A hydrogen atom emits a photon corresponding to an electron transition from `n = 5` to `n = 1`. The recoil speed of hydrogen atom is almost (mass of proton `~~1.6 xx 10^(-27) kg)`.

Options

A. `10^(-4)m//s`
B. `2xx10^(-2)m//s`
C. `4m//s`
D. `8xx10^(-2)m//s`

Answer

C

Explanation

Energy released from `n=5` to `n=1`
`E=13.6((1)/(1^(2))-(1)/(5^(2)))=13.6xx(24)/(25)eV`
Momentum of photon `=13.6xx(24)/(25)xx(1.6xx10^(-19))/(3xx10^(8))`
Momentum of H-atom `=(13.6xx24xx1.6xx10^(-19))/(25xx2xx10^(8))`
Velocity of H-atom `=(13.6xx24xx1.6xx10^(-19))/(75xx10^(8)xx1.67xx10^(-27))=4m//s`