Question

According to Bohr's atomic theory :-
(A) Kinetic energy of electron is $\propto \frac{Z^2}{n^2}$.
(B) The product of velocity (v) of electron and principal quantum number (n), 'vn' $\propto Z^2$.
(C) Frequency of revolution of electron in an orbit is $\propto \frac{Z^3}{n^3}$.
(D) Coulombic force of attraction on the electron is $\propto \frac{Z^3}{n^4}$.
Choose the most appropriate answer from the options given below:

• A. (C) Only
• B. (A) Only
• C. (A), (C) and (D) only
• D. (A) and (D) only

Answer 1

Answer: (D)

According to Bohr's theory :

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

$\Rightarrow KE\alpha \frac{z^2}{n^2}$

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

$\therefore v\times n\alpha z$

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

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

(D) $F=\frac{k{q}_1{q}_2}{r^2}=\frac{kz{e}^2}{r^2}$

$\{r\alpha \frac{n^2}{z}$

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

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