AcademyNuclear Physics
Academy
Nuclear Reactions
Level 1 - Physics topic page in Nuclear Physics.
Principle
Nuclear reactions conserve charge, nucleon number, energy, momentum, and relevant quantum numbers.
Notation
\(Q\)
reaction energy release
J, MeV
\(m_i\)
initial total rest mass
kg, u
\(m_f\)
final total rest mass
kg, u
\(K\)
kinetic energy
J, MeV
\(A\)
total nucleon number
1
\(Z\)
total proton number
1
Method
Derivation 1: Conservation checks
Balance nucleon number and charge before using energy.
Nucleon conservation
\[\sum A_i=\sum A_f\]
Charge conservation
\[\sum Z_i=\sum Z_f\]
Derivation 2: Q value
Mass difference becomes kinetic energy, radiation, or excitation energy.
Mass-energy balance
\[Q=(m_i-m_f)c^2\]
Kinetic-energy form
\[Q=K_f-K_i\]
Derivation 3: Threshold idea
If \(Q<0\), incoming kinetic energy must supply the missing rest energy and momentum constraint.
Endothermic reaction
\[Q<0\]
Threshold condition
\[K_{\mathrm{in}}>|Q|\quad\text{in the lab frame}\]
Rules
A conservation
\[\sum A_i=\sum A_f\]
Z conservation
\[\sum Z_i=\sum Z_f\]
Q value
\[Q=(m_i-m_f)c^2\]
Examples
Question
A reaction has
\[m_i-m_f=0.0040\,\mathrm u\]
Find \(Q\).Answer
\[Q=0.0040(931.5)=3.7\,\mathrm{MeV}\]
Checks
- Balance \(A\) and \(Z\) before calculating \(Q\).
- Positive \(Q\) means rest mass decreased.
- Momentum conservation affects kinetic-energy sharing.
- Atomic masses can be used when electron counts balance.