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Question

The key feature Of Bohr's theory Of spectrum Of hydrogen atom is the quantization Of angular momentum when an electron is revolving around a proton. We will extend this to a general rotational motion to find quantized rotational energy Of a diatomic molecule assuming it to be rigid. The rule to be applied is Bohr's quantization condition.A diatomic molecule has moment Of inertia I. By Bohr's quantization condition its rotational energy in the nth level (n=0 is not allowed) is


A
h2(n2)(8π2I)
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B
h2(n)(8π2I)
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C
nh28π2I
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D
n2h2(8π2I)
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Solution

The correct option is D n2h2(8π2I)
Given - * A Diatomic molecule- let, the structure of the molecule be like-

I=2mr2

we howe Rotational encrgy- E=12Iω2=mω2r2(1) By Bohr quantization of angular momentum 2 mwr2=nh2π(2) From eq(1) and (2) we get ,E=n2h216π2mr2=n2h28π2I

1994219_1068496_ans_86b7fb048fa04ad6bc709fc0c20ec337.JPG

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