A diatomic gas molecule consists of two atoms of mass separated by a fixed distance rotating about an axis as indicated in the figure. Assuming that its angular momentum is quantized as in the Bohr atom, we have to determine (a) the possible angular velocities and (b) the possible rotational energies. (c) We have to calculate, according to this model, in eV, of an molecule in which and .

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(a)

Let be the angular velocity with which the two atoms, each of mass , are rotating, as shown in the figure. The total angular momentum of this system about the axis of rotation will be

Applying the Bohr quantization condition on the angular momentum, we get

We thus note that the angular velocities are quantized and are given by the equation

(b)

The rotational energies of this system will be determined by the quantized angular velocities as follows:

(c)

We will calculate next using this model the ground state energy in eV of the molecule with and .

We will use the following data and values:

The ground state of the molecule will correspond to . Substituting the above data in the formula for the quantized rotator, we get