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.

Explanation

Number of spectral lines obtained due to transition of electrons from nth orbit ot lower orbit is given by
`N=(n(n-1))/(2)`
Case I
`6=(n(n_(1)-n))/(2)`
`rArr" " n_(1)^(2)-n_(1)-12=0rArr(n_(1)-4)(n_(1)+3)=0rArrn_(1)=4`
because `n_(1)` cannot be neatgive i.e., -3
Case II `" " 3=(n_(2)(n_(2)-1))/(2)`a
`rArr " " n_(2)^(2)-n_(2)-6=0rArr(n_(2)+2)(n_(2)-3)=0rArrn_(2)=3`
because `n_(2)` cannot be negaive i.e.,-2.
Velocity of electron in hydrogen atom in nth orbit.
`v_(n)prop(1)/(n)rArr(v_(n))/(n'_(n))=(n_(2))/(n_(1))rArr(v_(6))/(v_(3))=(3)/(4)`