For $Li^{2+}$ ion,the ratio of radii $r_2 : r_5$ will be

If the wavelength of an electromagnetic radiation is $2000 \ \text{Å}$, what is its energy in ergs?

What is the wave number of the lowest energy transition associated with the Lyman series?

Which one of the following statements is not correct?

When an electron in a hydrogen atom jumps from an infinite state to the first stationary state,the wavelength of the emitted radiation will be ...... (Rydberg constant = $1.097 \times 10^7 \ m^{-1}$):

$(i)$ 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.