The speed of an electron in first Bohr orbit is `(c )/(137)`, where c is the velocity of light in vacuum, then the speed of electron in second orbit is …………..

Options

A. `(1)/(2)((c)/(137))`
B. `2((c)/(137))`
C. `(1)/(4)((1)/(137))`
D. `(1)/(4)((1)/(137))`

Answer

A

Explanation

Angular momentum in `n^(th)` orbit,
`mvr_(n)=(nh)/(2pi)`
`:v=(nh)/(2pimr_(n))`
but `r_(n)ltn^(2)`
`:.r_(n)=Kn^(2)` (K constant)
`:.v=(nh)/(2pimKn^(2))`
`:.vprop(1)/(n)` (All others terms are constant)
`:.(v_(2))/(v_(1))=(n_(1))/(n_(2))`
`:.(v_(2))/(v_(1))=(1)/(2)`
`:.v_(2)=(v_(1))/(2)`
`:.v_(2)=(1)/(2)((c)/(137))`