An electron is moving in an orbit of a hydrogen atom from which there can be a maximum of six transition. An which there can be a maximum of three transition. Find ratio of the velocities of the electron in these two orbits.

Options

A. `1/2`
B. `2/1`
C. `5/4`
D. `3/4`

Answer

D

Explanation

Number of spectral lines obtained due to transition of electrons from nth orbit to lower orbit is,
`N=(n(n-1))/(2)`
Case I: `6=(n_(1)(n_(1)-1))/(2) implies n_(1)=4`
Case II `3=(n_(2)(n_(2)-1))/(2) implies n_(2)=3`
Velocity of electron in hydrogen atom in nth orbit
`v_(n) prop (1)/(n)`
`(v_(n))/(v_(n)')=(n_(2))/(n_(1))implies (v_(6))/(v_(3))=(3)/(4)`