A diatomic molecule is made of two masses m_1 | vedclass

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(A) The rotational energy of a system is given by $E = \frac{L^2}{2I}$,where $L$ is the angular momentum and $I$ is the moment of inertia.According to

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$\frac{(m_1 + m_2)n^2 h^2}{8 \pi^2 m_1 m_2 r^2}$

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(A) The rotational energy of a system is given by $E = \frac{L^2}{2I}$,where $L$ is the angular momentum and $I$ is the moment of inertia.According to Bohr's quantization rule,$L = \frac{nh}{2\pi}$.The moment of inertia $I$ for a diatomic molecule about its center of mass is $I = \mu r^2$,where $\mu = \frac{m_1 m_2}{m_1 + m_2}$ is the reduced mass.Substituting $L$ and $I$ into the energy formula:$E = \frac{(nh/2\pi)^2}{2(\frac{m_1 m_2}{m_1 + m_2})r^2}$$E = \frac{n^2 h^2}{4\pi^2 \cdot 2 \cdot \frac{m_1 m_2}{m_1 + m_2} r^2}$$E = \frac{(m_1 + m_2)n^2 h^2}{8\pi^2 m_1 m_2 r^2}$.

$A$ diatomic molecule is made of two masses $m_1$ and $m_2$ which are separated by a distance $r$. If we calculate its rotational energy by applying Bohr's rule of angular momentum quantization,its energy will be given by: ($n$ is an integer)

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