Physics 2000 Science Trek Isotopes & Radioactivity

Mass and Energy Conservation in Nuclear Decay

It seems to me that the mass conservation is being fudged a little. The mass of an electron is small, but it's not really zero. And neutrons are a little heavier than protons, so keeping the same mass umber doesn't necessarily mean you end up with exactly the same mass.

I'm glad you noticed that. Nature is supposed to balance the books exactly, and this looks like a case of sloppiness...but it's not so. Let me explain: we haven't talked about relativity, but you've probably heard of Einstein's most famous equation, E=mc2.

Sure. It means that mass (m) and energy (E) are really the same thing, and that you can convert one into the other using the speed of light, c. Oh, I see--you're saying that "mass conservation" has to take energy into account, too.

That's exactly right. If you add up all the mass and energy that's around before and after a nuclear reaction, you'll find that the totals come out exactly the same.

I'll use beta decay as an example to show you how this works. What you've got is a neutron decaying into a proton and an electron:

n => p + e-

As you said, the proton has slightly less mass than the neutron. The mass of the electron makes up for this somewhat, but if you do the math, you'll see that there's still some mass "missing" from the right side of the reaction. Energy takes up the slack: the electron comes out moving very fast, i.e., with lots of kinetic energy.

In other reactions, the "leftover" energy sometimes manifests itself in different ways. For example, the nucleus that comes out is sometimes in an excited state--the remaining protons and neutrons have more energy than usual. The atom eventually gets rid of this extra energy by giving off a gamma ray.

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