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 electron from `n^(th)` orbit to lower orbits is
`N=(n(n-1))/(2)`
In the first case, `N=6`
`:.6=n((n-1))/(2)rArrn=4`
In the second case, `N=3`
`:.3=(n)((n-1))/(2)rArrn=3`
Velocity of electron in hydrogen atom in `n^(th)` orbit is
`v_(n)=(2pie^(2))/(4piepsilon_(0)nh),v_(n)prop1/n:.(v_(6))/(v_(3))=3/4`