The energy of an electron in the ground state $(n=1)$ for $He^{+}$ ion is $-x \ J$. What is the energy for an electron in the $n=2$ state for $Be^{3+}$ ion in $J$?

If the wave number of radiation emitted for the electron transition from an excited state to ground state of hydrogen is $\frac{5x}{36} \ m^{-1}$,the wave number of radiation absorbed for the electron transition from the above excited state to the next immediate excited state in $m^{-1}$ is:

When an electron transitions from $n = 4$ to $n = 2$,the emitted spectral line will be ........

In Rutherford's experiment,generally the thin foil of heavy atoms,like gold,platinum etc. have been used to be bombarded by the $\alpha$-particles. If the thin foil of light atoms like aluminium etc. is used,what difference would be observed from the above results?

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 $He^{+}$?

The frequency of one of the lines in the Paschen series of a hydrogen atom is $2.340 \times 10^{11} \ Hz$. The quantum number $n_2$ which produces this transition is