Q. The ratio of the speed of the electron in the first Bohr orbit of hydrogen and the speed of light is equal to (where $e,h$ and $c$ have their usual meanings)
A) $2\pi hc/e^{2}$
B) $e^{2}h/2\pi c$
C) $e^{2}c/2\pi h$
D) $2\pi e^{2}/hc$
Explanation
(d) Speed of electron in $n^{th}$ orbit (in CGS) $v_{n} = \frac{2\pi Ze^{2}}{nh}(k = 1)$
For first orbit of $H_{1};n = 1$ and $Z = 1$
So $v = \frac{2\pi e^{2}}{h} \Rightarrow \frac{v}{c} = \frac{2\pi e^{2}}{hc}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.