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

Answer

C

Explanation

The hydrogen atom before the transition was at rest. Therefore, from conservation of momentum
`P_("H-atom") = P_("photon") = (E_("radiated"))/c`
`= (13.6[ 1/n_(1)^(2) - 1/n_(2)^(2)] eV)/c 1.6 xx 10^(-27) xxv`
`= (13.6 [ 1/1^(2) - 1/5^(2)] xx 1.6 xx 10^(-19))/(3 xx 10^(8))`
` Rightarrow v = 4.352 m//s = 4 m//s`