Well for your equipment it isnt a problem to shoot in this radioactive environment. For your filmstock it could be a problem.
As the radioactive radiation could be compared with x-ray, it is both radiation and therefor energy. You should have to look how much the radiation is what comes of. And look at the spectrum, wavelenghts, your filmstock is being in.
I was talking with my sister about it this morning, she is a Chemist, so i can't give you a specific explanation yet like this is exactly what is going to happen. But what could happen that with the amount of radiation and the time of being in the radiation area is that the black level would go up a bit, so you sort of flash youre material in a very ugly way.
I think it will be such small amounts that you will not be able to see it but i can imagine that if you would make it a chemical test you would be able to trase it. But i find it quite an interesting topic so i think the coming days i will try to look it up!!!!
greets,
martijn van broekhuizen