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The potential energy between atoms of a hydrogen mole- cule may be described by the Morse potential,
where Vo = 7 ×10—19 J, ro = 8×10—11 m, and a = 5×10—11 m.
Sketch a graph of V (r) versus r. Calculate the characteristic temperatures of vibration and rotation to compare with exper- imental data (see table on Section 8.4).
Physics
Note that
which shows the existence of a minimum at r = ro.
The characteristic temperature of rotation is given by
where I is the moment of inertia and M is the reduced mass of the hydrogen molecule.
From the frequency of vibrations,
we write the characteristic temperature of vibrations,
Now it is easy to check the numerical predictions.
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