The first use of quantum theory to explain the structure of the atom was made by

The wave number of the last line of the Lyman series of the atomic spectrum of the $H$ atom corresponds to :-

If a hydrogen atom is excited by an energy of $8.4 \ eV$,what will be the number of spectral lines emitted?

$(i)$ The energy associated with the first orbit in the hydrogen atom is $-2.18 \times 10^{-18} \, J \, atom^{-1}$. What is the energy associated with the fifth orbit?
$(ii)$ Calculate the radius of Bohr's fifth orbit for the hydrogen atom.

The speed of the electron (in $ms^{-1}$) in the third orbit of a hydrogen atom is approximately (mass of electron $= 9.1 \times 10^{-31} \ kg$).

The distance between the $4^{th}$ and $3^{rd}$ Bohr orbits of $He^{+}$ is $:-$