The energy level diagram for a hydrogen-like atom is shown in the figure. The radius of its first Bohr orbit is

The ratio of acceleration of the electron in a singly ionized Helium atom $(He^+)$ to that of a Hydrogen atom $(H)$ (both in the ground state) is:

When the electron orbiting in a hydrogen atom in its ground state moves to the third excited state,the de-Broglie wavelength associated with it

An excited hydrogen atom emits a photon of wavelength $\lambda$ in returning to the ground state. The quantum number $n$ of the excited state is ($R=$ Rydberg's constant).

Show that the first few frequencies of light that is emitted when electrons fall to the $n^{\text{th}}$ level from levels higher than $n$,are approximate harmonics (i.e.,in the ratio $1:2:3...$) when $n >> 1$.

In a hydrogen atom and a $Li^{2+}$ ion,the electron is in the second excited state. If $l_{H}$ and $l_{Li}$ are the angular momenta of the electrons and $E_H$ and $E_{Li}$ are their respective energies,then: