A single electron system has ionization energy $11180 kJ mo{l}^{-1}$. The number of protons in the nucleus of the system will be__________.

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 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 

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