Microwave Intensity 2 - Intensity Of Microwave Lines
As the separation between rotational levels is quite small, many rotational levels are populated at normal temperatures. As rotational transitions can therefore occur from a variety of levels, the population has a large effect on the spectrum. As the temperature increases, the population of levels with high J values increases and so transitions from these levels increase in intensity in the spectrum.
The population of a level with rotational quantum number J (NJ) compared to the population of the lowest level (J = 0) is given by:
This is not the only factor which governs the intensity of the lines in the microwave spectrum, however. The intensity also depends on:
the value of J - as the molecule rotates faster at higher J values, the change in the dipole moment increases leading to higher intensity,
the frequency of the transition as this affects the net absorption rate (i.e. the absorption minus the emission).
The overall intensity is given by:
Input values into the calculator below for the rotational constant, centrifugal constant (both in cm-1) and the temperature and press "calculate" to work out the transition energies (in cm-1), the relative populations and overall intensity. The extra factors lead to increased intensity for higher J values so the maximum in the intensity is at a higher J value than given by the population. Press "graphical" to see an interactive graph showing this.
