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Canadian Journal of Physics

SELECTIVE REFLECTION FROM MERCURY VAPOR AT HIGH PRESSURES

H. L. Welsh, John A. Galt

Published Jan 1, 1957• 14 citations
Publisher

Abstract

Selective reflection from mercury vapor in the region of the 2537 Å resonance line was investigated at pressures up to 340 atm. using reflection cells of special design. The results were interpreted on the basis of the classical theory of reflection from an absorbing medium. By fitting calculated curves to the experimental reflection contours, values of the oscillator strength, f, and the damping constant, γ, were determined. The f values so obtained are density-dependent and at high pressures are approximately equal to one half the value for the free atom. As predicted by theory, the damping constant varies directly as the density of the atoms in the vapor. This result contradicts the earlier work of Welsh, Kastner, and Lauriston (1950) in which it was concluded that γ varies as the square root of the density. A subsidiary reflection maximum was observed at 2540 Å; it is attributed to Hg2 molecules which occur in relatively large concentrations at high densities. Some preliminary observations on the selective reflection at the 1850 Å resonance line were made up to 4.4 atm.

DOI
10.1139/p57-011

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SELECTIVE REFLECTION FROM MERCURY AND CADMIUM VAPORS

H. L. Welsh, Jacob Kastner, A. C. Lauriston

Selective reflection from mercury and cadmium vapors in the neighborhood of the resonance lines was investigated quantitatively using incident light of continuous spectral distribution. For a given experimental arrangement the lowest vapor density (atoms per cubic centimeter) at which selective reflection could be detected at Hg 2537 Å, Cd 2288 Å, and Cd 3261 Å was inversely proportional to the oscillator strength (f-value) of the absorption line. Contours of the selective reflection of the Hg 2537 Å and Cd 2288 Å lines were obtained over a large range of vapor densities up to 80 × 1018 atoms per cc. At this density the cadmium reflection extended over several thousand cm.−1 compared to about a hundred cm.−1 for mercury. The general features of the reflection contours can be explained by the theory of reflection from an absorbing medium. Fitting a theoretical curve to the experimental reflection contour yields values of the oscillator strength and the damping constant. For Hg 2537 Å and Cd 2288 Å the f-values are 0.0268 and 1.40 respectively, in good agreement with those found by other methods. The damping constant, γ, varies as the square root of the number of atoms per cubic centimeter, indicating that the mechanism of selective reflection is not the same as that for absorption and emission. An empirical areal law for selective reflection confirms the relationship [Formula: see text]. A shift of the resonance frequency of the order of magnitude of the coupling shift calculated by Weisskopf was observed for Hg 2537 Å. Deviations from theory at both high and low pressures were observed for Cd 2288 Å. The low pressure deviation takes the form of a line of residual intensity at the resonance frequency, which may be due to a different kind of selective reflection.

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SELECTIVE REFLECTION FROM THE VAPORS OF THE ALKALI METALS

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Selective reflection from sodium, potassium, rubidium, and caesium vapors in the neighborhood of the resonance lines was observed for vapor pressures between 10 mm. and 1 atm., using a steel tube with a window of transparent magnesium oxide. Reflecting power as a function of frequency was measured by using incident light of continuous spectral distribution. The reflection contour for pressures up to ½ atm. is in good agreement with the theory of reflection from an absorbing medium. For each line the damping constant in the dispersion equations varies as the square root of the number of atoms per cubic centimeter, as was found previously for mercury and cadmium. For the two members of the resonance doublet the damping constants are proportional to the square roots of the oscillator strengths. In a region about 5 cm.−1 wide about each resonance frequency the reflected intensity measured experimentally is greater than that calculated. These lines of residual intensity may be due to a second kind of selective reflection. At pressures above ½ atm. the observed reflection contour cannot be explained by the simple anomalous dispersion theory.

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Resonance Broadening of the Sodium D-Lines in Absorption

Kenichi Watanabe

The resonance broadening of the sodium D-lines in absorption was determined by measuring the contour of the line wings directly. The vapor pressures of sodium ranged from 10-3 to 75 mm Hg, with negligible amount of foreign gases. Over nearly the entire range, the half-intensity width varied linearly with the density of the absorbing atoms; i.e. Δν1/2/N = 0.78 x 10-7 sec-1cm3 --the constant being about twice that predicted by Houston, but much less than the experimental result by Hughes and LLoyd. Above 5 mm pressure, the half-intensity width appeared to increase slightly faster than N. Somewhat in contradiction to theory, the relative width, Δν1/2,s/Δν1/2,1' was 1.16. The natural width measured was, within experimental error, consistent with previous values. The inverse square contour for the absorption coefficient was satisfactory up to 5 mm Hg; beyond this pressure an inverse cube contour fitted better. No definite evidence of van der Waal force was observed at high pressures; likewise, no appreciable shifts and asymmetries. MgO windows were used and the temperature determination was made reliable.

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Measurement of the Life of the Metastable Mercury Atom

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Half value time for the ${2}^{3}$${\mathrm{P}}_{0}$ state of Hg for various pressures of admixed ${\mathrm{N}}_{2}$--- A high speed rotating disk has been used to interrupt the total radiation from a water-cooled and magnetically controlled quartz mercury arc before optically exciting mercury vapor in a quartz resonance tube at room temperature. In the neighborhood of ${10}^{\ensuremath{-}4}$ sec. after the optical excitation a flash of visible radiation from another water-cooled and magnetically controlled mercury arc was passed through the resonance tube and the absorption spectrum photographed. The line 4047 ($2^{3}P_{0}\ensuremath{-}2^{3}S_{1}$) showed strong absorption when a few millimeters of nitrogen were introduced into the resonance tube. The lines 4077, 4358, 5461, 5770 and 5790 showed no measurable absorption under similar conditions. The rate of decay of the amount of 4047 absorbed with respect to the time-wait after excitation of the mercury vapor was taken as the rate of decay of the metastable $2^{3}P_{0}$ state. The life or half-value time of the state was found to vary markedly with the pressure of admixed nitrogen. The maximum life 4.2\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}4}$ sec. occurred for 6.8 mm of nitrogen. No absorption of 4047 was observed upon the introduction of hydrogen, argon, neon, or helium into the resonance tube.

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Resonance Broadening of Caesium

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The resonance broadening of homogeneous Cs vapor in absorption was studied by means of the contour method. The intensities were obtained via the method of "astigmatic photometry" by utilizing the astigmatism of the Rowland grating. The pressure of the homogeneous absorbing vapor ranged from ${10}^{\ensuremath{-}2}$ to 17.5 mm Hg. The half breadth $\ensuremath{\gamma}$ varied rather linearly with the number of atoms per unit volume, with $(\frac{{\ensuremath{\gamma}}_{1}}{N})\ifmmode\times\else\texttimes\fi{}{10}^{7}=1.45$, $(\frac{{\ensuremath{\gamma}}_{2}}{N})\ifmmode\times\else\texttimes\fi{}{10}^{7}$ for the $^{2}P_{\frac{3}{2}}$ and $^{2}P_{\frac{1}{2}}$ eomponents of the resonance lines, respectively. The average value of the ratio of half breadths $\frac{{\ensuremath{\gamma}}_{1}}{{\ensuremath{\gamma}}_{2}}$ was found to be 1.8. The experimental half-width $\ensuremath{\gamma}$ is found to be about 1\textonehalf{} times larger than that predicted by W. V. Houston. Below pressures of 10 mm Hg the lines exhibited symmetrical broadening according to the "dispersion" formula. At higher pressures indications of a violet and red asymmetry are present for the $^{2}P_{\frac{3}{2}}$ and $^{2}P_{\frac{1}{2}}$ components, respectively. A definite band on the red side of the $^{2}P_{\frac{3}{2}}$ and one on the violet side of the $^{2}P_{\frac{1}{2}}$ was observed.

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Resonance Broadening of the Sodium D Lines

Kenichi Watanabe

By direct measurement of the contours of the line wings, the resonance broadening of the sodium $D$ lines in absorption was determined for vapor pressures of sodium ranging from ${10}^{\ensuremath{-}3}$ to 70 mm Hg with negligible amount of foreign gases. Over nearly the entire range, the half-intensity width varied linearly with the density of the absorbing atoms; i.e., $\frac{\ensuremath{\Delta}{\ensuremath{\nu}}_{\frac{1}{2}}}{N}=0.80\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}7}$ ${\mathrm{sec}.}^{\ensuremath{-}1}$ ${\mathrm{cm}}^{\ensuremath{-}3}$---the constant being 1.6 times that predicted by theory but much less than the corresponding experimental results for potassium. Above 5 mm pressure, $\ensuremath{\Delta}{\ensuremath{\nu}}_{\frac{1}{2}}$ increased slightly faster than $N$; moreover, the contour for the absorption coefficient was more adequately represented by an inverse cube contour than by the inverse square. Somewhat in contradiction to theory, the relative width, $\frac{\ensuremath{\Delta}{\ensuremath{\nu}}_{\frac{1}{2},8}}{\ensuremath{\Delta}{\ensuremath{\nu}}_{\frac{1}{2},l}}$ was 1.12. No definite evidence of van der Waals force was observed at the higher pressures; likewise no appreciable shifts or asymmetries. The natural width measured was consistent with previous results.

Physical Review•Jan 15, 1941•42 citations
Selective reflection from mercury vapor in the region of the 2537 Å resonance line was investigated at pressures up to 340 atm. using reflection cells of special design. The results were interpreted on the basis of the classical theory of reflection from an absorbing medium. By fitting calculated curves to the experimental reflection contours, values of the oscillator strength, f, and the damping constant, γ, were determined. The f values so obtained are density-dependent and at high pressures are approximately equal to one half the value for the free atom. As predicted by theory, the damping constant varies directly as the density of the atoms in the vapor. This result contradicts the earlier work of Welsh, Kastner, and Lauriston (1950) in which it was concluded that γ varies as the square root of the density. A subsidiary reflection maximum was observed at 2540 Å; it is attributed to Hg2 molecules which occur in relatively large concentrations at high densities. Some preliminary observations on the selective reflection at the 1850 Å resonance line were made up to 4.4 atm.
Selective reflection from mercury and cadmium vapors in the neighborhood of the resonance lines was investigated quantitatively using incident light of continuous spectral distribution. For a given experimental arrangement the lowest vapor density (atoms per cubic centimeter) at which selective reflection could be detected at Hg 2537 Å, Cd 2288 Å, and Cd 3261 Å was inversely proportional to the oscillator strength (f-value) of the absorption line. Contours of the selective reflection of the Hg 2537 Å and Cd 2288 Å lines were obtained over a large range of vapor densities up to 80 × 1018 atoms per cc. At this density the cadmium reflection extended over several thousand cm.−1 compared to about a hundred cm.−1 for mercury. The general features of the reflection contours can be explained by the theory of reflection from an absorbing medium. Fitting a theoretical curve to the experimental reflection contour yields values of the oscillator strength and the damping constant. For Hg 2537 Å and Cd 2288 Å the f-values are 0.0268 and 1.40 respectively, in good agreement with those found by other methods. The damping constant, γ, varies as the square root of the number of atoms per cubic centimeter, indicating that the mechanism of selective reflection is not the same as that for absorption and emission. An empirical areal law for selective reflection confirms the relationship [Formula: see text]. A shift of the resonance frequency of the order of magnitude of the coupling shift calculated by Weisskopf was observed for Hg 2537 Å. Deviations from theory at both high and low pressures were observed for Cd 2288 Å. The low pressure deviation takes the form of a line of residual intensity at the resonance frequency, which may be due to a different kind of selective reflection.
Selective reflection from sodium, potassium, rubidium, and caesium vapors in the neighborhood of the resonance lines was observed for vapor pressures between 10 mm. and 1 atm., using a steel tube with a window of transparent magnesium oxide. Reflecting power as a function of frequency was measured by using incident light of continuous spectral distribution. The reflection contour for pressures up to ½ atm. is in good agreement with the theory of reflection from an absorbing medium. For each line the damping constant in the dispersion equations varies as the square root of the number of atoms per cubic centimeter, as was found previously for mercury and cadmium. For the two members of the resonance doublet the damping constants are proportional to the square roots of the oscillator strengths. In a region about 5 cm.−1 wide about each resonance frequency the reflected intensity measured experimentally is greater than that calculated. These lines of residual intensity may be due to a second kind of selective reflection. At pressures above ½ atm. the observed reflection contour cannot be explained by the simple anomalous dispersion theory.
The resonance broadening of the sodium D-lines in absorption was determined by measuring the contour of the line wings directly. The vapor pressures of sodium ranged from 10-3 to 75 mm Hg, with negligible amount of foreign gases. Over nearly the entire range, the half-intensity width varied linearly with the density of the absorbing atoms; i.e. Δν1/2/N = 0.78 x 10-7 sec-1cm3 --the constant being about twice that predicted by Houston, but much less than the experimental result by Hughes and LLoyd. Above 5 mm pressure, the half-intensity width appeared to increase slightly faster than N. Somewhat in contradiction to theory, the relative width, Δν1/2,s/Δν1/2,1' was 1.16. The natural width measured was, within experimental error, consistent with previous values. The inverse square contour for the absorption coefficient was satisfactory up to 5 mm Hg; beyond this pressure an inverse cube contour fitted better. No definite evidence of van der Waal force was observed at high pressures; likewise, no appreciable shifts and asymmetries. MgO windows were used and the temperature determination was made reliable.
Half value time for the 23{2}^{3}23P0{\mathrm{P}}_{0}P0​ state of Hg for various pressures of admixed N2{\mathrm{N}}_{2}N2​--- A high speed rotating disk has been used to interrupt the total radiation from a water-cooled and magnetically controlled quartz mercury arc before optically exciting mercury vapor in a quartz resonance tube at room temperature. In the neighborhood of ${10}^{\ensuremath{-}4}$ sec. after the optical excitation a flash of visible radiation from another water-cooled and magnetically controlled mercury arc was passed through the resonance tube and the absorption spectrum photographed. The line 4047 ($2^{3}P_{0}\ensuremath{-}2^{3}S_{1}$) showed strong absorption when a few millimeters of nitrogen were introduced into the resonance tube. The lines 4077, 4358, 5461, 5770 and 5790 showed no measurable absorption under similar conditions. The rate of decay of the amount of 4047 absorbed with respect to the time-wait after excitation of the mercury vapor was taken as the rate of decay of the metastable 23P02^{3}P_{0}23P0​ state. The life or half-value time of the state was found to vary markedly with the pressure of admixed nitrogen. The maximum life 4.2\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}4}$ sec. occurred for 6.8 mm of nitrogen. No absorption of 4047 was observed upon the introduction of hydrogen, argon, neon, or helium into the resonance tube.
The resonance broadening of homogeneous Cs vapor in absorption was studied by means of the contour method. The intensities were obtained via the method of "astigmatic photometry" by utilizing the astigmatism of the Rowland grating. The pressure of the homogeneous absorbing vapor ranged from ${10}^{\ensuremath{-}2}$ to 17.5 mm Hg. The half breadth $\ensuremath{\gamma}$ varied rather linearly with the number of atoms per unit volume, with $(\frac{{\ensuremath{\gamma}}_{1}}{N})\ifmmode\times\else\texttimes\fi{}{10}^{7}=1.45$, $(\frac{{\ensuremath{\gamma}}_{2}}{N})\ifmmode\times\else\texttimes\fi{}{10}^{7}$ for the 2P32^{2}P_{\frac{3}{2}}2P23​​ and 2P12^{2}P_{\frac{1}{2}}2P21​​ eomponents of the resonance lines, respectively. The average value of the ratio of half breadths $\frac{{\ensuremath{\gamma}}_{1}}{{\ensuremath{\gamma}}_{2}}$ was found to be 1.8. The experimental half-width $\ensuremath{\gamma}$ is found to be about 1\textonehalf{} times larger than that predicted by W. V. Houston. Below pressures of 10 mm Hg the lines exhibited symmetrical broadening according to the "dispersion" formula. At higher pressures indications of a violet and red asymmetry are present for the 2P32^{2}P_{\frac{3}{2}}2P23​​ and 2P12^{2}P_{\frac{1}{2}}2P21​​ components, respectively. A definite band on the red side of the 2P32^{2}P_{\frac{3}{2}}2P23​​ and one on the violet side of the 2P12^{2}P_{\frac{1}{2}}2P21​​ was observed.
By direct measurement of the contours of the line wings, the resonance broadening of the sodium DDD lines in absorption was determined for vapor pressures of sodium ranging from ${10}^{\ensuremath{-}3}$ to 70 mm Hg with negligible amount of foreign gases. Over nearly the entire range, the half-intensity width varied linearly with the density of the absorbing atoms; i.e., $\frac{\ensuremath{\Delta}{\ensuremath{\nu}}_{\frac{1}{2}}}{N}=0.80\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}7}$ ${\mathrm{sec}.}^{\ensuremath{-}1}$ ${\mathrm{cm}}^{\ensuremath{-}3}$---the constant being 1.6 times that predicted by theory but much less than the corresponding experimental results for potassium. Above 5 mm pressure, $\ensuremath{\Delta}{\ensuremath{\nu}}_{\frac{1}{2}}$ increased slightly faster than NNN; moreover, the contour for the absorption coefficient was more adequately represented by an inverse cube contour than by the inverse square. Somewhat in contradiction to theory, the relative width, $\frac{\ensuremath{\Delta}{\ensuremath{\nu}}_{\frac{1}{2},8}}{\ensuremath{\Delta}{\ensuremath{\nu}}_{\frac{1}{2},l}}$ was 1.12. No definite evidence of van der Waals force was observed at the higher pressures; likewise no appreciable shifts or asymmetries. The natural width measured was consistent with previous results.