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) $F =\frac{ kq _{1} q _{2}}{ r ^{2}}=\frac{ kze ^{2}}{ r ^{2}}$

$\left\{ r \alpha \frac{ n ^{2}}{ z }\right.$

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

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