Bohr Model: Orbits, Speed & Angular Momentum question from JEE Main 2012 (AIEEE)

Answer: (d)

1. Moment of inertia $I = \mu r^2$ with reduced mass $\mu = \frac{m_1 m_2}{m_1 + m_2}$.
2. Bohr rule $L = n\hbar$, so $E = \frac{L^2}{2I} = \frac{n^2\hbar^2 (m_1 + m_2)}{2 m_1 m_2 r^2}$.
3. Writing $h$ for $\hbar$ as the options do, $E = \frac{(m_1+m_2) n^2 h^2}{2 m_1 m_2 r^2}$.
4. So the answer is (d).