Hey guys, I tried posting my answers yesturday but I always get fucking database errors - they piss me fucking off. *mummbles*
I did the question two ways, the first of which was the way in which blackjack did it, and I got the same answer. Although I might point out that if you got a question like that, mention that one can't find the velocity (a vector), only the speed.
The other way I did it, which I admit i'm not too sure about, was by equating kinetic energy gained by the photon (13.25 eV) with the kinetic energy gained by the hydrogen atom, which was originally at rest.
i.e originally E (hydrogen atom) = 0 because it was at rest.
but afterwards, shouldn't it equal 13.25 eV? By doing it this way you get an answer of around 50000m/s which is remarkably different from the 4m/s obtained by equating conservation of momentum.
Anyway, I think this last example is somewhat flawed, but the thought did cross my mind.