Introduction to High Resolution Spectroscopy 

Introduction Rotational Vibrational Miscellaneous

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:

(2j+1) times by boltzmann factor

where EJ is the energy of the level in joules.

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:

intensity is proportional to the square of the frequency times (J+1) times the Boltzmann factor

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.

Once you have covered all of the available resources for rotational spectroscopy, you should test your knowledge and understanding with the self test.

intensity of microwave lines

 
rotational constant
B (cm-1)


centrifugal constant
D (cm-1)

temperature (K)






      J             energy            population     transition energy     intensity


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