If the potential energy of an electron in a hydrogen atom is $-3.02 \ eV$,then the electron is present in which of the following excited states?

According to Bohr's model,the energy of an electron is given by $E = -\frac{2.176 \times 10^{-18}}{n^2} \, J \, atom^{-1}$. Calculate the minimum energy required to remove an electron from the $3^{rd}$ orbit of a $He^{+}$ ion,and also calculate the corresponding wavelength of the photon.

The wavelength of a particular electron transition for $He^{+}$ is $100 \ nm$. The wavelength (in $\mathring{A}$) of $H$ atom for the same transition is

The frequency of a certain line of the Lyman series of the atomic spectrum of the $H$ atom satisfies the following conditions:
$(i)$ It is the sum of the frequency of another Lyman line and a Balmer line.
$(ii)$ It is the sum of the frequency of a certain line,a Lyman line,and a Paschen line.
$(iii)$ It is the sum of the frequency of a Lyman and a Paschen line but no Brackett line.
To what transition does this frequency correspond?

The ionization energy of a hydrogen atom is $13.6 \ eV$. The energy required to ionize a hydrogen atom in its second excited state is ........... $eV$.

The energy of an electron in an orbit of a hydrogen-like ion with an orbit radius of $52.9 \ pm$ in $J$ is (ground state energy of an electron in a hydrogen atom is $-2.18 \times 10^{-18} \ J$).