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)

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