Atoms & Nuclei

JEE Main level, single correct, medium

90 of 239

Question 90 of 239

A diatomic molecule is made of two masses m1m_1 and m2m_2 which are separated by a distance rr. If we calculate its rotational energy by applying Bohr's rule of angular momentum quantization, its energy will be given by ( nn is an integer)

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Answer: (D) (m1+m2)n2h22m1m2r2\frac{\left(m_1+m_2\right) n^2 h^2}{2 m_1 m_2 r^2}

r1=m2rm1+m2;r2=m1rm1+m2r_1=\frac{m_2 r}{m_1+m_2} ; r_2=\frac{m_1 r}{m_1+m_2}
(l1+l2)ω=nh2π=nh\left(l_1+l_2\right) \omega=\frac{n h}{2 \pi}=nh
K.E=12(l1+l2)ω2=n2h2(m1+m2)2m1m2r2K . E=\frac{1}{2}\left(l_1+l_2\right) \omega^2=\frac{n^2 h^2\left(m_1+m_2\right)}{2 m_1 m_2 r^2}

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