Modern Physics 1 Question 30
27. It is found that the excitation frequency from ground to the first excited state of rotation for the CO molecule is close to $\frac{4}{\pi} \times 10^{11} Hz$. Then the moment of inertia of $CO$ molecule about its centre of mass is close to (Take $\left.h=2 \pi \times 10^{-34} J-s\right)$
(a) $2.76 \times 10^{-46} kg-m^{2}$
(b) $1.87 \times 10^{-46} kg-m^{2}$
(c) $4.67 \times 10^{-47} kg-m^{2}$
(d) $1.17 \times 10^{-47} kg-m^{2}$
(2010)
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Solution:
- $h v=K _2-K _1=\frac{3 h^{2}}{8 \pi^{2} I}$
$$ \begin{aligned} \therefore I=\frac{3 h}{8 \pi^{2} f} & =\frac{3 \times 2 \pi \times 10^{-34} \times \pi}{8 \times \pi^{2} \times 4 \times 10^{11}} \\ & =1.87 \times 10^{-46} kgm^{2} \end{aligned} $$
