The nucleus is the small, dense region at the center of an atom, consisting of nucleons: protons and neutrons.
Intrinsic properties include mass number (A), which is the total number of nucleons, and atomic number (Z), the number of protons.
The mass of a nucleus is always less than the sum of the masses of its individual nucleons. This difference is known as the mass defect.
The nucleus is often modeled as a sphere. The radius (R) follows the empirical relation:
Where R0 is a constant approximately equal to 1.2 to 1.5 fm (femtometers).
The matter density of a nucleus is remarkably constant across different elements, implying that nuclear matter is incompressible. The charge density follows a similar distribution, being roughly constant at the center and dropping off at the surface.
Binding Energy (B.E.) is the energy required to completely disassemble a nucleus into its constituent protons and neutrons.
The plot of B.E. per nucleon (B.E./A) against A is a fundamental graph in nuclear physics:
The packing fraction is defined as the mass defect per nucleon. It provides a measure of nuclear stability; a lower packing fraction typically indicates a more stable nucleus.
The N/Z plot (Segre Chart) shows the relationship between the number of neutrons (N) and protons (Z) for stable nuclei.
Total angular momentum (J) is the vector sum of the orbital and intrinsic spin angular momenta of all nucleons.
Parity describes the symmetry of the wave function under spatial inversion. It is an important quantum number in nuclear reactions.
Alpha decay is the process where an unstable nucleus emits an alpha particle (a Helium-4 nucleus).
The Q-value represents the energy released in the reaction, which is shared as kinetic energy between the alpha particle and the recoil nucleus.
Classically, an alpha particle cannot escape the nucleus because its energy is less than the potential barrier height. Gamow's theory explains this using quantum tunneling.
The theory assumes the alpha particle pre-exists inside the nucleus and "tunnels" through the Coulomb barrier. The probability of escape (transparency of the barrier) is highly sensitive to the energy of the particle, explaining the wide range of half-lives observed.
The Geiger-Nuttall Law provides an empirical relationship between the decay constant (λ) and the range (R) of the emitted alpha particles:
Where A and B are constants. Modern versions relate log λ to the energy (E) of the alpha particle.
Alpha particles are emitted with discrete energies, resulting in a line spectrum. This provides evidence that nuclei possess discrete energy levels.
Tip: In diagrams of the B.E. curve, always label the position of Iron (Fe) as the most stable point. For Alpha decay, remember the Geiger-Nuttall law implies that high-energy emitters have very short half-lives.