Unit 4: Nuclear Physics

1. General Properties of Nuclei
2. Binding Energy and Stability
3. Radioactivity: Alpha, Beta, and Gamma Decay
4. Nuclear Models (Liquid Drop & Shell Model)
5. Nuclear Fission and Fusion
6. Particle Detectors and Accelerators
7. Exam Focus Corner

1. General Properties of Nuclei

The nucleus is the small, dense central core of an atom consisting of Nucleons (protons and neutrons).

Nuclear Radius: Measured in femtometers (fm). It follows the relation R = R₀ A^1/3, where R₀ ≈ 1.2 fm.
Nuclear Density: The density of nuclear matter is extremely high (≈ 10¹⁷ kg/m³) and is independent of the mass number A.
Nuclear Charge: Determined by the number of protons (Ze).

2. Binding Energy and Stability

Binding Energy (B.E.) is the energy required to split a nucleus into its individual nucleons. It arises from the Mass Defect—the difference between the sum of individual nucleon masses and the actual nuclear mass.

[Image of binding energy per nucleon curve vs mass number]

B.E. = Δ m · c² = [Z m_p + (A-Z)m_n - M] · c²

Stability: The B.E. per nucleon curve shows a maximum near A=56 (Iron), indicating that intermediate nuclei are the most stable. Light nuclei undergo Fusion and heavy nuclei undergo Fission to reach this stable state.

3. Radioactivity

Radioactivity is the spontaneous disintegration of unstable nuclei by emitting radiation. It follows an exponential decay law: N = N₀ e^{-λ t}.

Type	Emitted Particle	Effect on (A, Z)
Alpha (α)	Helium Nucleus (⁴₂He)	A \to A-4, Z \to Z-2
Beta (β)	Electron (e^-) or Positron (e⁺)	Z \to Z ± 1 (A stays same)
Gamma (γ)	High-energy Photon	No change in A or Z

4. Nuclear Models

To explain various properties of the nucleus, two primary models are used:

Liquid Drop Model: Treats the nucleus as a drop of incompressible fluid. It successfully explains Nuclear Fission and the Semi-Empirical Mass Formula.
Shell Model: Assumes nucleons move in discrete energy levels (shells) similar to electrons. It explains Magic Numbers (2, 8, 20, 28, 50, 82, 126) where nuclei are exceptionally stable.

5. Nuclear Fission and Fusion

Nuclear Fission:

A heavy nucleus splits into two smaller nuclei with the release of a large amount of energy and extra neutrons. Used in nuclear reactors (controlled) and atomic bombs (uncontrolled).

Nuclear Fusion:

Two light nuclei combine to form a heavier, more stable nucleus. This process powers the Sun and stars. It requires extremely high temperatures (millions of degrees) to overcome Coulomb repulsion.

6. Particle Detectors and Accelerators

Detectors: Devices like the Geiger-Muller (G.M.) Counter and Scintillation Counter detect radiation by utilizing ionization or light flashes.
Accelerators: Devices like the Cyclotron use electromagnetic fields to accelerate charged particles to high speeds for nuclear bombardment experiments.

[Image of a cyclotron particle accelerator diagram]

Exam Focus Corner

Frequently Asked Questions

Define Half-life (T_1/2): It is the time required for half of the initial radioactive nuclei to decay. T_1/2 = 0.693 / λ.
Why is the neutron-to-proton ratio (N/Z) important? For light nuclei, N/Z ≈ 1. For heavy nuclei, more neutrons are needed to provide enough "nuclear glue" to counteract the electrostatic repulsion of protons.

Common Mistakes

Mass Defect Units: Ensure you convert atomic mass units (amu) to MeV correctly (1 amu ≈ 931.5 MeV).
Fission vs. Fusion: Remember that Fission is "splitting" and Fusion is "joining." Don't swap their definitions in energy calculations.

Exam Tips

Tip: When explaining the B.E. per nucleon curve, always draw the graph. It is often a compulsory 5-mark question and perfectly illustrates why fission and fusion occur.