Irradiated Chicken?

While antiquing with Hero recently, I pointed out a collection of Vaseline glass telling him that it iridesceses under black light because it contains 2% uranium dioxide. I was very smug sharing this information since Hero is very smart and very scientific and I thought my knowledge would impress him. The rest of the conversation went something like this:

JerseyGranny: I have a piece of Vaseline glass, you know.
Hero [disinterested]: Oh, yeah?
JerseyGranny: Yes, the Hen-On-A-Nest dish that's sitting on top of the microwave.
Hero [very interested]: On top of the microwave?? Um, is there another place you can put it?
JerseyGranny: Um, yeah...why?
Hero [very scientifically]: I'm not sure how much radiation microwaves give off but it's best to put the thing somewhere else.
JerseyGranny [clearly showing her unscientific prowess]: Ok, but what does that matter? What would happen?
Hero: The chicken may become radioactive.

Immdiately upon returning home, I moved the thing somewhere else.