Calculate the ratio of the velocity of light and the velocity of electron in the first orbit of a hydrogen atom. (Given, $h = 6.624 \times 10^{- 27} e r g - s e c$ ; $m = 9.108 \times 10^{- 28} g$ , $r = 0.529 \times 10^{- 8} c m$ ).

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Solution

$v = \frac{h}{2 π m r}$
$= \frac{6.624 \times 10^{- 27}}{2 \times 3.14 \times 9.108 \times 10^{- 28} \times 0.529 \times 10^{- 8}}$
$= 2.189 \times 10^{8} c m / s e c$
$\frac{c}{v} = \frac{3 \times 10^{10}}{2.189 \times 10^{8}} = 137$ .

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