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 meanings)

Options

A. `2pihc//e^(2)`
B. `e^(2)h//2pic`
C. `e^(2)c//2pih`
D. `2pie^(2)//hc`

Answer

D

Explanation

Speed of electron in nth orbit `("in" CGS) v_(n) = (2piZe^(2))/(nh) (k = 1)`
For first orbit `H_(2) , n = 1` and `Z = 1`
So `v = (2pie^(2))/(h) rArr (v)/(c ) = (2pie^(2))/(hc)`