Chapter 30: Nuclear Physics and Radioactivity

30-1 Structure and Properties of the Nucleus

The atomic nucleus is composed of protons and neutrons, collectively called nucleons. Its size and mass are fundamental properties studied in nuclear physics.

• Wave-Particle Duality: The size of the nucleus is not sharply defined due to quantum effects. High-energy electron scattering experiments yield the nuclear radius:

• Atomic Mass Unit (u): Masses of atoms are measured relative to carbon-12, which is defined as exactly 12 u.

• Rest Masses: Electrons are much less massive than nucleons.

• Isotope Notation: where A is mass number, Z is atomic number, X is element symbol.

Example: Estimate the diameter of the smallest and largest naturally occurring nuclei using .

30-3 Radioactivity

Radioactivity is the spontaneous emission of radiation by unstable nuclei. Discovered in the late 19th century, it was studied by Marie and Pierre Curie, who isolated polonium and radium.

• Types of Radioactive Rays:

  1. Alpha rays (α): Helium nuclei; low penetration (stopped by paper).

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

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

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

30-4 Alpha Decay

Alpha decay occurs when a nucleus emits an alpha particle (helium nucleus). This process typically happens in heavy nuclei where the strong nuclear force cannot hold the nucleus together.

• General Equation:

• Disintegration Energy: The mass of the parent nucleus is greater than the sum of the masses of the daughter nucleus and the alpha particle; the difference is released as energy.

• Example:

30-5 Beta Decay

Beta decay involves the emission of an electron (β−) or positron (β+) from the nucleus, and is governed by the weak nuclear force.

• Electron Emission:

• Positron Emission:

• Electron Capture:

• Neutrinos: Neutral, nearly massless particles, difficult to detect; symbol (nu).

30-6 Gamma Decay

Gamma decay is the emission of high-energy photons when a nucleus transitions from an excited state to a lower energy state. This process does not change the number of protons or neutrons.

• Example:

30-7 Conservation of Nucleon Number and Other Conservation Laws

Radioactive decay processes obey several conservation laws, including conservation of nucleon number, electric charge, linear and angular momentum, and mass-energy.

30-8 Half-Life and Rate of Decay

Nuclear decay is a random, statistical process. The rate at which nuclei decay is proportional to the number of undecayed nuclei present.

• Decay Rate Equation:

• Exponential Decay Law:

• Half-Life (): The time required for half the nuclei in a sample to decay.

• Key Properties:

  • Half-life depends only on the nature of the element, not on amount, temperature, or pressure.

  • After n half-lives, the fraction remaining is .

• Example: After 5 half-lives, of the original nuclei remain.

Brachytherapy and Radioactive Isotopes in Medicine

What is Brachytherapy?

Brachytherapy is a form of radiation therapy where radioactive sources are placed directly inside or next to the area requiring treatment. It allows for high doses to the tumor with rapid dose fall-off, sparing surrounding healthy tissue.

• "Brachy" means "short" in Greek; therapy is localized.

• Used for various anatomical sites, most commonly cervix, vagina, and prostate cancers.

• Emitted radiation is low energy and does not travel far.

• Results in heterogeneous dose distributions compared to external beam radiation therapy (EBRT).

Common Brachytherapy Isotopes

Additional info: HVL = Half Value Layer, the thickness of lead required to reduce radiation intensity by half. Γ is the exposure rate constant. f is the dose rate conversion factor.

Applications in Cancer Treatment

• Cervical Cancer: Targets include the cervix and adjacent tissues. Applicators such as the Fletcher-Suit-Delclos (FSD) system are commonly used.

• Prostate Cancer: TRUS (Transrectal Ultrasound) guided implants are used for precise placement of radioactive sources.

• Bladder/Rectum Points: ICRU 38 reference points are used to monitor dose to critical structures.

Summary of Key Concepts

• Nuclei contain protons and neutrons (nucleons).

• Atomic mass number (A) and atomic number (Z) define isotopes.

• Binding energy is the difference between the mass of the nucleus and its constituents.

• Radioactive decay types: alpha (helium nucleus), beta (electron/positron), gamma (photon).

• Strong nuclear force binds nucleons; weak nuclear force governs beta decay.

• Conservation laws: charge, momentum, mass-energy, nucleon number.

• Radioactive decay follows exponential law; half-life is a key parameter.

• Brachytherapy uses radioactive isotopes for targeted cancer treatment.