$A$ diatomic molecule has moment of inertia $I$. By applying Bohr's quantization condition,its rotational energy in the $n^{\text{th}}$ level is $[n \geq 1]$ $(h = \text{Planck's constant})$

The number of absorption transitions between the first and the fourth energy states of a hydrogen atom is $3$. The number of emission transitions between these states will be

In Bohr's model of the hydrogen atom,which of the following pairs of quantities are quantized?

An electron moves in a Bohr orbit. The magnetic field at the centre is proportional to

The inverse square law in electrostatics is $|\vec F| = \frac{{{e^2}}}{{4\pi { \in _0}{r^2}}}$ for the force between an electron and a proton. The $\frac{1}{r^2}$ dependence of $|\vec F|$ can be understood in quantum theory as being due to the fact that the particle of light (photon) is massless. If photons had a mass $m_p$,the force would be modified to $|\vec F| = \frac{{{e^2}}}{{4\pi { \in _0}}}\left( {\frac{1}{{{r^2}}} + \frac{\lambda }{r}} \right)\left( {{e^{ - \lambda r}}} \right)$ where $\lambda = \frac{{{m_p}c}}{\hbar }$ and $\hbar = \frac{h}{{2\pi }}$. Estimate the change in the ground state energy of a $H$-atom if $m_p$ were $10^{-6}$ times the mass of an electron.

The total energy of an electron in the $n^{th}$ orbit of a hydrogen atom is $E_n$. The total energy of an electron in the $n^{th}$ orbit of a $He^+$ ion is .........