Gamma rays r commonly formed when a particle and an antiparticle collide ( in fact, annihilate ). This results in no matter or antimatter but only energy in the form of gamma rays.



Since a particle n an antiparticle need to collide, the rxn is not possible without one of the reactants. So, reaction is of first order of both reactants (particle n antiparticle) as rate determining step inolves both.



Thr4 overall order is 2 as it is first order in particle n antiparticle.



I hope my explanation is the correct reason.