Nuclear properties are crucial for understanding atomic behavior. This section dives into the mass, charge, and size of nuclei, which determine how atoms interact and react.

We'll explore how nuclear composition affects stability, and how measuring techniques reveal the tiny world inside atoms. These concepts are key to grasping nuclear forces and reactions.

Nuclear Mass and Composition

Fundamental Units and Atomic Structure

• Atomic mass unit (amu) defined as 1/12 the mass of a carbon-12 atom, approximately $1.66 × 10^{-27}$ kg
• Mass number represents the total number of protons and neutrons in an atomic nucleus
• Atomic number indicates the number of protons in the nucleus, determines the element's identity
• Neutron number calculated by subtracting the atomic number from the mass number
• Nuclide notation uses the format $^A_Z X$, where A is the mass number, Z is the atomic number, and X is the element symbol

Isotopes and Nuclear Variations

• Isotopes consist of atoms with the same atomic number but different numbers of neutrons
• Varying neutron numbers affect nuclear stability and radioactive properties
• Isobars share the same mass number but have different atomic numbers (calcium-40 and argon-40)
• Isotones have the same number of neutrons but different numbers of protons (carbon-13 and nitrogen-14)
• Nuclear binding energy measures the energy required to break apart a nucleus into its constituent nucleons

Nuclear Size and Radius

Nuclear Dimensions and Measurement Techniques

• Nuclear radius typically ranges from 1 to 10 femtometers (1 fm = $10^{-15}$ m)
• Nuclear volume increases proportionally to the mass number
• Empirical formula for nuclear radius: $R = r_0 A^{1/3}$, where $r_0$ ≈ 1.2 fm and A is the mass number
• Electron scattering experiments reveal information about nuclear size and shape
• Rutherford scattering provided early evidence for the existence of a small, dense nucleus

Advanced Nuclear Size Concepts

• Root-mean-square (RMS) radius measures the average distance of nuclear matter from the center
• RMS radius calculated using the formula: $R_{rms} = \sqrt{\frac{\int r^2 \rho(r) d^3r}{\int \rho(r) d^3r}}$, where $\rho(r)$ is the nuclear density distribution
• Nuclear skin refers to the diffuse outer region of the nucleus where proton and neutron densities differ
• Skin thickness varies among nuclei, influencing nuclear reactions and properties

Nuclear Charge and Density

Nuclear Density Characteristics

• Nuclear density remains approximately constant across all nuclei at $\sim 2.3 × 10^{17}$ kg/m³
• Nucleon hard-core repulsion prevents further compression of nuclear matter
• Nuclear incompressibility explains the resistance of nuclei to density changes
• Neutron stars represent extremely dense states of nuclear matter, reaching densities of $10^{17}$ kg/m³ or higher

Charge Distribution and Nuclear Structure

• Proton charge distribution within the nucleus determines its electromagnetic properties
• Charge radius slightly smaller than the mass radius due to the neutron distribution
• Electron scattering experiments reveal non-uniform charge distributions in many nuclei
• Nuclear shell model explains charge distribution patterns observed in different elements
• Deformed nuclei (uranium-235) exhibit non-spherical charge distributions, influencing nuclear reactions and fission processes