Pair Production: Energetic $\gamma$-ray photon ($h\nu$) absorbed by nucleus, creating an electron ($e^-$) and a positron ($e^+$). $$ h\nu \to e^+ + e^- $$ Minimum energy for $\gamma$-photon: $2 m_e c^2 \approx 1.02 \text{ MeV}$.
Pair Annihilation: Electron and positron combine, producing two $\gamma$-photons. $$ e^+ + e^- \to h\nu + h\nu $$

Neutron-proton ratio ($N/Z$):
- Lighter nuclei: $N/Z \approx 1$ for stability.
- Heavy nuclei: $N/Z > 1$ for stability (more neutrons needed to counteract proton repulsion).
Even/Odd numbers of $Z$ or $N$:
- Even $Z$, Even $N$ (even-even) are most stable ($\approx 60\%$ of stable nuclides).
- Odd $Z$, Odd $N$ (odd-odd) are least stable (only 5 known).
Binding Energy per Nucleon: Higher B.E./nucleon $\implies$ more stable nucleus.

Mass Defect ($\Delta m$): $\Delta m = (Z m_p + (A-Z) m_n) - M_\text{nucleus}$. ($M_\text{nucleus}$ is actual mass of nucleus).
Binding Energy (B.E.): Energy equivalent to mass defect. B.E. $= \Delta m c^2$. If $\Delta m$ is in amu, B.E. $= \Delta m \times 931 \text{ MeV}$.
Packing Fraction: $\frac{\Delta m}{A}$. Smaller value means greater stability.
B.E. per Nucleon: $\frac{\text{B.E.}}{A}$.

Graph of B.E./nucleon vs. mass number ($A$).

Peaks at $A=4, 8, 12, 16, 20$ (e.g., $^4_2He, ^8_4Be, ^{12}_6C, ^{16}_8O, ^{20}_{10}Ne$) indicating higher stability.
Maximum B.E./nucleon for $A=56$ ($^{56}_{26}Fe$), value is $8.8 \text{ MeV/nucleon}$.
For $A > 56$, B.E./nucleon gradually decreases (e.g., for $U^{238}$, it's $7.5 \text{ MeV}$).

Process where identity of a nucleus changes due to bombardment by energetic particles.

$X(a,b)Y \implies X + a \to Y + b + Q$

Q-value: Energy absorbed (endothermic, $Q<0$) or released (exothermic, $Q>0$). $Q = (\text{Mass of reactants} - \text{Mass of products})c^2$.
Conservation Laws:
- Mass number ($A$) conserved.
- Charge number ($Z$) conserved.
- Momentum conserved.
- Total energy conserved.
Common Reactions: $(p,n), (p,\alpha), (p,\gamma), (n,p), (\gamma,n)$.

Splitting of a heavy nucleus into two lighter nuclei with energy liberation.

Discovered by Otto Hahn and Fritz Strassmann.
Example: $^1_0n + ^{235}_{92}U \to ^{236}_{92}U^* \to ^{141}_{56}Ba + ^{92}_{36}Kr + 3^1_0n + Q$.
Energy released: $\approx 200 \text{ MeV}$ per fission.
Neutrons released are fast ($2 \text{ MeV}$), need to be slowed down for chain reaction.

Self-sustaining sequence of nuclear fissions.

Neutron Reproduction Factor ($k$): $\frac{\text{Rate of neutron production}}{\text{Rate of neutron loss}}$.
- $k=1$: Steady (critical size/mass).
- $k>1$: Accelerates (supercritical, atom bomb).
- $k<1$: Halts (subcritical).

Controlled Chain Reaction	Uncontrolled Chain Reaction
Controlled artificially	No control
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