Find recoil speed (approximately in `ms^(-1))` when a hydrogen atom emits a photon during the transition from `n = 5 to n = 1`

Options

A. `4.718 m s^(-1)`
B. `7.418 m s^(-1)`
C. `4.178 m s^(-1)`
D. `7.148 m s^(-1)`

Answer

C

Explanation

`E = R_(oo) hc (1 - (1)/(25))`
Momentum of the photon emitted is, `p`
`m v = p`
`(p)/(m) = ((1.097 xx 10^(7)) (6.626 xx 10^(-34)) 24)/((25) (1.67 xx 10^(-27))) = 4.178 m s^(-1)`