Unless there's some subtlety, I'd compute the photon energy at 193nm, compare it with the bond energy, and attribute the excess to kinetic energy - of which, as a refinement, bromine gets a small share to be computed from the conservation of momentum.
Assuming zero speed before the photolysis, even rotational, is reasonable. At room temperature or 26meV, it makes little as compared to a UV photon.
"Translationally excited" must mean "moving". Nice not to be a student any more.
To choose your noble gas, look if it shall be light or heavy so hydrogen transfers more of its momentum to it at shocks.
My doubts:
- Bromine not excited. A heavy atom, with UV light.
- Dissociation into neutral atoms.