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

Answer

D

Explanation

`v_(n)=e^(2)/(2in_(0) nh)`
`v_(1)=e^(2)/(2 in_(0) h)`
`v_(1)=e^(2)/(2 in_(0) h) (2pi c)/(2 pi c)`
`v_(1)/c= (2pi e^(2))/(4 pi in_(0) hc)`
`v_(1)/c=(2pi e^(2))/(hc) ("In C.G.S. unit "1/(4pi epsi_(0))=1)`