Creative Commons, by Steve Hopson, www.stevehopson.com. via Wikimedia commons

How many bananas does it take to kill someone?

Short answer: It depends how you want them to die.

Long answer: An average banana is about 125 grams, or a little more than one fourth of a pound. If you’re insane you might wonder how many you need to kill someone. It turns out the answer depends on how you want them to die- the more bananas at your disposal, the more options you have. So how do you kill someone with just a banana, barring the use crazy gadgets like a cannon that fires bananas? And none of this “slipping on a banana peel and breaking a bone” crap either. I want the bananas to do the heavy lifting. I want bona fide weaponized bananas that can kill a normal healthy person.

 

 

1 Banana: Choking is the obvious solution here. I found a statement from the American Association of Pediatrics which explains why certain foods seem to be associated more strongly with choking hazards, such as hotdogs, whole grapes, and balloons [1]. Why do these foods make such great (or terrible) choking hazards? In the case of the hot dog it’s because, “it is cylindrical, airway sized, and compressible, which allows it to wedge tightly into a child’s hypopharynx and completely occlude the airway.” It sounds like a banana would do the trick just as well, even though the AAP statement doesn’t explicitly mention them.

 

 

88 Bananas: If you dropped enough bananas from a high enough height it should be enough to kill a person. To get a sense for why this is the case, consider a human falling from a great height into water. Fatal impacts with water have been well studied, and the most common class of fatal injury is “crushing of the thoracic cage with resultant bilateral rib fractures and penetration of the vital organs,” with impact velocities being in the range of 32-34 m/s (72-76 mph) [2].

Since the density of bananas is comparable to water (they’re actually 75% water by weight [3]), I expect you could kill someone by turning this situation upside down, literally. If we flip the reference frames so that the the person is stationary and some large mass of water (or bananas) is rushing towards them then we should expect the same physics will apply. All we have to do is estimate the mass of bananas and drop height needed for a lethal impact.

Let’s just find the mass of a sphere of bananas whose terminal velocity is comparable to the fatal impact speed (it’s a common misconception that terminal velocity is one speed – it depends on the geometry and density of the falling body). I find that an 11 kg (24 lb) banana ball, which is not much larger than a basketball, would be falling at lethal speeds if dropped from a tall building [4]. At 125 grams per banana, this is about 88 bananas if they were smooshed into a sphere. This might not seem like much, but remember that these bananas are hitting at highway speeds. Don’t think “Mario Kart,” think cannon ball.

 

 

195 Bananas: Bananas contain a relativity high dose of potassium in the form of a salt called potassium chloride (KCl). While potassium is essential to healthy humans [5], anything can be bad or even dangerous in large enough doses. The daily recommended value is thought to be between 1600 to 2000 mg, and bananas contain about 1/4th of that with 451 mg [6].

So what if you got too much potassium? In toxicology, the LD-50 is a metric that used to describe a lethal dose of a chemical in 50% of cases. Equivalently, if exposed to an amount equal to the LD-50 you’d have a 50% chance of dying. I couldn’t find the LD-50 for KCl in humans, but it’s been found to be 2600 mg/kilogram (of body mass) in rats [7]. Assuming it’s the same for humans, the LD50 for an ordinary mass human (65 kg, 143 lbs) is 169 grams (0.37 lbs).

Since the K is responsible for 52% of the mass of KCl, and since a banana contains 451 mg of K, it means a banana contains a total of 867 mg of KCl. Thus, a person would have to eat 195 bananas to get a lethal dose of KCl. Don’t worry if you’ve eaten 194 in your lifetime. Your next one won’t kill you, you’d have to eat all 195 bananas in a sitting. Also, this is not a good way to die. Potassium overdoses induce a condition called hyperkalemia, which can seriously mess up your heart. For this reason, large doses of KCl are actually administered as a part of the lethal injection.

 

 

50 Million Bananas: A small fraction of the potassium in bananas is radioactive. Don’t worry, lots of things are radioactive and in small enough doses they’re harmless. The specific radioactive isotope is potassium-40, which accounts for 0.01% of potassium and has a billion year half life.

“Seiverts” are good units to measure radioactive doses – they tell you the amount of energy delivered by ionizing radiation. More Sv’s means more death. The “banana equivalent dose” from radioactive potassium is taken to be about 0.1 microSeiverts [8]. Again, don’t let this scare you. This dose is about a hundredth of a dental X-ray.

Lethal radiation doses are in the neighborhood of 5 Seiverts. This isn’t an exact science though; people have survived more and been killed by less depending on the acuteness of the incident and the health and age of the individual. Anyway, to reach a 5 Sv dose with 0.1 microSv per banana, you would have to eat 50 million bananas. In terms of banana mass, this is close to the mass of a nuclear submarine. In terms of potassium mass, it’s like eating a semi-truck. Put yet another way… don’t worry about it, the KCl poisoning would get you first.

 

 

2 × 1039 Bananas: As is tradition, we can make a black hole if we put enough stuff together in one spot. A constant density sphere, if made large enough, will eventually fall within its own Schwarzchild radius and collapse into a black hole. To do this, you would need 2 × 1039 bananas. This banana-ball/black hole would have a radius of 400 million kilometers (250 million mi). Centered at the sun, it extends out past the asteroid belt so you wouldn’t so much be killing someone as much as you’d be killing everyone.

 

 


 

 

image credit: Wikimedia Commons

 


 

 

Have a question? Send it to matt@quarksandcoffee.com