THE ROTATIONAL SPECTRUM OF A DIATOMIC MOLECULE

INTRODUCTION - SIMPLE MECHANICS AND WAVES

Figure 1 (applet) should be here!

There is a theory in elementary physics that you might have seen. It says that it is possible to study the dynamics of a "dumbbell" rotor, of the type shown in Figure 1, by a simple transformation. The two masses rotating about their centre of gravity can be replaced by a single mass, called the "reduced mass", rotating on a circle with a radius equal to the distance between the original masses as shown in Figure 2. The reduced mass is given by the equation:

M = m1.m2/(m1 + m2) .......(1)

Now why would we wish to do such a thing? The answer as follows: We can think of Figure 1 as representing a diatomic molecule; the values of m1 and m2 are the weights of the two atoms and r is the distance between them: a total of 3 parameters. After the transformation we have one less parameter, so any calculations on the physics of the system become somewhat simpler.


In the last part of the first "Dry Lab", you learned that a particle moving on a circle can be considered to have an associated wavelength that limits the momentum (to integral multiples of mvr), and thus the possible radii. Any particle moving in a circle is subject to the same physics. Although Bohr theory has now been superceded by a wave-mechanical treatment which completely abandons any attempt to treat the electron as a particle in an orbit, the basic idea can be applied to other systems. This includes the "reduced mass" whirling in its "orbit" that was described above. The main difference is that the radius is essentially fixed. The rotational motion of molecules and the information about their geometries which can be deduced by microwave absorption spectroscopy is the subject of this lab.

You will go through the steps involved in obtaining an experimental value for the bond length in a diatomic molecule from its microwave (rotational) spectrum.

Click here to go to part 2