A stationary hydrogen atom emits a photon corresponding to first line of the Lyman series. What velocity does the atom acquire?

Explanation

In the rest frame of the original excited nucleus we have the equation `O=vec(P)_(gamma)+vec(P)_(H)(3)/(4) ħ=c|vec(P)_(gamma)|+P_(H)^(2)//2M`
(`(3)/(4) ħR` is the energy available in `n=2rarr=1` transition corresponding to the first Lyman line.)
Then `V_(H)=(3 ħR)/(4mc)=3.3//s`