Make Bananas, Not Bombs

A friend of mine posted an interesting fact to Facebook today. Turns out that bananas give off a relatively high level of radiation compared to other foods. Many foods give off small amounts of radiation, but the level for bananas is particularly high, due to the presence of potassium-40. This has given rise to the Banana Equivalent Dose as a measure to compare the radiation found in foods following a nuclear accident. Specifically, the average radiation given off by a banana is 3520 picocuries per kg. A curie is 3.7×10¹⁰ decays per second, so 3520 picocuries (pico = 10^-12) is a very small amount of radiation.

I wanted to put this number into perspective. Specifically, I wanted to compare the radiation given off by a banana to something more spectacular, like Little Boy, the nuclear bomb dropped on Hiroshima in World War 2. Doing so lead to some interesting and surprising results. Read on…

Disclaimer: I am not a physicist. Please do point out any mistakes I make in the following, it should be very interesting!

First of all, I wanted to know how many bananas it would take to equal the amount of radioactive material in the Hiroshima bomb. According to Wikipedia, Little Boy contained 65kg of Uranium. In reality it was only 80% enriched, but for simplicity I will round up to 100% Uranium-235, bearing in mind that modern nuclear bombs are much, much bigger than was Little Boy. The radioactive decay rate of this much Uranium can be determined by the equation:

Where:

• A = the radioactivity in decays per second (Becquerel)

• t_1/2 = the half-life of Uranium-235 in seconds which is (703800000 years)*(31556926 seconds/year) = 2.22097645 * 10¹⁶ seconds
• N is the number of Uranium-235 atoms which is (64000 g)/(238.02891 g/mol) = 268.875 mol * 6.022141*10²³ mol^-1 = 1.6192*10²⁶ molecules

(thank you to Ben Keller for reminding me how to do this)

Therefore, the activity of 65kg of Uranium is:

(note the conversion from Becquerel to Curie)

Comparing this to the 3520 picocuries per kg for a banana gives us the mass of bananas required to equal the radioactivity of one Little Boy:

So approximately 38788 metric tons of banana to equal the radioactivity of one Little Boy. Given that Wikipedia list the average weight of a banana as 125 grams, or 1 eighth of a kilogram, this equals approximately 310 307 272 bananas. That’d feed alot of monkeys.

It may seem like a lot, but according to Wikipedia, the world-wide production of bananas in 2007 was 72.5 million metric tons. This means that the radiation held by the world-wide production of bananas is approximately equivalent to 1870 Hiroshima bombs! Good thing we never get all those bananas in one place.

When I shared these preliminary results with some of my friends, one common train of thought that resulted from our discussion was “I wonder if dropping 38788 metric tons of banana would do as much damage as dropping a Hiroshima-sized nuclear bomb” (This should give you a rather terrifying insight into how my friends and I think).

First of all, how much area would be taken up by that much banana? To figure this our requires knowing the density of banana. Through Google, I found the value of 1.14 g/cm³ mentioned in several places. I couldn’t find the original source for this, but it seems like a reasonable value, given that it is only slightly above the density of water (1.00 g/cm³). Using the density we can determine the volume taken up by 38788 metric tons of banana:

If we assume that these bananas are packed into a sphere with no space in between, we can determine radius by using the equation for the volume of a sphere and solving for radius:

So this would be a sphere with a diameter of 40.6 meters… that’s alot of banana.

But how much damage would this do compared to the nuclear bomb? Well, obviously unlike the the bomb, no nuclear reaction will occur when the bananas hit the ground. But, there will be a large amount of kinetic energy. How much?

According to Wikipedia, Little Boy fell for 47 seconds before hitting the ground. Given that the gravitational acceleration on earth is 9.81 m/s², this means that our ball of bananas will be travelling approximately 461 m/s when it hits the ground (ignoring drag, which will in reality reduce this speed). Plugging this into the equation for kinetic energy yields:

By comparison, Little Boy had a yield of 63 Terajoules. The nuclear bomb still does far more damage than our giant falling ball of banana.

Food for thought.