Question

The frequency of an electron is $n$ when it is revolving around nucleus of hydrogen atom in $1st$ orbit. The frequency of same electron when it is revolving in $2nd$ orbit is

• A. $4n$
• B. $\frac{n}{4}$
• C. $8n$
• D. $\frac{n}{8}$

Answer 1

The correct option is D $\frac{n}{8}$

Angular velocity $\omega =\frac{v}{r}$

but $v\propto \frac{1}{n}$ and $r\propto n^2$

$\Rightarrow \omega \propto \frac{1}{n^3}$

$\therefore \frac{{\omega }_1}{{\omega }_2}=\frac{n_1}{n_2}=\frac{1}{\frac{1}{8}}$

$\Rightarrow n_2=\frac{n}{8}$