The wavelength of a spectral line emitted by a hydrogen atom in the Lyman series is $\frac{16}{15 R} \ cm$. What is the value of $n_2$? $(R = \text{Rydberg constant})$

If the shortest wavelength of the hydrogen atom in the Lyman series is $x$, then the longest wavelength in the Balmer series of $He^+$ is:

In the ground state of $He^{+}$ ion,how much energy must be supplied to the electron so that the second line of the Balmer series is obtained in its spectrum? ................. $eV$

The electron present in an excited state of $He^{+}$ ion shows separation (ionization) on collision with an electron having $2.5 \ eV$ energy. What will be the minimum value of $n$ for this electron of $He^{+}$ ion?

The ground state energy of a $H$ atom is given as $-13.6 \, eV$. The energy of the second excited state will be .......... $eV$.

The wavenumber of the first line $(n_2=3)$ in the Balmer series of hydrogen is $\bar{\nu}_1 \ cm^{-1}$. What is the wavenumber (in $cm^{-1}$) of the second line $(n_2=4)$ in the Balmer series of $He^{+}$?