Nuclear Fission and Fusion

$E = mc^2$

$1$ u $= 931.5$ MeV/c².

Mass defect ($\Delta m$): difference between mass of separate nucleons and assembled nucleus.

Binding energy: $BE = \Delta m \times c^2$ — energy needed to separate the nucleus into individual nucleons.

BE per nucleon: measures stability. Peak at Fe-56 (~8.8 MeV).

Heavy nucleus splits into lighter nuclei + neutrons + energy.

$^{235}_{92}U + ^1_0 n \to ^{141}_{56}Ba + ^{92}_{36}Kr + 3^1_0 n + \sim 200 \text{ MeV}$

Chain reaction: Each fission releases 2-3 neutrons → can trigger more fissions.

Reactor: Moderator (slow neutrons), control rods (absorb neutrons), coolant.

Light nuclei combine: $^2 H + ^3 H \to ^4 He + ^1 n + 17.6$ MeV.

Requires: >100 million K, high density, long confinement time.

Advantages: abundant fuel, less waste, no CO₂, no meltdown risk. Challenges: containing plasma at extreme temperatures.

Both move products toward Fe-56 (higher BE per nucleon). The increase in BE per nucleon × number of nucleons = energy released.

• $E = mc^2$; $1$ u = 931.5 MeV
• BE per nucleon peaks at Fe-56
• Fission: heavy → lighter + energy; chain reaction; reactor controls
• Fusion: light → heavier + energy; needs extreme T for plasma