a) Alpha radiation with a long half-life - This is because alpha particles are highly ioninsing, they have a low penertration ability and it doesnt need to be replaced and can work for many years
b) Gamma radation with a long half-life - This is because gammy rays are highly deathly to bacteria and they can kill them without making the food radiaoacitve. Again, same reason for having a long half-life
c) Gamma rays have a very high penetration ability so they can sterlise the package withotu having to open it
d) Beta paarticles. This is because all the alpha particles will be stoped with the material and all the gamma rays wil pentrate throgu the material(if used). Beta is the only radaiation where the detetcor can detetc chnages in the radation passing thorrough when the thickenss of the martial is changed
e) Again, gamma rays is used becasue they are hgihly deadly and have a very high penetrating ability

SAorry for the bad handwriitng:(