What is the range of photon energies can be effectively used to split a diatomic molecule like hydrogen?
If the photon's $E=\hbar\omega=h\nu=\frac{hc}{\lambda} $ energy is greater than the energy of the bond which you want to break up it will break it up. It's always best to use higher energy photons but not too high because it may break up bonds which were unwanted to break up in your reaction . So the best for you is to use blue or higher energy UV light for your experiment.You need to deal with the rate of the reformation of bromine molecules, there will be an equlibrium between the production and decomposition of bromine molecules depending on the intensity, not the energy of the light. If the photons has higher energies than a given bond they will always break it up, this is why gamma radiation is so dangerous. The absorbtion spectrum doesn't have a lot connections to this phenomena. You can use the Maxwell-Boltzmann distribution 
$$f_{v}(v_{i})=\sqrt{\frac{m}{2\pi k_{B}T}}exp\left[-\frac{mv_{i}^{2}}{2k_{B}T}\right]$$
to determine the Doppler-effect's impact on the absorption spectrum depending on the temperature and to construct an absorbtion function explicitly. The doppler effect will affect the percieved frequency and energy of the light by gas particles so if you want to be as accurate as possible, you need to calculate it.The Maxwell-Boltzmann distribution is only suitable in low temperatures (below several thousand Kelvins).