When an electron makes a transition from $(n+1)$ state to $n^{th}$ state,the frequency of emitted radiation is related to $n$ according to $(n >> 1)$:

The work functions of two metals ($M_A$ and $M_B$) are in the $1:2$ ratio. When these metals are exposed to photons of energy $6 \ eV$, the kinetic energy of liberated electrons of $M_A:M_B$ is in the ratio of $2.642:1$. The work functions (in $eV$) of $M_A$ and $M_B$ are respectively.

$(i)$ 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.

Calculate the wavelength of the emitted radiation when an electron transitions from $n = 3$ to $n = 2$ in a hydrogen atom. To which region does this radiation belong?

If the ionization energy of a hydrogen atom is $E$,then the ionization energy of $Li^{2+}$ will be ............ $E$.

Find the radius of the fourth orbit of a hydrogen atom if its radius of the first orbit is $R \text{ pm}$.