"Tonight, find out why you could be putting your whole family at risk by serving foods high in radioactivity. That's right, radioactivity. Find out more about this shocking, potentially lethal news here on KEOW tonight at 10 o'clock."
Let's just go ahead and beat the 10 o'clock news to the punch -- frankly, I'm surprised it hasn't been done yet somewhere (or maybe it has?) -- and get to the meat of the matter: Yes, that banana you're eating is radioactive.
Bananas are just one of many foods that we eat on a daily basis which, thanks to ingredients like potassium and radium, produce naturally-occurring and measurable amounts of radiation. In fact, that banana is so good at producing a constant, easily measurable amount of radiation that it's used as a convenient yardstick for measuring radioactivity, which is normally measured in extremely small units called "picocuries." (Yes, after Marie Curie.)
An average banana contains about 520 picocuries, due to the high amount of potassium present in the fruit. All potassium also contains the naturally occurring radionuclide potassium-40. Since many people don't have any concept of how large or small a picocurie is, the "banana equivalent dose" is often used to explain how radioactive a given object is.