The atomic nucleus is the heart of an atom, containing protons and neutrons held together by the strong nuclear force. This dense core determines an element's identity and isotopic properties, while electrons orbiting it influence chemical behavior.

Nuclear properties like density, force, and stability are crucial in understanding atomic structure and behavior. The nuclear force's strength over short distances allows nuclei to remain stable despite electromagnetic repulsion, leading to fascinating phenomena in nuclear physics.

Atomic Nucleus

Structure of atomic nuclei

• Nucleus is the dense, central core of an atom contains protons and neutrons (nucleons)
  • Protons are positively charged particles contribute to the atomic number and determine the element's identity
  • Neutrons are electrically neutral particles affect the mass number and isotopic properties
• Nucleons are held together by the strong nuclear force overcomes the electromagnetic repulsion between protons
• Electrons orbit the nucleus in shells or orbitals determine the chemical properties and reactivity of an atom (electron configuration)

Atomic number vs mass number

• Atomic number ($Z$) represents the number of protons in an atom's nucleus defines the element and its chemical properties (periodic table)
  • Equal to the number of electrons in a neutral atom maintains electrical neutrality
• Mass number ($A$) is the total number of nucleons (protons + neutrons) in an atom's nucleus represents the approximate atomic mass (atomic mass unit, amu)
• Isotopes are atoms of the same element with different numbers of neutrons have the same atomic number ($Z$) but different mass numbers ($A$) (carbon-12, carbon-13, carbon-14)
  • Isotopes have similar chemical properties but different physical properties (radioactivity, stability)

Nuclear Properties

Nuclear density calculation and significance

• Nuclear density is the mass per unit volume of the nucleus calculated using the formula $\rho = \frac{m}{V} = \frac{m}{\frac{4}{3}\pi r^3}$, where $m$ is the mass and $r$ is the radius of the nucleus
• Typical nuclear density is approximately $2.3 \times 10^{17}$ kg/m³ extremely high compared to everyday matter (water density: 1000 kg/m³)
• High nuclear density indicates the compactness and stability of the nucleus explains the large amount of energy released in nuclear reactions (fission, fusion)

Properties of nuclear force

• Nuclear force (strong force) is the fundamental force that holds nucleons together an attractive force between protons and neutrons
• Nuclear force is a short-range force effective only over distances comparable to nuclear size ($10^{-15}$ m)
• Nuclear force is the strongest of the four fundamental forces (gravitational, electromagnetic, weak, strong)
• Nuclear force overcomes the electrostatic repulsion between positively charged protons binds nucleons tightly, making the nucleus stable

Nuclear vs electromagnetic forces

• Nuclear force (strong force) is the strongest of the four fundamental forces an attractive force between all nucleons (protons and neutrons)
  • Nuclear force is a short-range force effective only over distances comparable to nuclear size ($10^{-15}$ m)
• Electromagnetic force is a repulsive force between protons due to their positive charges an infinite range force that decreases with distance according to Coulomb's law
  • Electromagnetic force is much weaker than the nuclear force at short distances ($10^{-15}$ m)
• Nuclear force is about 100 times stronger than the electromagnetic force at nuclear distances dominates at short ranges, allowing the nucleus to remain stable despite the electromagnetic repulsion between protons
  • This stability is quantified by the binding energy, which represents the energy required to break apart a nucleus

Nuclear Models and Stability

• The liquid drop model describes the nucleus as a dense, incompressible fluid of nucleons helps explain nuclear fission and fusion processes
• The nuclear shell model describes the arrangement of nucleons in energy levels or shells explains magic numbers and nuclear stability
• Nuclear stability is determined by the ratio of protons to neutrons in the nucleus affects the likelihood of radioactive decay
• Radioactive decay occurs when unstable nuclei emit particles or energy to achieve a more stable configuration (alpha, beta, gamma decay)