# Why does mass change in to energy during a nuclear change?

I have been doing some research on nuclear changes and I have found that the energy released during a nuclear change comes from a minuscule amount of mass that is converted in to energy. After making some more research it seemed completely logical because of Einstein’s famous energy equation, but I was left with a couple of questions roaming my mind.

1. Why does mass change in to energy during a nuclear change?

2. What prevents matter from changing to energy and vice versa in a normal state?

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Your second question is answered in the answers to question What keeps mass from turning into energy?, and the first one is sort of answered in the replies to Conversion of mass and energy. – John Rennie Feb 17 '14 at 12:26

With regard to mass and energy, nuclear reactions are no different than anything else. Also, mass doesn't turn into energy. Mass is energy.

$E = mc^2$ is the shortened version of the equation $E = \sqrt{(mc^2)^2 + (pc)^2}$, where $p$ is momentum. This equation describes any physical system. Take a box and put in whatever you want - compressed springs, balls at the top of hills, gasoline and oxygen, Uranium-235, black holes, anything. When you're all done, the box will have some total amount of mass, energy, and momentum. If you know any two of them, you can find the third using that equation I just gave.

When your box has zero momentum, the equation simplifies to $E = mc^2$. This doesn't say that mass is turning into energy. It says that however much energy is in there, you can find the mass by dividing the energy by c^2. Or however much mass is in there, you can find the energy by multiplying by c^2.

For example, if you take an ordinary spring and compress it, you've added potential energy to it. Its mass goes up. This might seem strange, but it's true. Any time you compress a spring you increase its mass. The mass increase is just very, very small. Similarly, if you heat up a gas, you add thermal energy to it, and this increases its mass. Mass and energy move in lockstep no matter what you do. Probably, before learning relativity, most people think that the only way to add mass to the box is to put more stuff in it. But that's simply not true. You can just take the box and squeeze it down to a smaller size, doing work against its internal pressure. This will add energy and make the mass of the box go up, even though you didn't add any stuff to it. The mass goes up just because you added energy, and energy and mass are simply the same thing.

Because energy is conserved, if you lock your box up so nothing comes in or out, its energy won't change, and therefore its mass won't change. Even if a nuclear bomb goes off inside the box, its mass won't change. What does happen is that the mass of the nuclei go down, but the explosion creates lots of other stuff - photons and neutrons and things, and these have exactly enough energy to compensate for the mass/energy lost by the nuclei.

Now you can imagine opening your box. Again some sort of nuclear reaction occurs. The nuclei give off photons, which shoot out of the box. The box has lost some energy, and therefore it's lost some mass, too. But there is nothing special about a nuclear process. If there's some chemical change in the box so that the box gives off light, the mass of the box will still go down.

The chemist Lavoisier is famous for discovering a law of conservation of mass. He found that if you burn a piece of wood in some oxygen, the mass of ashes plus the carbon dioxide created is equal to the original mass of the wood and oxygen. He was actually wrong about that, though. When you burn some wood in oxygen, photons escape, carrying away energy. The mass of the ash and carbon dioxide is actually slightly smaller than the mass of the original wood and oxygen. However, for chemical reactions this change in mass is so small Lavoisier never had a chance to measure it. The mass change is about one part in $\alpha^2 \frac{m_e}{m_n}$ with $\alpha$ the fine structure constant, $m_e$ the mass of an electron, and $m_n$ the mass of a nucleon. This works out to around one part in a hundred million.

In nuclear reactions, the change in mass is larger, around one part in a thousand. The physics is all fundamentally the same though. The mass-energy relationship is just as true for chemistry or electromagnetism or whatever as it is for nuclear binding energies.

So it is not really accurate to say that mass changes into energy. Instead, when a reaction occurs that loses energy in some way - e.g. by giving off photons - the energy and mass both go down because energy and mass are the same thing as long as there is no net momentum.

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