The ratio of the speed of the electrons in the ground state of hydrogen to the speed of light in vacuum is

Options

A. `(1)/(2)`
B. `(2)/(237)`
C. `(1)/(137)`
D. `(1)/(237)`

Answer

C

Explanation

Second of the electron in the ground state of hydrogen atom is
`v=(2pie^(2))/(4piepsilon_(0)h)=(c )/(137)=c alpha`
where, c = speed of light in vacuum
`alpha=(e^(2))/(2epsilon_(0)hc)` is the fine structure constant. It is a pure number whose value is `(1)/(137)." "therefore(v)/(c )=(1)/(137)`