Chemistry - Atomic Structure Question with Solution | TestHub

According to the Bohr's atomic theory, the kinetic energy of an electron is directly proportional to the square of the atomic number and inversely proportional to the square of the principal quantum number. 

(A) $\mathrm{KE}=13.6\frac{{\mathrm{z}}^2}{{\mathrm{n}}^2}\frac{\mathrm{eV}}{\mathrm{atom}}\Rightarrow \mathrm{KE\alpha }\frac{{\mathrm{z}}^2}{{\mathrm{n}}^2}$

(B) speed of ${\mathrm{e}}^{-}\mathrm{\alpha }\frac{\mathrm{z}}{\mathrm{n}}$

$\therefore \mathrm{v}\times \mathrm{n\alpha z}$

(C) Frequency of revolution of ${\mathrm{e}}^{-}=\frac{\mathrm{v}}{2\mathrm{\pi r}}$

$\therefore$ Frequency $\mathrm{\alpha }\frac{{\mathrm{z}}^2}{{\mathrm{n}}^3}$

(D) Coulombic force of attraction on the electron is directly proportional to the square of the atomic number and inversely proportional to the fourth power of the principal quantum number. 

 $\mathrm{F}=\frac{{\mathrm{kq}}_1{\mathrm{q}}_2}{{\mathrm{r}}^2}=\frac{{\mathrm{kze}}^2}{{\mathrm{r}}^2} \left\{\mathrm{r\alpha }\frac{{\mathrm{n}}^2}{\mathrm{z}}\right.$

$\Rightarrow \mathrm{F\alpha }\frac{\mathrm{z}}{{\left(\frac{{\mathrm{n}}^2}{\mathrm{z}}\right)}^2}$

$\Rightarrow \mathrm{F\alpha }\frac{{\mathrm{z}}^3}{{\mathrm{n}}^4}$