The ratio of the speed of the electron in the first Bohr orbit of hydrogen and the speed of light is equal to (where `e, h and c` have their usual meaning in cgs system)

Options

A. `2 pi h // e^(2)`
B. `e r^(2) h// 2 pi c`
C. `e ^(2) c// 2 pi h`
D. `2 pi e^(2)// h c`

Answer

D

Explanation

`v_(n) = k (2 pi e^(2))/(n h)`
We know that in cgs system`k = 1`
`:. v_(n) = (2 pi e^(2))/(n h) implies v_(1) = (2 pi e^(2))/(h)`
So `(v_(1))/(c) = k (2 pi e^(2))/(c h)`