The frequency of radiation absorbed or emitted when transition occurs between two stationary states with energies $E_1$ (lower) and $E_2$ (higher) is given by

Positronium consists of an electron and a positron (a particle which has the same mass as an electron,but opposite charge) orbiting round their common centre of mass. Calculate the value of the Rydberg constant for this system.

The radius of $3^{rd}$ orbit of hydrogen atom is $R \text{ pm}$. The radius of $2^{nd}$ orbit of $He^{+}$ ion (in $\text{pm}$) is

The binding energy of an $e^-$ in the ground state of a hydrogen atom is $13.6 \ eV$. The energy required to remove an electron from the ground state of a $He^+$ ion is:

For the $H$ spectrum,the limiting line in the $Balmer$ series has a frequency of ...... $(R_\infty = 3.29 \times 10^{15} \text{ cycles/s})$

For any given series of spectral lines of atomic hydrogen,let $\Delta \bar{\nu} = \Delta \bar{\nu}_{\max} - \Delta \bar{\nu}_{\min}$ be the difference in maximum and minimum wavenumbers in $cm^{-1}$. The ratio $\Delta \bar{\nu}_{\text{Lyman}} / \Delta \bar{\nu}_{\text{Balmer}}$ is