For determining the vibrational temperature of N2(C) state by Boltzmann plot method, the graph is plotted in two ways:
1) log (intensity* transition frequency4*franck condon factor) on y-axis and energy on x-axis
2) Population density ratio on y-axis and wavenumber x-axis.
Both give a straight line. I want to know the relation between both methods and whether they are interchangeable.
They are more or less equivalent. Wavenumber and energy are related by a factor of hc. The intensity is proportional to density x v^4 x FC factor, if you neglect the dependence of Re^2 on transition number, and the intensity is optically thin. (If those were not at least approximately true, the straight line fit would fail).
I think you meant divided by on the first one and log on the second.
They are more or less equivalent. Wavenumber and energy are related by a factor of hc. The intensity is proportional to density x v^4 x FC factor, if you neglect the dependence of Re^2 on transition number, and the intensity is optically thin. (If those were not at least approximately true, the straight line fit would fail).
I think you meant divided by on the first one and log on the second.
Brett,
I too am puzzled by the coefficient for spontaneous emissions from vibrational transitions. Einstein (1917) reckoned that it increases with the third power of the frequency, whereas Goody and Yung (1989), Eq. 2.52 have it related to the square of the frequency. Here, you seem to be suggesting it increases with the fourth power of the frequency. Do you know where can I find a clear description of how to obtain the correct Einstein coefficient?
Yes, the A coefficient goes as the cube of the frequency. A coefficient times density is a rate (e.g. photons/s/m3). To convert to intensity, multiply by energy per photon, which is proportional to frequency : hence v^4.
I am not familiar with Goody and Yung's text but from the google books preview their eq 2.52 is a ratio of A and B (they call it C) coefficients, so is not the same as intensity.
The correct form of the Einstein coefficient(s) probably appears later in their text (not part of the free preview), but should also be found in any of a number of molecular spectroscopy books, such as that of Herzberg.
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