An electron, `e_(1)` is moving in the fifth stationary state, and another electron `e_(2)` is moving in the fourth stationary state. The radius of orbit of electron `e_(1)` is five times the radius of orbit of electron `e_(2)` calculate the ratio of velocity of electron `e_(1)(v_(1))` to the velocity of electron `e_(2)(v_(2))`.

Options

A. ` 5 : 1`
B. `4 : 1`
C. `1 : 5`
D. `1 : 4`

Answer

D

Explanation

From the expression of Bohr's theory, we know that
`m_(e )v_(1)r_(1)=n_(1)(h)/(2pi)`
& `m_(e) v_(2)r_(2)=n_(2)(h)/(2pi)`
`(m_(e )v_(1)r_(1))/(m_(e )v_(2)r_(2))=(n_(1))/(n_(2))(h)/(2pi)xx(2pi)/(h)`
Given, `r_(1)=5r_(2), n_(1)=5, n_(2)=4`
`(m_(e )xxv_(1)xx5r_(2))/(m_(e )xxv_(2)xxr_(2))=(5)/(4)`
`implies (v_(1))/(v_(2))=(5)/(4xx5)=(1)/(4)=1 : 4`