Chapter 30: Nuclear Physics and Radioactivity

30.1 Structure and Properties of the Nucleus

The atomic nucleus is the dense central core of an atom, composed of protons and neutrons, collectively known as nucleons. Understanding the structure and properties of the nucleus is fundamental to nuclear physics.

• Proton: Positively charged particle; mass approximately kg.

• Neutron: Electrically neutral particle; slightly more massive than the proton.

• Nucleons: Collective term for protons and neutrons.

• Nuclide: A specific type of nucleus, defined by its number of protons and neutrons.

• Atomic Number (Z): Number of protons in the nucleus; determines the element.

• Atomic Mass Number (A): Total number of nucleons (protons + neutrons).

• Neutron Number (N):

• Isotopes: Nuclei with the same Z (element) but different N (neutron number).

• Natural Abundance: The percentage of a particular isotope found in nature.

• Nuclide Symbol: (where X is the chemical symbol, A is mass number, Z is atomic number).

• Unified Atomic Mass Unit (u): Defined as 1/12 the mass of a carbon-12 atom; kg.

• Nuclear Size: The radius of a nucleus is approximately , where m.

Example: Carbon-14: has 6 protons and 8 neutrons.

30.2 Binding Energy and Nuclear Forces

The stability of a nucleus is determined by the binding energy, which is the energy required to disassemble the nucleus into its constituent protons and neutrons.

• Mass Defect: The mass of a nucleus is less than the sum of the masses of its individual nucleons. The difference is called the mass defect ().

• Binding Energy (BE): The energy equivalent of the mass defect, given by .

• Binding Energy per Nucleon: ; a measure of nuclear stability.

• Strong Nuclear Force: The force that binds nucleons together; very strong but short-ranged (effective over distances m).

• Coulomb Force: The electrostatic repulsion between protons; long-ranged and increases with Z.

• Weak Nuclear Force: Responsible for certain types of nuclear decay (e.g., beta decay).

Example: The binding energy of helium-4 is much higher per nucleon than that of deuterium, making it more stable.

30.3 Radioactivity

Radioactivity is the spontaneous emission of particles or electromagnetic radiation from unstable nuclei. Discovered in the late 19th century, it is a key phenomenon in nuclear physics.

• Types of Radioactive Emissions:

  • Alpha (α) Rays: Helium nuclei (); low penetration (stopped by paper).

  • Beta (β) Rays: Electrons or positrons; moderate penetration (stopped by a few mm of aluminum).

  • Gamma (γ) Rays: High-energy photons; high penetration (stopped by several cm of lead).

• Magnetic Field Effects: Alpha and beta rays are deflected in opposite directions; gamma rays are unaffected.

Example: Polonium and radium are highly radioactive elements discovered by Marie and Pierre Curie.

30.4 Alpha Decay

Alpha decay is a process in which an unstable nucleus emits an alpha particle (helium nucleus), resulting in a new element with atomic number reduced by 2 and mass number reduced by 4.

• General Equation:

• Disintegration Energy: The mass difference between the parent and the sum of the daughter and alpha particle is released as energy.

• Stability: Alpha decay is common in heavy nuclei where the strong nuclear force cannot counteract the Coulomb repulsion.

• Applications: Alpha sources are used in smoke detectors.

Example:

30.5 Beta Decay

Beta decay involves the transformation of a neutron into a proton (or vice versa), accompanied by the emission of a beta particle (electron or positron) and a neutrino or antineutrino.

• Beta-minus (β-) Decay: Neutron decays into a proton, electron, and antineutrino.

  • Equation:

  • Example:

• Beta-plus (β+) Decay: Proton decays into a neutron, positron, and neutrino.

  • Equation:

• Electron Capture: A nucleus captures one of its own inner electrons, converting a proton into a neutron.

• Neutrino (ν): Nearly massless, neutral particle; interacts very weakly with matter.

• Weak Nuclear Force: Governs beta decay processes.

Example: Beta decay of carbon-14 is used in radiocarbon dating.

30.6 Gamma Decay

Gamma decay occurs when a nucleus in an excited state releases energy by emitting a gamma photon, transitioning to a lower energy state. No change in atomic number or mass number occurs.

• Gamma Ray: High-energy electromagnetic radiation.

• Analogy: Similar to photons emitted when electrons drop to lower energy levels in atoms.

30.7 Conservation of Nucleon Number and Other Conservation Laws

Several conservation laws govern nuclear reactions and decays:

• Conservation of Nucleon Number (A): The total number of nucleons remains constant in nuclear reactions.

• Conservation of Charge (Z): Total electric charge is conserved.

• Conservation of Linear and Angular Momentum: Both are conserved in nuclear processes.

• Conservation of Mass-Energy: Total mass-energy is conserved.

Table: Types of Radioactive Decay

30.8 Half-Life and Rate of Decay

Nuclear decay is a random, statistical process. The half-life is the time required for half the nuclei in a sample to decay.

• Decay Law: The rate of decay is proportional to the number of undecayed nuclei:

• Solution: The number of nuclei remaining after time t:

• Half-Life (T1/2): Related to the decay constant by:

30.10 Decay Series

A decay series is a sequence of radioactive decays that certain heavy nuclei undergo, producing a series of different elements and isotopes until a stable nucleus is formed.

• Example: Uranium-238 decays through a series of alpha and beta decays to eventually form lead-206.

• Significance: Explains the presence of certain isotopes in nature.

30.11 Radioactive Dating

Radioactive dating uses the known half-lives of isotopes to determine the age of materials.

• Radiocarbon Dating: Measures the ratio of carbon-14 to carbon-12 in organic material. Useful for dating objects up to about 60,000 years old.

• Other Isotopes: Uranium-238 (half-life years) is used for dating rocks and the Earth.

• Principle: After death, the intake of carbon-14 stops, and its decay allows age determination.

Example: The age of ancient wooden artifacts can be determined by measuring their carbon-14 content.

30.12 Stability and Tunneling

Some nuclei are unstable but do not decay immediately due to the presence of an energy barrier. Quantum tunneling allows particles to escape even when they do not have enough energy classically.

• Alpha Decay and Tunneling: The alpha particle escapes the nucleus by tunneling through the potential barrier.

• Heisenberg Uncertainty Principle: Allows for temporary violations of energy conservation, enabling tunneling.

• Variation in Half-Lives: The probability of tunneling (and thus decay) depends on the height and width of the barrier.

30.13 Detection of Particles

Charged and neutral particles from nuclear processes are detected using specialized instruments.

• Geiger Counter: Gas-filled tube that detects ionizing radiation by electrical pulses.

• Scintillation Counter: Uses materials that emit light when struck by radiation; light is amplified and detected.

• Cloud Chamber: Supercooled gas; charged particles leave visible tracks of droplets.

• Bubble Chamber: Superheated liquid; tracks of bubbles form along the path of charged particles.

• Wire Drift Chamber: Advanced detector measuring the position and timing of particle interactions with high precision.

Example: Geiger counters are commonly used for radiation safety monitoring.

Additional info: Where the original slides referenced equations or tables without explicit content, standard nuclear physics equations and examples have been provided for completeness.