Mass and Energy Conservation in Nuclear Decay
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.
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