The wavelength of the spectral line obtained in the spectrum of $Li^{2+}$ ion, when the transition takes place between two levels whose sum is $4$ and difference is $2$, is

What is the amount of energy associated with the first orbit of a monopositive helium ion? $[R_{H} = 2.18 \times 10^{-18} \ J]$

The energy of the second excited state of the $Li^{2+}$ ion is ............... $eV$.

The wave number of the first emission line in the Balmer series of $H$ atom spectrum is ($R =$ Rydberg constant).

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?

For a hydrogen-like species,the ratio of velocities of electrons in the $I, II,$ and $III$ orbits,i.e.,$V_1 : V_2 : V_3$,will be: