← Where nuclear energy comes from

Where the released energy comes from

Fission releases a large amount of energy. So does fusion. One change splits the heaviest nuclei, the other merges the lightest, opposite changes in every obvious way. Yet both release energy, and for the same reason.

In the mass defect lesson you saw the fact: in an energy-releasing nuclear reaction, the products together have slightly less mass than the reactants, and that missing mass is the reaction's mass defect. That lesson named the quantity and stopped. This lesson is the why it put off: what the missing mass has to do with the released energy.

Add up the masses of a nuclear reaction's reactants. Then add up the masses of its products.

For an energy-releasing reaction, the products' total is slightly smaller.

the fission's mass ledgermass before: the uranium-235 nucleus + the absorbed neutronmass after: the fragments + the neutrons, about 0.1% lessthe difference, about 0.1% of the masscarried away as released energy
The fission's mass ledger: the products' written total is about 0.1% less, and the difference left as released energy.

Now count the protons and neutrons on each side: the counts balance exactly.

So the missing mass is not a missing particle. Every proton and neutron is still there; the total mass has fallen anyway.

The released energy comes from exactly that missing mass: because the total mass of the products is slightly less than the total mass of the reactants, and the missing mass has been carried away as released energy in line with E = mc².

The ledger balances: the mass that left the reaction is exactly the mass equivalent of the energy that left it.

One mechanism covers both changes.

In a uranium-235 fission, the fragments and neutrons together have about 0.1% less mass than the original nucleus plus its absorbed neutron.

In fusion, a helium-4 nucleus made by fusing hydrogen has about 0.7% less mass than the separate nuclei that formed it.

the fusion's mass ledgermass before: the separate hydrogen nucleimass after: the helium-4 nucleus, about 0.7% lessthe difference, about 0.7% of the masscarried away as released energy
The fusion's mass ledger: the same story with a bigger fraction, about 0.7% carried away as released energy.

Fission or fusion, the story is the same: a little mass leaves, and the released energy is that mass, converted.

before the mergeafter the mergedeuterium (hydrogen-2)tritium (hydrogen-3)helium-4free neutronpale = protonhalf-tone = neutronthe particle counts balance; the mass total still falls
Count the particles: nothing is missing from the count. The mass total falls anyway, and that is the mass the energy came from.

A uranium-235 nucleus plus its absorbed neutron have a certain total mass. After the fission, the fragments and neutrons together have about 0.1% less mass. Where did the missing 0.1% go?

Count the protons and neutrons before and after: the counts balance, so no particle is missing.

The missing 0.1% is mass that the reaction converted.

The products carry that converted mass away as the released energy.

The missing 0.1% of the mass was carried away as the fission's released energy.

A helium-4 nucleus made by fusing hydrogen has about 0.7% less mass than the separate nuclei that formed it. Nikau asks: did the fusion lose protons or neutrons?

Count the protons and neutrons: every one that went in is still in the products.

The 0.7% is missing from the mass total, not from the particle count.

That missing mass left the reaction as the released energy.

No. The fusion kept every proton and neutron; the missing 0.7% of mass left as released energy.

An energy-releasing nuclear reaction runs once. How does the products' total mass compare with the reactants' total mass?

After an energy-releasing nuclear reaction, how does the total count of protons and neutrons compare with the count before?

Blanka says: 'Fission and fusion release energy for the same reason: the products end up with slightly less total mass, and that missing mass leaves the reaction as the released energy.' Is Blanka correct?

Your turn

Why does a fusion release energy?

In a uranium-235 fission, the fragments and neutrons together have about 0.1% less mass than the original nucleus plus its absorbed neutron. What happened to that missing 0.1%?

Two light nuclei merge, and the new nucleus plus a free neutron together have slightly less mass than the two nuclei had. Which quantity matches the missing mass exactly?