Bananas are slightly radioactive because they are rich in potassium, and one of its natural isotopes (variants) is potassium-40, which is radioactive. A lorry full of bananas is radioactive enough to trigger a false alarm on a radiation detector looking for smuggled nuclear weapons. But you can’t become radioactive by eating bananas, because you already are radioactive!
A typical adult contains around 140g of potassium, of which about 16mg is potassium-40 – making you 280 times more radioactive than a banana. Eating one increases your total amount of potassium-40 by 0.4 per cent, which is detectable with a sensitive Geiger counter, but the effect is temporary since your metabolism closely regulates the amount of potassium in your body, and you will excrete the excess within a few hours.