Q. In the Bohr model of the hydrogen atom, let $R,v$ and $E$ represent the radius of the orbit, the speed of electron and the total energy of the electron respectively. Which of the following quantity is proportional to the quantum number $n$
A) $R/E$
B) $E/v$
C) $RE$
D) $uR$
Explanation
(d) Rydberg constant $R = \frac{\varepsilon_{0}n^{2}h^{2}}{\pi mZe^{2}}$
Velocity $v = \frac{Ze^{2}}{2\varepsilon_{0}nh}$ and energy $E = - \frac{mZ^{2}e^{4}}{8\varepsilon_{0}^{2}n^{2}h^{2}}$
Now, it is clear from above expressions $R.v \propto n$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.