The energy of the third orbit of $Li^{2+}$ ion (in $J$) is

$(i)$ What is the energy of an electron for hydrogen in $J \ atom^{-1}$ and $J \ mol^{-1}$?
$(ii)$ Calculate the energy of this electron per mole for the first transition ($n=1$ to $n=2$).
$(iii)$ Calculate the ionization energy of hydrogen.

The wavelength of the radiation emitted,when in a hydrogen atom an electron falls from infinity to stationary state $n=1$,would be ............... $nm$ (Rydberg constant $= 1.097 \times 10^7 \ m^{-1}$)

The maximum energy is present in any electron at

Calculate the energy associated with the first orbit of $He^{+}$. What is the radius of this orbit?

Explain the hydrogen spectrum using Bohr's model.