How many bananas would you need to eat to die of radiation poisoning?

Most people know that bananas are full of potassium. In fact a single banana contains approximately 450 mg of potassium. Of this potassium about 0.01% of it contains potassium-40 a highly radioactive isotope.

Essentially from the information above we can say that bananas have around 45 micrograms of radioactive material.

Before we can do any equations or draw any conclusions we must first learn more about potassium-40, our radioactive isotope. Since it is radioactive it has a half-life of 10*(9) years or 3 X 10^16 seconds.

Beta Decay of a potassium-40: Beta Decay essentially means radiatiove decay when an electron is released. Beta decays make up 89% of all decays for potassium-40. There are other types of decay (alpha, beta, gamma).

Basically all of these very confusing values contribute to the idea that potassium-40 has an extremely long half life and will take a long time to break down.

The q-value of the Beta Decays is 1311 KeV or 1.18*10^-13 joules. Essentially this value represents the energy released from the parent isotope (potassium-40) to the daughter isotope. When the parent isotope begins to break down, it emits energy. This energy represents the q-value.

We know that our half life is 1.28 X 10(9), which is a very large half-life. Basically this means that the isotope will take a much longer time to break down.

To calculate the amount of atoms of potassium-40 we do:

45 micrograms (amount of radioactive material per banana) of potassium 40 = 1.125 micromoles = 6.77*10^17 atoms of potassium 40. We get this by multiplying the number of micromoles by avogadro's constant (the amount of atoms in one mole).

To calculate the amount of atoms of potassium-40 we do:

45 micrograms (amount of radioactive material per banana) of potassium 40 = 1.125 micromoles = 6.77*10^17 atoms of potassium 40. We get this by multiplying the number of micromoles by avogadro's constant (the amount of atoms in one mole).

Take the energy per decay: 1.18 X 10(-13) and divide it by the half life decay rate: 3 X10^16. Then multiply by the number of atoms of potassium-40 in a banana: 6.77 X10^17. This will give us the energy released per second per banana which is 2.66 X 10^-12 joules per second per banana.

Grays is a type of unit that measures absorbed dose. To begin feeling sick you would need approx 2 grays, and to die you would need closer to 3-5 grays of radiation. Grays are equivalent to joules per kilo. Therefore 5 grays would require 5 joules per kilo. Lets say we are dealing with an 80 kilo man (176 lb). You would need 400 joules per second.

400 Joules per second divided by 2.66 X 10^-12 (energy released per second per banana) = 1.503 X 10^14. You would need to eat 150 trillion bananas in a second!

Obviously this is not a logical possibility. Firstly it is unlikely that there are even 154 trillion bananas on the planet. Another reason this is not feasible is the simple fact that bananas still have 450 mg of potassium. Potassium is a metal, therefore if you were to eat anywhere near to this amount of bananas you would die because of huge electrolyte imbalance. Lastly potassium in high doses is extremely dangerous (KCl, Potassium Chloride is used for lethal injections).

Logan Konarek

Great blog. Had in depth analysis of the banana using many physics concepts. Extensive research is evident.

ReplyDeleteInteresting topic, Logan David.I learned a lot about radioactive isotopes! I feel educated enough in the topic of banana radioactivity to explain to somebody who believes bananas can be harmful why it is totally fine to enjoy this delicious fruit.

ReplyDeleteReally cool topic! 154 trillion bananas is a lot! I found the calculations really interesting!

ReplyDeleteMaggie

ReplyDeleteThought this was really cool to read and learned alot about radioactive isotopes.

I hate banana's so I don't need to think about eating 154 trillion bananas.

ReplyDeleteRyan K.

ReplyDeleteI never knew that Bananas could be so dangerous due to the radiation. I really enjoyed the blog post.

I appreciate you explaining the many big words you used in your blog. It helped me understand the meaning of everything you were saying. Super cool blog dude.

ReplyDeleteI'm on my 149,999,999,999,999 th banana and am now I am starting to get worried about eating the next one. Thanks a lot!

ReplyDelete