How does Einstein’s famous E=mc2 relate to a nuclear bomb?

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I get the basics, energy equal mass times velocity squared, but how does that create a nuclear reaction large enough to make a bomb?

In: Physics its not just velocity squared, “c” stands for the speed of light.

And the answer is that when you make a nuclear fission bomb, like those dropped on japan, a tiny fraction of the mass of the uranium/plutonium is converted entirely into energy.

essentially it shows that you can convert mass to energy, and energy to mass. So if you were to take 1kg of something, and completely convert it to energy, it would release c^2 Joules of energy, or 90,000,000,000, this is an insane amount of energy, and yo’ud never realistically be able to convert that much mass.

But, with a Fission nuclear bomb, you are converting mass to energy, just very tiny amounts of mass. But because the conversion is still massive, even a tiny little bit of mass releases lots and lots of energy. When you convert mass to energy, you get energy equal to the mass used times “c” the speed of light (which is a HUGE number) squared. When Uranium is split into lighter atoms in a nuclear bomb those lighter atoms weigh in total less than the starting Uranium. The difference in mass is released as energy. The energy contained in a substance is equal to its mass times the speed of light times the speed of light again.

What that means is that if you can convert a tiny bit of mass into energy, you’ll get an absolutely massive amount of energy out of the reaction.

Thats what a nuclear bomb does. It creates just the right conditions to turn a grain of enriched uranium or plutonium into a city leveling blast of energy. If you gathered up all the protons and neutrons inside the core of the nuclear bomb after it exploded and weighed it it would weigh slightly less than before it exploded. The lost mass is accounted for by it being converted to energy. The binding energy that holds the neutrons and protons together inside the atom contributes to the total mass of the atom.

During fission this energy is released. You can take this difference in mass and multiply it by c^2 to get the amount of energy released.

An awful lot of energy for a tiny amount of mass. As the others have said there is a lot of energy in mass.

So what does that mean with a nuclear bomb?

Let’s take a real life example.

The nuclear bomb dropped on Hiroshima had a core of 64kg of uranium. It wasn’t a very efficient bomb so about 1kg of that uranium underwent fission. Of that 1kg less than 1g was converted to energy through the splitting of uranium atoms (this released the energy that held them together). The explosion was equivalent to about 15 THOUSAND tons of TNT. This killed about 70,000 people instantly. There are many steps into making a bomb. And this formula doesn’t really explain how the bomb work at all. What does it do then? It allows scientists to measure how much energy would be produced by measuring mass deficit: the difference between mass of an atom and total mass of its constituent measured individually. And it also suggests the possibility of storing and releasing a large amount of energy from something relatively lightweight, which allow the bomb to actually be delivered.

The mechanism that allow the bomb to actually explode is atomic chain reaction; kind of like how fire is a chemical chain reaction. An atom can split (or fuse), releasing energy, and part of this energy trigger other atoms to split (or fuse). If done correctly, this chain reaction can sustain itself, and it happen extremely fast, releasing a huge amount of energy. What you need is the right type of atoms (that release enough energy), the correct shape (so that energy released from an atom go on to trigger more reaction), and some sort of mechanism to ensure that there is an initial trigger of the chain reaction.

I would suggest reading about the Devil Core, one of the infamous example of atomic chain reaction. A tiny difference in the shape of the material allow the chain reaction to sustain itself, releasing a huge amount of energy, killing a scientist studying it, and harming several other people in the room. E=mc^2 doesn’t tell you how to make a nuclear bomb, or even how it really works, or if it is possible to make one. This is a total misconception that has been promulgated since the 1940s.

What it tells you is why a nuclear bomb does not violate the rule that says you can’t make energy come from nothing (the law of conservation of mass and energy). When a nuclear bomb goes off, a HUGE amount of energy is released — way more than you could account for by chemical means. Where does that come from? E=mc^2 tells you that you must be converting some mass to energy, and indeed, you can use E=mc^2 to see exactly how much mass is converted (or how much energy is converted from the mass) every time you split a uranium-235 or plutonium-239 atom.

To understand how to make a nuclear bomb, and how it works, you need to understand the phenomena of nuclear fission (and/or fusion). E=mc^2 tells you why these release so much energy, but it doesn’t tell you that these phenomena exist or how they work (other than the energy release). It doesn’t give a recipe to nuclear bombs. But it does give the right idea that mass is not a fundamental property but results from the amount of energy contained.

It does give a glimpse at nuclear bombs: you would know the masses of atoms, small and large. You would know that larger atoms are more heavy than the combined masses of smaller atoms (that’s called mass defect). Pre-Einstein this might just be a curiosity, maybe even a fluke you put down to bad measurements.
But post-Einstein, now there is the elephant in the room this mass difference might represent energy, and if you split heavy atoms this energy must be released. and if you run the numbers, the energy released “per gram of fuel” is really really high.

Really really high amount of energy released is a bomb, or power plant, or both. That excites a lot of people enough to throw huge amounts of money at it.