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The key feature of Bohr'[s spectrum of h...

The key feature of Bohr'[s 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 quntized rotantized rotational energy of a diatomic molecule assuming it to be right . The rate to energy applied is Bohr's quantization condition
it is found that the excitation from ground to the first excited state of rotation for the `CO` molecule is close to `(4)/(pi) xx 10^(11) Hz` then the moment of inertia of `CO` molecule about its center of mass is close to
`(Take h = 2 pi xx 10^(-34) J s )`

A

`2.76 xx 10^(-46) kg m^(2)`

B

`1.87 xx 10^(-46) kg m^(2)`

C

`4.67 xx 10^(-47) kg m^(2)`

D

`1.17 xx 10^(-47) kg m^(2)`

Text Solution

Verified by Experts

The correct Answer is:
B
Energy given = change in kinetic energy
`hv= K_(1) - K_(i) = (h^(2))/(8n pi^(2) 1) (2^(2) - 1^(2))` [from(i)]
`rArr hv = (3h^(2))/(8 n^(2) 1 ) `
rArr 1 = (3h)/(8 pi^(2) v ) = (3 xx 2 pi xx 10^(-34))/(8 pi ^(2) xx (4)/(pi) xx 10^(11) = (3)/(10) xx 10^(-45)`
` = 1.87 xx 10^(-46) kg m^(2)`
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