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

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 n text th level ( n =0 is not allowed) is (A) (1/ n 2)(( h 2/8 π2 I )) (B) (1/ n )(( h 2/8 π2 I )) (C) n (( h 2/8 π2 I )) (D) n2(( h 2/8 π2 I ))

Tardigrade Admin · Accepted Answer

L =( nh /2 π) K . E .=( L 2/2 I )=(( nh /2 π))2 (1/2 I )

$\frac{1}{n ^{2}} (\frac{h ^{2}}{8 π ^{2} I})$

$\frac{1}{n} (\frac{h ^{2}}{8 π ^{2} I})$

$n (\frac{h ^{2}}{8 π ^{2} I})$

$n^{2} (\frac{h ^{2}}{8 π ^{2} I})$

$L = \frac{nh}{2 π}$
$K . E . = \frac{L ^{2}}{2 I} = (\frac{nh}{2 π})^{2} \frac{1}{2 I}$

n21​(8π2Ih2​)

n1​(8π2Ih2​)

n(8π2Ih2​)

n2(8π2Ih2​)

L=2πnh​ K.E.=2IL2​=(2πnh​)22I1​

$\frac{1}{n ^{2}} (\frac{h ^{2}}{8 π ^{2} I})$

$\frac{1}{n} (\frac{h ^{2}}{8 π ^{2} I})$

$n (\frac{h ^{2}}{8 π ^{2} I})$

$n^{2} (\frac{h ^{2}}{8 π ^{2} I})$

$L = \frac{nh}{2 π}$
$K . E . = \frac{L ^{2}}{2 I} = (\frac{nh}{2 π})^{2} \frac{1}{2 I}$