Q. The ratio of speed of an electron in ground state in Bohrs first orbit of hydrogen atom to velocity of light in air is
A) $\frac{e^{2}}{2\varepsilon_{0}hc}$
B) $\frac{2e^{2}\varepsilon_{0}}{hc}$
C) $\frac{e^{3}}{2\varepsilon_{0}hc}$
D) $\frac{2\varepsilon_{0}hc}{e^{2}}$
Explanation
(a) 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.