Question

Choose the correct relation on the basis of bohr's theory.

• A. $\text{Velocity of electron}\propto \frac{1}{n}$
• B. $\text{Frequency of revolution}\propto \frac{Z^2}{n^3}$
• C. $\text{Radius of orbit}\propto \frac{n^2}{Z}$
• D. $\text{Force on electron}\propto \frac{Z^3}{n^4}$

Answer 1

Answer: (A), (B), (C), (D)

$\text{Force on electron}\propto \frac{Z^3}{n^4}$

(a) Velocity of electron in $n_{th}$ bohr's orbit $\left(v\right)=2.18\times {10}^6\times \frac{Z}{n}\Rightarrow v\propto \frac{Z}{n}\text{or}v\propto \frac{1}{n}$
(b) Frequency of electron in $n_{th}$ bohr's orbit $\left(f\right)=\frac{v}{2\pi r}\text{or}f\propto \frac{v}{r}\propto \frac{Z/n}{n^2/Z}$
$f\propto \frac{Z^2}{n^3}$
(c) Radius of electron in $n_{th}$ bohr's orbit $\left(r\right)=0.529\frac{n^2}{Z}\stackrel{o}{A}$
$r\propto \frac{n^2}{Z}\stackrel{o}{A}$
$\left(d\right)F=\frac{m{v}^2}{r}\therefore F\propto \frac{v^2}{r}\frac{\left(Z^2/n^2\right)}{n^2/Z}F\propto \frac{Z^3}{n^4}$
Thus option (A,B,C,D) are correct.