# Meltdowns, Bombs, and the Math behind it.

## How reactor meltdowns actually release more radiation than nuclear bombs.

(We do the math so you don’t have to)

Criticisms of nuclear programs are commonplace in the media — stories on nuclear meltdowns and nuclear weapon fallout scares are routine. Though, few understand that the dangers posed by potential meltdowns or fallout are only spontaneous reactions caused by our good friends fission fragments. To help you out, StrategicSwag is here to shed some light on the matter whether you find yourself discussing such cataclysmic affairs over Thanksgiving dinner or drinks with someone you just met on Tinder.

First, let’s review what happens during a nuclear meltdown. (Note: it’s not the same as an atom’s midlife crisis…or should we say half life crisis?).

Simply, a meltdown takes place when the cooling system of a reactor stops removing the heat from the fuel, leading to overheating of metals and melting the whole shebang into a mound of highly radioactive slag. The experience is similar to leaving out ice cream on a summer day, except swap out the delicious sweetness with a healthy dose of fatal radiation instead. Nuclear meltdowns by design are very unlikely to occur under normal operating practices. However, in large scale accidents, they are a failure of the system and over release massive amounts of radiation into the environment. In fact, when talking about nuclear meltdowns, some nuclear engineers offer a clever saying, “It’s always messier when you don’t see it coming.” You see, it turns out that nuclear meltdowns do release larger amounts of radiation to the environment than nuclear weapons, especially if the fuel has been operating longer.

At first this may seem counterintuitive, but don’t fear! Some simple calculations can help us gauge the hows and why of this released radiation. Thankfully, our resident nuclear engineer at StrategicSwag is here to help out with the nitty gritty approximations for power from U-235 and calculating yield from nuclear weapons.

Say you want to produce 1 MW of power from U-235 in any given light water reactor — you actually only need about 1 gram of U-235 to fission. And if you’re operating a nuclear power plant the size of the Diablo Canyon plant in California, your reactor will produce approximately 9,944,983 MWh of electricity per year.

But wait! There’s more! As we know, nuclear power plant systems do not operate at 100% efficiency. In fact, only about 32% of the thermal power created in any nuclear reactor gets converted to electrical power. So, how much thermal power is actually generated? Only about 31,078,071.875 MWh. And how many grams of U-235 fission is this? If you’ve been following our rule of thumb, it is actually 31,078,071.875 grams or 31,078.071875 kilograms, if you’re a math savvy wonk (StrategicSwag making arithmetic teachers proud since 2014).

Second, in order to compare the radiation levels of a meltdown against fallout, you need to calculate the yield of U-235 in a typical fission weapon. According to our resident engineer, 1 pound of U-235 will produce a yield of about 8 kilotons. In order to make an accurate comparison, we should convert this ratio to kilograms. Thankfully, we at StrategicSwag have someone more qualified to make that calculation: Siri.

Simple enough (maybe we didn’t need Siri). But, to take it a step further, we need to calculate the yield on this amount of material. Because there are 8 kilotons to every pound and there are 2.2 pounds per kilogram, she tells us:

At almost 18 kilotons, the yield from one pound of U-235 material is only slightly more than the Hiroshima bomb, Little Boy (16kt).

Now, let’s put on our wonk hats and talk analysis. We just calculated that a nuclear power plant such as the Diablo Canyon Unit that will burn 31,078.072 kilograms of U-235 in one year. In short, the spent fuel from this plant alone can contain the fission fragments necessary for over 31 thousand Hiroshima bombs in just one year. So, now imagine a nuclear meltdown where the core fuel and a spent fuel pool suffer catastrophic failure and radiation is subsequently released in the air, ground, and water. Even if only a hundredth of the potential radiation is released from this plant, it is still 300 times the amount of fission fragments that would be released from a basic fission weapon. This is why nuclear meltdowns are bad news and areas such as Pripyat and Fukushima still pose environmental risks, as opposed to the sites of Hiroshima and Nagasaki.

To return to our original point, keep in mind that nuclear fallout from explosions are especially hazardous due to fission fragments, which are very energetic and short-lived. So, if you find yourself in the plume of a nuclear explosion, you would more than likely receive a nasty dose of radiation. Yet, a reactor meltdown would still release large amounts of longer lived radiation into the atmosphere and also contaminate the surrounding area along with short-lived isotopes.

So, you might be asking yourself: what does this mean? Is nuclear power bad?

No, nothing of the sort. In fact, we at StrategicSwag are generally huge proponents of nuclear power (if you hadn’t guessed by now), though it is still good to be aware of the implications of nuclear power and why supporting newer reactor generations and safety systems is important. Further, we should look forward to Gen III+ and Gen IV reactors in order to prevent disasters like Fukushima and Chernobyl.

To wrap this all up, while the number of released radiation stemming from nuclear meltdowns and weapon explosions may be surprising, know that radiation in reactors is stored in spent fuel and only released under (very unlikely) catastrophic events. Although there is no doubt that nuclear power (as with all other technologies) has its drawbacks, the continued safe operation of reactors internationally demonstrates the solid track record of this technology. For the most part, nuclear power is a reliable, safe, and resilient energy source.

Now, feel free to use this information to impress that cute barista at Starbucks or sound cool at family gatherings this coming holiday season.

NOTE: This is just a fun little thought experiment, let’s not forget about the prompt radiation created by the nuclear weapons which make up a large portion of nuclear fallout!

Written by: Cervando A. Bañuelos II
Edited by: Marianne Nari Fisher

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