In the nuclear reaction ${}^{1}_{1}H + {}^{3}_{1}H \rightarrow {}^{2}_{1}H + {}^{2}_{1}H$, the Q-value of the reaction is approximately (given: $m({}^1H) = 1.007825$ u, $m({}^2H) = 2.014102$ u, $m({}^3H) = 3.016049$ u, 1 u = 931.5 MeV):

Nucleus: protons + neutrons (nucleons). Atomic number $Z$ = protons. Mass number $A$ = protons + neutrons. Binding energy/nucleon: peaks at Fe-56. Nuclear radius: $R = R_0 A^{1/3}$ where $R_0 = 1.2$ fm (femtometre = $10^{-15}$ m). Nuclear density: $\sim 10^{17}$ kg/m$^3$ (constant for all nuclei). Strong nuclear force: short range (~1-3 fm), stronger than electromagnetic, holds nucleus together.

Three types: $\alpha$ decay: emits $^4_2He$; $A\to A-4$, $Z\to Z-2$. $\beta^-$ decay: neutron $\to$ proton + $e^-$ + $\bar{\nu}_e$; $A$ same, $Z\to Z+1$. $\beta^+$ decay: proton $\to$ neutron + $e^+$ + $\nu_e$; $A$ same, $Z\to Z-1$. $\gamma$ decay: excited nucleus emits $\gamma$ photon, no change in $A$ or $Z$. Law of decay: $N = N_0 e^{-\lambda t}$; half-life: $T_{1/2} = \ln2/\lambda = 0.693/\lambda$.

Fission: heavy nucleus splits into two medium-sized fragments + neutrons + energy. $^{235}U + n \to$ fission products + 2-3 neutrons + ~200 MeV. Chain reaction: released neutrons trigger more fissions. Controlled (nuclear reactor): moderator slows neutrons (graphite, heavy water). Uncontrolled: nuclear bomb (critical mass, no control rods). Nuclear reactors use U-235 (0.7% of natural uranium) or Pu-239. India: Kudankulam (PWR), Tarapur, etc.

Fusion: light nuclei combine to form heavier nucleus + energy. Sun\'s energy: proton-proton chain ($4^1H \to ^4He + 2e^+ + 2\nu + \gamma + 26.7$ MeV). D-T fusion for reactors: $^2H + ^3H \to ^4He + n + 17.6$ MeV. Requires very high temperature (~$10^7-10^8$ K) for nuclei to overcome Coulomb barrier → thermonuclear fusion. Challenges: plasma confinement (tokamak: magnetic confinement), sustained reaction. ITER project in France aims to achieve sustained fusion. Hydrogen bomb: uncontrolled D-T fusion triggered by fission bomb.

The mass of a nucleus is always less than the sum of its constituent protons and neutrons. That difference, the mass defect $\Delta m$, appears as binding energy through $E = \Delta mc^2$, and 1 atomic mass unit corresponds to 931.5 MeV. Binding energy per nucleon, not total binding energy, measures stability — and it peaks near iron-56 at about 8.8 MeV, which is why iron is the endpoint of stellar fusion.

The binding energy per nucleon curve rises steeply for light nuclei and falls gently for heavy ones. Fusing two light nuclei moves the product up the curve, and splitting a heavy nucleus moves the fragments up it too. Both therefore end with more tightly bound nuclei and release the difference as energy. This single curve explains both processes, which is why questions so often supply it as a graph.

Activity falls exponentially as $N = N_0e^{-\lambda t}$, with half-life $T_{1/2} = 0.693/\lambda$ and mean life $\tau = 1/\lambda$, so $\tau$ is always longer than the half-life. Alpha decay reduces mass number by 4 and atomic number by 2; beta-minus decay leaves mass number unchanged and raises atomic number by 1; gamma emission changes neither and simply releases excess energy. Most decay-chain questions reduce to applying these three rules in sequence.