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THE ROTATIONAL SPECTRUM OF A DIATOMIC MOLECULE

**INTRODUCTION - SIMPLE MECHANICS AND WAVES**

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 = m_{1}.m_{2}/(m_{1} + m_{2})
.......(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 m_{1} and
m_{2} 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has now been superceded by a wave-mechanical treatment which completely abandons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.

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here to go to part 2