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