A proton and a ${\mathrm{Li}}^{3+}$ nucleus are accelerated by the same potential. If ${\lambda }_{\mathrm{Li}}$ and ${\lambda }_{\mathrm{p}}$ denote the de Broglie wavelengths of ${\mathrm{Li}}^{3+}$ and proton respectively, then the value of $\frac{{\lambda }_{\mathrm{Li}}}{{\lambda }_{\mathrm{p}}}$ is $x\times {10}^{-1}$. The value of $\mathrm{x}$ is _____ (Rounded off to the nearest integer) [Mass of ${\mathrm{Li}}^{3+}=8.3$ mass of proton]

The wavelength of electrons accelerated from rest through a potential difference of $40\mathrm{kV}$ is $\mathrm{X}\times {10}^{-12} \mathrm{m}.$ The value of $\mathrm{x}$ is. (Nearest integer)

Given: Mass of electron $=9.1\times {10}^{-31} \mathrm{kg}$

Charge on an electron $=1.6\times {10}^{-19}\mathrm{C}$

Planck's constant $=6.63\times {10}^{-34}\mathrm{Js}$

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 

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