Question

The ratio of the speed of the electron in the ground state of hydrogen atom to the speed of light in vacuum is

• A. $\frac{1}{2}$
• B. $\frac{2}{237}$
• C. $\frac{1}{137}$
• D. $\frac{1}{237}$

Answer 1

Answer: (C)

$\frac{1}{137}$

Answer 2

Speed of the electron in the ground state of hydrogen atom is $v = \frac{2\pi e^{2}}{4\pi\varepsilon_{0}h}$ $= \frac{c}{137} = c\alpha$ where, $c =$ speed of light in vacuum, $\alpha = \frac{e^{2}}{2\varepsilon_{0}hc}$ is the fine structure constant. It is a pure number whose value is $\frac{1}{137}$ $\therefore \frac{v}{c} = \frac{1}{137}$