1.1.1.2 Structure of the Atom

The modern understanding of atomic structure is based on a central nucleus surrounded by a delocalized electron cloud, governed by the laws of quantum mechanics. This architecture defines an element’s chemical identity, nuclear stability, and radioactive behavior.

Nucleus (Protons and Neutrons) vs. Electron Cloud

The atom consists of two distinct regions:

The nucleus, occupying a volume of approximately $10^{- 15}$ m (1 femtometer), contains protons (positively charged, $+ e$ ) and neutrons (electrically neutral), collectively called nucleons. Despite its minuscule size (about 1/100,000th of the atomic diameter), the nucleus contains over 99.9% of the atom’s mass. It is bound together by the strong nuclear force, which overcomes the electrostatic repulsion between protons at short ranges (< 2–3 fm).
The electron cloud extends over a region of ~ $10^{- 10}$ m (1 Ångström) and consists of electrons (mass $m_{e} \approx 9.11 \times 10^{- 31}$ kg, charge $- e$ ) occupying quantized energy states (orbitals) described by wavefunctions $ψ_{n, ℓ, m_{ℓ}}$ . Electrons are bound to the nucleus by the Coulomb attraction but do not follow classical trajectories; instead, their positions are described probabilistically by $| ψ |^{2}$ . The electron cloud governs chemical properties, bonding, and electromagnetic interactions, while the nucleus determines isotopic identity and radioactive behavior.

Atomic Number (Z), Mass Number (A), and Neutron Number (N)

Three fundamental integers characterize any nuclide:

Atomic number ( $Z$ ): The number of protons in the nucleus. It uniquely defines the chemical element (e.g., $Z = 6$ → carbon). In a neutral atom, $Z$ also equals the number of electrons.
Neutron number ( $N$ ): The number of neutrons in the nucleus. Neutrons provide additional strong-force binding without adding Coulomb repulsion, stabilizing heavier nuclei.
Mass number ( $A$ ): The total number of nucleons, $A = Z + N$ . It approximates the atomic mass in atomic mass units (u), since $m_{p} \approx m_{n} \approx 1 u$ .

These quantities are conventionally written in nuclide notation:

$_{Z}^{A} X$

where X is the chemical symbol (e.g., $_{6}^{12} C$ , $_{92}^{235} U$ ).

Isotopes, Isotones, Isobars, and Isomers

Nuclides are classified based on similarities in $Z$ , $N$ , or $A$ :

Isotopes: Nuclides with the same $Z$ (same element) but different $N$ (and thus different $A$ ). For example, carbon-12 ( $_{6}^{12} C$ ), carbon-13 ( $_{6}^{13} C$ ), and carbon-14 ( $_{6}^{14} C$ ) are isotopes of carbon. Isotopes exhibit nearly identical chemical behavior but differ in nuclear stability, mass, and neutron interaction cross-sections.
Isobars: Nuclides with the same mass number $A$ but different $Z$ and $N$ . For instance, $_{6}^{14} C$ and $_{7}^{14} N$ are isobars. Isobars often participate in beta decay chains, as one transforms into the other to achieve a more stable N/Z ratio.
Isotones: Nuclides with the same neutron number $N$ but different $Z$ . Example: $_{6}^{13} C$ ( $N = 7$ ) and $_{7}^{14} N$ ( $N = 7$ ) are isotones. Isotones help reveal nuclear shell structure effects.
Nuclear isomers: Excited, metastable states of the same nuclide (same $Z$ , $N$ , $A$ ) with measurably long lifetimes (typically > $10^{- 9}$ s). Denoted with an “m” (e.g., $_{43}^{99 m} Tc$ ), isomers decay to the ground state via gamma emission or internal conversion. They are crucial in medical imaging and nuclear spectroscopy.

Together, these classifications form the basis for organizing nuclides on the chart of the nuclides, a two-dimensional map of $N$ vs. $Z$ that reveals patterns of stability, decay modes, and nuclear structure.