Fission: a heavy nucleus splits into two smaller ones

1. Very heavy nuclei are only just holding themselves together, so a small disturbance is enough to break one apart.

2. The disturbance is usually a slow-moving neutron, which works well because it has no charge and so is not repelled as it approaches the positive nucleus.

3. The nucleus absorbs the neutron, becomes even more unstable, and splits into two daughter nuclei of roughly comparable size, plus a few spare neutrons.

4. A typical fission of uranium-235 is written as a nuclide equation.

   $${}_{92}^{235}U+{}_0^{1}n\to {}_{56}^{141}Ba+{}_{36}^{92}Kr+3{}_0^{1}n$$

5. Both totals balance across the arrow: the nucleon numbers give $235+1=141+92+3$, and the proton numbers give $92+0=56+36$.

6. Those spare neutrons can go on to split further uranium nuclei, so one fission triggers others in a chain reaction.

7. Fission is not a decay you have to wait for: it is induced by firing a neutron in, which is what makes it controllable in a reactor.

Fusion: two light nuclei join to make a heavier one

1. Fusion runs the process in the opposite direction: instead of a heavy nucleus breaking up, two light nuclei merge.

2. The standard example joins two isotopes of hydrogen, deuterium and tritium.

   $${}_1^{2}H+{}_1^{3}H\to {}_2^{4}He+{}_0^{1}n$$

3. Again the numbers balance: $2+3=4+1$ for the nucleon numbers, and $1+1=2+0$ for the proton numbers.

4. Fusion is far harder to achieve than fission, because both nuclei are positively charged and repel each other strongly as they get close.

5. Overcoming that repulsion needs extremely high temperatures to give the nuclei enough speed, and extremely high pressures to make collisions frequent enough.

6. Those conditions exist in the core of a star, which is why fusion is the energy source of the Sun but is still difficult to sustain on Earth.

Where the energy comes from: a small loss of mass

1. In both processes, the total mass of everything produced is slightly less than the total mass of everything that went in.
2. That missing mass has been converted into energy, which appears mostly as the kinetic energy of the fast-moving products.
3. The mass lost is a tiny fraction of the total, but the energy it releases per nucleus is enormous compared with any chemical reaction such as burning.
4. Nucleon number and proton number are still conserved in the equation, because those are counts of particles rather than measurements of mass.
5. Splitting the heaviest nuclei and joining the lightest both move the material towards nuclei that are more stable, and that is why energy comes out of two processes that look like opposites.