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Wavenumber Calibration Tables from Heterodyne Frequency Measurements - banner


Appendix: Useful Equations and Formulas

Conversion factors:

dipole moment or transition moment:
1 debye = 3.335 64 × 10-30 C·m
wavenumber:
1 cm-1 = 29 979.2458 MHz
pressure:
1 atm = 101 325. Pa (pascal)
1 torr = 133.322 Pa
absorption intensity:
1 cm-2 atm-1 at 296 K = 4.033 × 10-20 cm/molecule


Useful equations:

Boltzmann factor:
Ni = Nj exp(-1.439 Eij / T),
where Ni is the population of the ith level and Nj is the population of the jth level with energy difference in cm-1 of Eij at a temperature of T kelvin.

Doppler half-width at half intensity, γD :
γD = 3.581 × 10-7 ν (T/M )1/2,
where ν is the frequency in the same units as γD , T is the temperature in kelvin, and M is the mass of the molecule in atomic mass units.

Peak intensity of a Doppler shaped line:
% transmission = 100 exp(-1.1494 × 1014 Slp/γD),
where S is the intensity given in the tables, l is the pathlength in cm, and p is the pressure in Pa.

Peak intensity of a Lorentzian line:
% transmission = 100 exp(-0.7789 × 1014 Slp/γL),
where S is the intensity given in the tables, γL is the Lorentzian half-width at half height, l is the pathlength in cm, and p is the pressure in Pa.


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