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Q.
The ratio of the speed of the electron in the ground state of hydrogen atom to the speed of light in vacuum is
Atoms
Solution:
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
$\frac{1}{137}$
$\therefore \frac{v}{c} = \frac{1}{137}$