Bananas contain relatively high amount of potassium; naturally occurring potassium contains a small amount of Potassium-40 which is a radioactive isotope, decaying into Argon-40 and emitting beta radiation. Large quantities of bananas have even been known to cause false alarms passing through radiation detection procedures at ports in the US, meant to screen for smuggling of radioactive materials.

Exposure to radiation is a significant risk factor in developing cancers, as radiation damage to DNA can lead to cancerous mutations in cells, and is thought to be responsible for around 10% of cancers. But before you eschew bananas, consider that potassium also serves several necessary functions in the body – notably in blood clotting and regulating blood pressure (along with sodium). The radiation exposure associated with eating a banana is practically zero, while low blood-potassium can lead to high blood pressure, and other severe health problems. Overall the health benefits of a plentiful supply of dietary potassium, far outweigh the negligible risk of cancer from consuming more potassium-40; eating one banana per day would constitute around 1% of your typical background dose (from natural radiation in the air, from your clothes, other food, etc.).

Interestingly one informal expression often used is the “Banana Equivalent Dose”; comparing sources of radiation to the dose one might expect from eating a single, 150g banana. The point of using this term is that it can ground small doses of radiation in reality – a dental x-ray is equivalent to around 50 bananas, while the typical, daily background dose is around 100 bananas. The lethal dose is around 100,000,000 bananas in a single sitting. That said, the radiation exposure from eating bananas does not accumulate from eating more bananas – your body only stores a certain amount of potassium before the excess is excreted, so eating a lot of bananas doesn’t typically increase your risk.

With all of this in mind, we can actually quantify the point at which the banana changes from being a delicious snack, to a dangerous health risk. Studies have been performed looking at the cumulative doses of radiation people are exposed to and the resulting incidence of various cancers. The lowest radiation dose per year that can be clearly linked to an increased risk of developing cancer is 50 mSv, or 500,000 in Banana Equivalent Dose. By a nice coincidence, this is almost exactly one banana per minute. I cannot recommend eating bananas at this rate.

It is also worth noting that all the food we eat is very faintly radioactive, because the carbon that makes it up contains a minority of Carbon-14; also a radioactive isotope, which decays into Nitrogen-14 through beta decay. Carbon-14 has a very low abundance compared to the stable Carbon-12, so overall the effect is smaller than that of the potassium for a banana.

By far the most radioactive food we eat are brazil nuts, which contain traces of Radium as well as being rich in potassium. Per weight, brazil nuts are around 50 times as radioactive as bananas. You may have a very slightly increased risk of cancer if you eat more than 3 tons of brazil nuts per year.

References and further reading:

Radiological alerts triggered by banana shipments:

http://www.nti.org/analysis/articles/radiological-nuclear-detection-devices/

Radiation-induced cancer:

https://en.wikipedia.org/wiki/Radiation-induced_cancer

The banana equivalent dose:

http://www.ppe.gla.ac.uk/~protopop/teaching/NPP/P2-NPP.pdf

Cancer risks attributable to low doses of radiation:

http://www.pnas.org/content/100/24/13761.long

Radioactivity from natural sources, including various foodstuffs:

http://www.physics.isu.edu/radinf/natural.htm