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A diatomic gas molecule consists of two atoms of mass m seperated by a fixed distance d rotating about an axis as shown. Assuming that its angular momentum is quantized just as in the Bohr atom, determine a) the quantized angular speed, b) the quantized rotational energy.

Note: The diagram consists of two point masses of mass m rotating about an axis with angular speed &omega seperated by a distance d.

Here is my solution:

The assumption made by Bohr under his model of the hydrogen atom: angular momentum is quantized according to L = nh/(2&pi)

The following model of quantized &omega and E of the diatomic molecule will use the same assumption.

L = 2mvr = nh/(2&pi)

Substitute: v = r&omega

2m(r&omega)r = nh/(2&pi)

Substituing: r = 1/2d, and solving for &omega we find:

&omega = nh/(&pi md^{2})

For rotational E:

E =1/2I&omega^{2}

I = 2mr^{2}

Substituting: r = 1/2d into I

I = 1/2md^{2}

Substituting I and &omega^{2}in E:

We find:

E = n^{2}h^{2}/(4m&pi^{2}d^{2})

Is my solution correct?

Thanks

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# Quantized angular momentum of diatomic gas molecule: Bohr Model

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