Nuclear Reactions (Q-value)
Q = Δm · c² — preset D-T, D-D, p-Li fusion and U-235 fission reactions.
Key Notes
A nuclear reaction is when a projectile (n, α, γ, etc.) hits a target nucleus, producing a new nucleus + ejecta.
Standard notation: target(projectile, ejected)product. Example: ¹⁴N(α, p)¹⁷O = α-particle + N-14 → O-17 + proton.
Conservation laws: charge (Z), mass number (A), energy, momentum, and angular momentum are ALL conserved.
Q-value: Q = (initial rest mass − final rest mass)·c² = total kinetic energy released.
Endothermic (Q < 0): require minimum (threshold) KE of projectile. Exothermic (Q > 0): release energy.
Reaction cross-section σ measures probability — typical units: barn = 10⁻²⁸ m². Depends strongly on energy.
Compound nucleus model (Bohr): projectile is absorbed first, then a 'hot' compound nucleus decays.
Direct reactions: fast, single-step (e.g., pickup or stripping). Compound-nucleus: slower, statistical.
Formulas
Q-value of a reaction
Sum of rest masses; Q > 0 ⇒ exothermic.
Standard notation
Target X, projectile a, ejectile b, residue Y.
Threshold energy (endothermic)
Minimum lab KE of projectile to make Q < 0 reaction proceed.
Important Points
Conservation of A and Z gives you DAUGHTER nucleus quickly: write A and Z on both sides and balance.
Q > 0 ⇒ reaction proceeds spontaneously (energy released). Q < 0 ⇒ need to inject energy.
Rutherford's 1919 experiment ¹⁴N(α,p)¹⁷O was the FIRST artificially-induced nuclear transmutation.
Cross-section σ is highly energy-dependent — sharp peaks (resonances) at compound-nucleus excitation energies.
Slow neutrons (thermal) have HUGE cross-sections for many nuclei because they spend more time inside.
Fission and fusion are special cases of nuclear reactions with very large |Q|.
Nuclear Reactions (Q-value) notes from sciphylab (also known as SciPhy, SciPhy Lab, SciPhy Labs, Physics Lab). Class 12 physics revision for JEE Mains, JEE Advanced, NEET UG, AP Physics 1/2/C, SAT, and CUET-UG.