Chapter 41: Nuclear Physics and Radioactivity

41.1 Structure and Properties of the Nucleus

The atomic nucleus is the central part of an atom, composed of protons and neutrons, collectively called nucleons. The properties and composition of nuclei are fundamental to understanding nuclear physics.

• Proton: Positively charged particle, mass kg.

• Neutron: Electrically neutral particle, mass kg.

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

• Atomic number (): Number of protons in the nucleus.

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

• Neutron number ():

• Isotopes: Nuclei with the same but different .

• Natural abundance: Percentage of a particular isotope in nature.

The size of the nucleus is estimated using high-energy electron scattering:

Example: Density comparison for Aluminum ():

• Nuclear density: kg/m3

• Solid Aluminum density: kg/m3

Atomic masses are measured in unified atomic mass units (u):

• kg MeV/

• J

41.2 Binding Energy and Nuclear Forces

The binding energy of a nucleus is the energy required to disassemble it into its constituent protons and neutrons. The mass of a nucleus is less than the sum of its separate nucleons due to this binding energy, which is released during formation.

• Binding energy (): MeV/u

• Binding energy per nucleon:

• Higher binding energy per nucleon means greater nuclear stability.

• More massive nuclei require extra neutrons to overcome proton-proton Coulomb repulsion.

Example:

• For He: Mass of nucleus = 4.002603 u, Mass of constituents = 4.032980 u

• For Fe: Mass elements – mass nucleus = 0.528 u, MeV, MeV per nucleon

The strong nuclear force binds nucleons together; it is very strong but short-range (essentially zero beyond m). The weak nuclear force governs certain types of decay, such as beta decay.

41.3 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.

• Alpha rays: Helium nuclei, low penetration (stopped by paper).

• Beta rays: Electrons, moderate penetration (stopped by a few mm of aluminum).

• Gamma rays: Electromagnetic radiation, high penetration (stopped by several cm of lead).

• Alpha and beta rays are deflected in opposite directions by a magnetic field; gamma rays are not deflected.

41.4 Alpha Decay

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

• General form:

• Disintegration energy: Difference in mass between parent and products, converted to energy.

Example: u MeV

41.5 Beta Decay

Beta decay is the process by which a nucleus emits an electron (or positron), changing a neutron to a proton (or vice versa). This process is governed by the weak nuclear force.

• Fundamental process:

• The electron is created in the decay, not from atomic orbitals.

• The neutrino is required for conservation of energy and momentum; it has negligible mass.

• General form:

• Electron capture:

Example: Mass difference: u MeV

41.6 Gamma Decay

Gamma decay involves the emission of high-energy photons (gamma rays) when a nucleus transitions from an excited state to a lower energy state. This is analogous to photon emission by electrons in atoms.

• Gamma rays have energies in the keV to MeV range.

• No change in nucleon number or atomic number.

41.7 Conservation of Nucleon Number and Other Conservation Laws

Radioactive decay processes obey several conservation laws:

• Nucleon number: Total number of nucleons is conserved.

• Electric charge: Conserved in all nuclear reactions.

• Linear and angular momentum: Conserved.

• Mass-energy: Conserved.

41.8 Half-Life and Rate of Decay

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

• Decay rate equation:

• Solution:

• Half-life ():

• Activity ():

• Units: 1 Becquerel (Bq) = 1 disintegration/sec; 1 Curie (Ci) = Bq

Example: For (half-life 5730 yr), s-1. For nuclei, activity decays/sec.

41.9 Decay Series

A decay series occurs when a radioactive isotope decays to another radioactive isotope, which then decays further, and so on. This process can produce nuclei not found naturally.

• Example: The decay series starting with .

41.10 Radioactive Dating

Radioactive dating uses the known half-life of isotopes to determine the age of materials. Carbon-14 dating is used for organic materials, while other isotopes (e.g., Uranium-238) are used for geological dating.

• Carbon-14: Half-life = 5730 years; used for dating up to ~60,000 years.

• Ratio of to in living organisms matches the atmosphere; after death, decays and the ratio decreases.

• Uranium-238: Half-life = years; used for dating rocks billions of years old.

Example: If a bone fragment (200 g carbon) registers 16 decays/s, and living matter has % , its age can be calculated using the decay equations above.

Summary of Key Concepts

• Nuclei are made of protons and neutrons (nucleons).

• Atomic number () and mass number () specify a nuclide.

• Binding energy is the mass difference between nucleus and constituents, indicating stability.

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

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

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

• Radioactive decay is statistical; described by .

• Half-life is the time for half the nuclei to decay.