Where does the energy come from?
Put an atom on a scale and it weighs less than the parts it's made of. You start knowing nothing. You finish having calculated, by hand, the energy that powers the Sun.
Here's the claim this issue will prove: nuclear energy isn't burning anything. When the particles in an atom's core rearrange into a tighter shape, a tiny amount of their mass disappears, and that mass comes out as energy. Coal, gasoline and wood all work by rearranging electrons. Nuclear reactions rearrange the core itself, and that's why they're millions of times stronger.
Before you read anything, guess.
Your guesses are locked in and we'll come back to them at the end. Guessing first, even wrongly, makes the real answer stick.
Weigh an atom against its own parts.
Every atom has a tiny core, the nucleus, built from two kinds of particles: protons and neutrons. A proton weighs 1.007276 atomic mass units (u). A neutron weighs 1.008665 u. So a nucleus should just weigh the sum of its parts.
It doesn't. Put the loose parts on one side of a scale and the finished nucleus on the other, and the nucleus is lighter. Every time.
The missing mass has a name: the mass defect. It didn't vanish. When the parts snapped together, they let go of energy, and energy carries mass with it. Run it backwards and you'd have to put that energy back in to pull the nucleus apart. That energy is called the binding energy.
is the number of protons, the number of neutrons. For helium the missing mass is under 1%. That sounds like nothing. Level 5 will show why it's enormous.
Why some atoms hold on tighter than others.
Inside a nucleus there's a tug of war. A very strong glue, the strong nuclear force, holds each particle to the ones right next to it, and only those. Meanwhile every proton is positively charged, so every proton pushes every other proton away, all the way across the nucleus.
Small nuclei are mostly surface, so many particles have few neighbours to hold. Big nuclei have lots of protons all pushing on each other. Somewhere in the middle, the glue wins by the most. Build nuclei and find where.
That tug of war is one equation. Each piece is a term you just watched as a bar. Tap each one:
The first term holds the nucleus together. The other three cost energy. Tap a term.
The 's are just numbers measured from real atoms: about 15.8, 17.8, 0.71 and 23.7 MeV. With four numbers, this formula gets the binding energy of hundreds of nuclei right to within about 1%.
Mission: power a city of a million people.
A city that size uses about 4 billion kilowatt-hours of electricity a year. You're the chief engineer, and every option on the table is one engineers have actually considered. Collect lessons by trying different paths; three lessons clears the level.
Everything wants to roll down to iron.
Take the glue-per-particle number from Level 2 and plot it for every atom, upside down. You get a valley. The lower an atom sits, the more tightly it's held, and iron is at the bottom.
Any reaction that moves atoms downhill releases energy. Heavy atoms roll down by splitting, which is called fission. Light atoms roll down by joining, which is called fusion. Try both.
Notice the asymmetry. Splitting one uranium atom releases about 170 to 200 MeV. Fusing hydrogen releases only 17.6 MeV, but it uses far fewer particles, so per kilogram fusion wins by about four times. And iron gives you nothing either way. That's why stars that make iron in their cores are about to die.
The proof, one step at a time.
You've seen that mass goes missing, and that the tighter a nucleus is held, the more mass it lost. Now the exact link between missing mass and energy.
Einstein's result from 1905: mass and energy are the same thing measured in different units. The conversion factor is the speed of light, squared.
Light travels metres per second. Squared, that's . So a tiny mass is a huge amount of energy. Slide it:
Protons and neutrons snap together and the nucleus comes out lighter. Using , what must have happened to energy?
Energy left, so the nucleus is lighter by exactly that energy divided by . Flip it around and you have the binding energy:
Atom masses are tiny, so we measure them in u. Run on exactly 1 u and convert joules to MeV, and you always get the same number:
So: missing mass in u, times 931.5, is the energy released in MeV. Check it on helium: MeV.
Your turn: the reaction that could power the world.
This is the fusion reaction that reactors like ITER are built around. Two heavy forms of hydrogen, deuterium (H-2) and tritium (H-3), fuse into helium and throw out a neutron:
Use the tools from Level 5 to find out how much energy one reaction releases.
How did your gut do?
If fusion is so good, why don't we have it yet?
That's the whole method of nuclear physics in miniature: weigh the before and after, find the mass that went missing, and multiply by c².