If in hydrogen atom, radius of $n^{ ext {th }}$ Bohr orbit is $r_n$, frequency of revolution of ele

Question

If in hydrogen atom, radius of $n^{	ext {th }}$ Bohr orbit is $r_n$, frequency of revolution of electron in $n^{	ext {th }}$ orbit is $f_n$, choose the correct option.

Professor PC Thomas Classes · Answer

(d) : Radius of $n^{	ext {th }}$ orbit $r_n \propto n^2$, graph between $r_n$ and $n$ is a parabola. Also, $\frac{r_n}{r_1}=\left(\frac{n}{1}ight)^2 \Rightarrow \log _e\left(\frac{r_n}{r_1}ight)=2 \log _e(e)$ Comparing this equation with $y=m x+c$, Graph between $\log _e\left(\frac{r_n}{r_1}ight)$ and $\log _e(n)$ will be a straight line, passing from origin. Similarly it can be proved that graph between $\log _e\left(\frac{f_n}{f_1}ight)$ and $\log _e n$ is a straight line. But with negative slops.