The orbital frequency of an electron in the hydrogen atom is proportional to

For any given series of spectral lines of atomic hydrogen, let  $\mathrm{\Delta }\stackrel{-}{\mathrm{v}}={\stackrel{-}{\mathrm{v}}}_{\mathrm{m}\mathrm{a}\mathrm{x}}-{\stackrel{-}{\mathrm{v}}}_{\mathrm{m}\mathrm{i}\mathrm{n}}$  be the difference in maximum and minimum wave number in $\mathrm{c}{\mathrm{m}}^{-1}$. 

The ratio $\mathrm{\Delta }{\stackrel{-}{\mathrm{v}}}_{\mathrm{L}\mathrm{y}\mathrm{m}\mathrm{a}\mathrm{n}}/\mathrm{\Delta }{\stackrel{-}{\mathrm{v}}}_{\mathrm{B}\mathrm{a}\mathrm{l}\mathrm{m}\mathrm{a}\mathrm{r}}$ is

Given below are two statements :
Statement I : According to Bohr's model of an atom, qualitatively the magnitude of velocity of electron increases with decrease in positive charges on the nucleus as there is no strong hold on the electron by the nucleus.
Statement II : According to Bohr's model of an atom, qualitatively the magnitude of velocity of electron increases with decrease in principle quantum number.

In the light of the above statements, choose the most appropriate answer from the options given below:

The longest wavelength of light that can be used for the ionisation of lithium atom $\left(\mathrm{Li}\right)$ in its ground state is $\mathrm{x}\times {10}^{-8} \mathrm{m}$. The value of $\mathrm{x}$ is (Nearest Integer)

(Given : Energy of the electron in the first shell of the hydrogen atom is $-2.2\times {10}^{-18} \mathrm{J}$; $\mathrm{h}=6.63\times {10}^{-34}\mathrm{Js}$ and $\mathrm{c}=3\times {10}^8{ \mathrm{ms}}^{-1}$)

The figure below is the plot of potential energy versus internuclear distance $\left(\mathrm{d}\right)$ of ${\mathrm{H}}_2$ molecule in the electronic ground state. The value of the net potential energy ${\mathrm{E}}_0$ (as indicated in the figure) is $-5.24649\times {10}^{\mathrm{n}}$ $\mathrm{kJ} {\mathrm{mol}}^{-1},$ for $\mathrm{d}={\mathrm{d}}_0$ at which the electron-electron repulsion and the nucleus-nucleus repulsion energies are absent, find the value of $\mathrm{n}$ to the nearest integer value.

As reference, the potential energy of $\mathrm{H}$ atom is taken as zero when its electron and the nucleus are infinitely far apart.

Use Avogadro constant as $6.023\times {10}^{23} {\mathrm{mol}}^{-1}.$  Give an answer to the nearest integer value.

The electron in the ${\mathrm{n}}^{\mathrm{th} }$ orbit of ${\mathrm{Li}}^{2+}$  is excited to $(\mathrm{n}+1)$ orbit using the radiation of energy $1.47\times {10}^{-17} \mathrm{J}$ (as shown in the diagram). The value of $\mathrm{n}$ is ___________

Given : ${\mathrm{R}}_{\mathrm{H}}=2.18\times {10}^{-18} \mathrm{J}$

The ionization energy of gaseous $\mathrm{Na}$ atoms is $495.5 \mathrm{kJ} {\mathrm{mol}}^{-1}$. The lowest possible frequency of light that ionizes a sodium atom is 

$(\text{h}=\text{6.626}\times 10^{-34} Js, N_{\text{A}}=\text{6.022}\times 10^{23} {mol}^{-1})$