The angular momentum of the orbital electron is an integral multiple of:

The ratio of the areas of the electron orbits for the second excited state to the first excited state for the hydrogen atom is

The time period of revolution of an electron in its ground state orbit in a hydrogen atom is $1.6 \times 10^{-16} \; s$. The frequency of revolution of the electron in its first excited state (in $s^{-1}$) is:

An electron from various excited states of a hydrogen atom emits radiation to return to the ground state. Let $\lambda_n$ and $\lambda_g$ be the de Broglie wavelength of the electron in the $n^{th}$ state and the ground state,respectively. Let $\Lambda_n$ be the wavelength of the emitted photon in the transition from the $n^{th}$ state to the ground state. For large $n$,which of the following relations holds true ($A, B$ are constants)?

Consider a hydrogen-like atom whose energy in the $n^{th}$ excited state is given by $E_n = - \frac{13.6 Z^2}{n^2}$. When this excited atom makes a transition from an excited state to the ground state, the most energetic photons have energy $E_{max} = 52.224 \ eV$ and the least energetic photons have energy $E_{min} = 1.224 \ eV$. The atomic number of the atom is:

In a hypothetical Bohr hydrogen atom, if the mass of the electron is doubled, then the energy of the electron in the first orbit is: (in $\text{ eV}$)