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On the Width and Intensity of the Absorption Line of Mercury.
Chr. Füchtbauer and G. Joos. Über Intensität und Verbreitung von Spektrallinien. Physikalische Zeitschrift 23, p. 73, 1922.
The width of the emission and absorption lines of gases under normal conditions for obtaining a spectrum is extremely small; therefore the study of the distribution of intensity as a function of wavelength is in this case possible only either with an enormous dispersion of the spectral instrument (for example, Michelson’s echelon grating), or by the interference method. If, into a volume filled with the vapor under investigation suitable for it at very low pressure, another gas, completely transparent in the given region of the spectrum, is introduced, then the absorption line is broadened, and the more so, the greater the pressure of the foreign inert gas. Taking advantage of this circumstance, Füchtbauer and his collaborators were able to apply the ordinary photometric method to the study of spectral lines. In the paper reviewed, the results are reported of measurements made on the mercury absorption line 253.7 μμ. As transparent inert gases admixed with saturated mercury vapor, \(H_2\), \(N_2\), and \(CO_2\) were used, the limiting pressure being 50 atmospheres. The results of the work are as follows:
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The form of the absorption curve in the presence of different gases is different. For \(CO_2\) and \(N_2\) the curve is asymmetric with respect to the maximum of absorption; for \(H_2\) almost complete symmetry is obtained.
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The so-called “width” of a spectral line (i.e., the distance in wavelengths, or in frequencies, between those two ordinates of the absorption curve that are half the maximum) for \(H_2\) and \(N_2\) proves to be quite proportional to the pressure.
For \(CO_2\) no such proportionality has been found; the “width” in this case is approximately proportional to \(p^{1/3}\).
- The fraction of light transmitted in passing through a thickness \(l\) of the absorbing gas, according to Bouguer’s law, may be expressed as follows:
\[ q = e^{-4\pi n k \frac{l}{\lambda}} \]
where \(n\) is the refractive index, \(k\) the absorption coefficient, \(\lambda\) the wavelength. In the absorption curves, the values of \(nk\) are plotted on the ordinate axis, while
\[ \int_{0}^{\infty} nk\, d\nu \]
corresponds to the “magnitude” of the total absorption.
In Füchtbauer’s experiments the magnitude of the absorption (computed graphically with the aid of a planimeter) proved, for all gases, to depend on the pressure. The value of the integral decreases linearly as the pressure is increased.
This decrease is especially considerable for \(CO_2\).
4. In the classical theory of dispersion the number of dispersing electrons is expressed as follows:
\[ N=\frac{4\pi m}{e^2}\int_0^\infty n\kappa\,d\nu, \]
where \(\nu\) is the frequency of the light oscillations, and \(e\) and \(m\) are the charge and mass of the electron. On the other hand, knowing the pressure of mercury vapor, one can calculate the number \(M\) of all mercury atoms.
In Füchtbauer’s experiments
\[ \frac{M}{N}=45.4, \]
i.e., only less than \(2\%\) of the total number of mercury atoms simultaneously take part in the absorption of light of \(253.7\ \mu\mu\).
5. With increasing pressure the maximum of the absorption curve shifts toward the red side of the spectrum. The shift is proportional to the pressure for \(H_2\) and \(CO_2\), and increases according to a more complex law for \(N_2\).
The present work is the first strictly quantitative study of the influence of various factors on the broadening of the spectral line of so simple a body as monatomic mercury. The experimental results do not fit within the framework of any of the existing theories.
S. Vavilov.