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The key feature of Bohr's theory of spec...

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 n`.^(th)` level (`n=0` is not allowed) is:

A

`(1)/(n^(2))((h^(2))/(8pi^(2)I))`

B

`(1)/(n)((h^(2))/(8pi^(2)I))`

C

`n((h^(2))/(8pi^(2)I))`

D

`n^(2)((h^(2))/(8pi^(2)I))`

Text Solution

Verified by Experts

The correct Answer is:
D
`E_(n)=1/2 I omega^(2)=((I omega)^(2))/(2 I)=((nh//2pi)^(2))/(2 I)=(n^(2)h^(2))/(8pi^(2) I)`
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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 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 n^(th) level ( n = 0 is not allowed ) is

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 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 n^(th) level ( n = 0 is not allowed ) is

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 quantized rotational energy of a diatomic molecule assuming it to be rigid.The rule to be applied is Bohr's quantization condition. In a CO molecule, the distance between C (mass = 12 a. m. u ) and O (mass = 16 a.m.u) where 1 a.m.u = (5)/(3) xx 10^(-27) kg , is close to

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 quantized rotational energy of a diatomic molecule assuming it to be rigid.The rule to be applied is Bohr's quantization condition. In a CO molecule, the distance between C (mass = 12 a. m. u ) and O (mass = 16 a.m.u) where 1 a.m.u = (5)/(3) xx 10^(-27) kg , is close to

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 quantized rotational energy of a diatomic molecule assuming it to be rigid.The rule to be 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 )

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