Q. The orbital frequency of an electron in the hydrogen atom is proportional to
A) $n^{3}$
B) $n^{- 3}$
C) n
D) $n^{0}$
Explanation
(b) Time period of electron, T= $\frac{4\varepsilon_{0}^{2}n^{3}h^{3}}{mZ^{2}e^{4}}$
$\therefore\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ T \propto n^{3}$
$\therefore\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \frac{1}{frequency\ (f)}\ \propto n^{3}$
or $\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ f \propto n^{- 3}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.