AcademyNuclear Physics

Academy

Fission

Level 1 - Physics topic page in Nuclear Physics.

Principle

Fission releases energy when a heavy nucleus splits into more tightly bound medium-mass nuclei.

Notation

\(Q\)
fission energy release
J, MeV
\(\nu\)
average neutrons emitted per fission
1
\(k\)
neutron multiplication factor
1
\(E_f\)
energy released per fission
J, MeV
\(P\)
reactor power
\(\mathrm{W}\)
\(\Phi\)
neutron flux
\(\mathrm{m^{-2}\,s^{-1}}\)

Method

Derivation 1: Binding-energy gain

Heavy nuclei sit below the peak of the binding-energy-per-nucleon curve.

Energy release
\[Q=(m_i-m_f)c^2\]
Binding-energy form
\[Q=B_f-B_i\]

Derivation 2: Chain reaction

Emitted neutrons can trigger further fissions.

Subcritical
\[k<1\]
Critical
\[k=1\]
Supercritical
\[k>1\]

Derivation 3: Power from fission rate

Macroscopic power is microscopic energy release times event rate.

Fission rate
\[\dot N_f=\frac{P}{E_f}\]
Energy over time
\[E=P\Delta t\]

Rules

Fission Q
\[Q=(m_i-m_f)c^2\]
Power relation
\[P=\dot N_fE_f\]
Criticality
\[k=1\]

Examples

Question
If one fission releases
\[200\,\mathrm{MeV}\]
estimate joules per fission.
Answer
\[200\,\mathrm{MeV}=200(1.60\times10^{-13})=3.2\times10^{-11}\,\mathrm J\]

Checks

  • Fission energy mostly appears as fragment kinetic energy, then heat.
  • Delayed neutrons make controlled reactors possible.
  • Critical does not mean explosive; it means steady neutron population.
  • Control rods reduce the effective multiplication factor.