An electron is moving in an orbit of a hydrogen atom from which there can be a maximum of six transitions. An electron is moving in orbit of another hydrogen atom from which there can be a maximum of three transitions. The ratio of velocity of the electron in these two orbits is

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)`
I Case `6=(n_(1)(n_(1)-1))/(2)`
`rArr n_(1)=4`
II Case `e=(n_(2)(n_(2)-1))/(2)`
`rArr 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))`
`rArr (v_(6))/(v_(3))=(3)/(4)`