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 find structure constant it Is a pure number whose value is $\frac{1}{137}$

$\therefore\frac{v}{c} = \frac{1}{137}$