_{21}$ is the chance per unit time that a molecule will jump spontaneously from quantum state 2 to quantum state 1, $\ensuremath{\nu}$ is the frequency of the light emitted in such a jump, ${p}_{1}$ and ${p}_{2}$ are the a priori probabilities of quantum states 1 and 2, and $\ensuremath{\alpha}$ is the absorption coefficient of the substance measured under conditions such that ${N}_{1}$ is the number of molecules per unit volume in the lower quantum state 1. The integral $\ensuremath{\int}\ensuremath{\alpha}d\ensuremath{\nu}$ is to be taken over the total effective width of the absorption line corresponding to the passage of molecules from quantum state 1 to quantum state 2. The mean life $\ensuremath{\tau}$ of molecules which decay from state 2 to state 1 is the reciprocal of ${A}_{21}$. Values of ${A}_{21}$ and $\ensuremath{\tau}$ are calculated from existing data for the mercury line $\ensuremath{\lambda}2537$, for a number of lines belonging to the alkali doublets, for the iodine line $\ensuremath{\lambda}5461$, and for a very considerable number of lines belonging to the rotation-oscillation spectra of the hydrogen halides. The values obtained agree with the meager data made available by other experimental methods. From these results the following conclusions are drawn.The mean life of molecules and atoms in upper quantum states may vary for different states at least over the range 1 to ${10}^{\ensuremath{-}8}$ seconds. The rate of decay is not a simple function of the frequency of the emitted light. The rate corresponding to the emission of a line of high frequency may be greater or less than that for a line of lower frequency. The data now available for the alkali doublets $1s\ensuremath{-}m{p}_{1}$ and $1s\ensuremath{-}m{p}_{2}$ indicate a higher rate of decay the smaller the change in total quantum number for the line under consideration. The rate of decay from a given $m{p}_{1}$ state is $m$ times as great as from the corresponding $m{p}_{2}$ state (already stated in another form by F\"uchtbauer and Hofmann). In the case of the rotation-oscillation spectra of the hydrogen halides the rate of decay is greater for quantum states with one unit of oscillation and many of rotation, than for those with one unit of oscillation and only a few of rotation; and in the case of different molecules but the same quantum numbers the rate of decay is greater for the molecule with the greater frequency of oscillation.Finally the possibility and method of calculating absolute values of ${A}_{21}$ from the Bohr correspondence principle is indicated.

Duration of Molecules in Upper Quantum States

Values of rate of decay and mean life of atoms and molecules in upper quantum states calculated from data on the intensity of absorption lines.—By combining Fuchtbauer's method of determining from the intensity of absorption lines the probability that a molecule will absorb a quantum of energy, with Einstein's views as to the mechanism of light absorption and emission, the following equation is derived for calculating the rate at which molecules jump from upper to lower quantum states: A21=8πν2/c2N1p1/p2∫0∞αdν where A21 is the chance per unit time that a molecule will jump spontaneously from quantum state 2 to quantum state 1, ν is the frequency of the light emitted in such a jump, p1 and p2 are the a priori probabilities of quantum states 1 and 2, and α is the absorption coefficient of the substance measured under conditions such that N1 is the number of molecules per unit volume in the lower quantum state 1. The integral ∫αdν is to be taken over the total effective width of the absorption line corresponding to the passage of molecules from quantum state 1 to quantum state 2. The mean life τ of molecules which decay from state 2 to state 1 is the reciprocal of A21. Values of A21 and τ are calculated from existing data for the mercury line λ2537, for a number of lines belonging to the alkali doublets, for the iodine line λ5461, and for a very considerable number of lines belonging to the rotation-oscillation spectra of the hydrogen halides. The values obtained agree with the meager data made available by other experimental methods. From these results the following conclusions are drawn. The mean life of molecules and atoms in upper quantum states may vary for different states at least over the range 1 to 10-8 seconds. The rate of decay is not a simple function of the frequency of the emitted light. The rate corresponding to the emission of a line of high frequency may be greater or less than that for a line of lower frequency. The data now available for the alkali doublets 1s-mp1 and 1s-mp2 indicate a higher rate of decay the smaller the change in total quantum number for the line under consideration. The rate of decay from a given mp1 state is m times as great as from the corresponding mp2 state (already stated in another form by Fuchtbauer and Hofmann). In the case of the rotation-oscillation spectra of the hydrogen halides the rate of decay is greater for quantum states with one unit of oscillation and many of rotation, than for those with one unit of oscillation and only a few of rotation; and in the case of different molecules but the same quantum numbers the rate of decay is greater for the molecule with the greater frequency of oscillation. Finally the possibility and method of calculating absolute values of A21 from the Bohr correspondence principle is indicated.