Atoms, Molecules, and the Structure of Matter

Last Updated May 28, 2026

Atoms, molecules, and the structure of matter occupy a central place in physics because they explain how the visible diversity of the material world arises from a limited set of underlying constituents arranged in lawful ways. The world appears continuous at ordinary scale, yet modern physics and chemistry show that matter is structured discretely: atoms possess internal organization, atoms combine into molecules, and those molecules generate the larger-scale properties of gases, liquids, solids, reactions, spectra, crystals, polymers, biological materials, and engineered devices. In this sense, the atomic and molecular view of matter is one of the great bridges between microscopic theory and macroscopic reality.

This bridge did not emerge all at once. The atomic idea has ancient philosophical roots, but it became a modern scientific framework only when it was tied to quantitative evidence, chemical regularity, kinetic reasoning, spectroscopy, scattering, and the mathematics of quantum structure. Dalton gave atomic theory an early modern form in chemistry; Avogadro clarified the distinction between atoms and molecules; Perrin helped make molecular reality empirically persuasive through Brownian motion; Rutherford transformed the atom by revealing the nucleus; Bohr connected atomic structure to spectral regularity; and Schrödinger’s wave mechanics made it possible to describe atomic and molecular behavior in explicitly quantum terms.

This article develops Atoms, Molecules, and the Structure of Matter as a foundational topic within the Physics knowledge series. It explains how the atomic view became scientifically credible, how atoms are structured, how molecules form, why bonding depends on energy and quantum state, how spectra reveal discrete structure, and how matter’s larger-scale properties emerge from microscopic organization. It also follows the mathematics-first and computation-aware structure used throughout the series while keeping the article body readable. Selected R and Python workflows appear here, while the full GitHub repository contains advanced research-style computational workflows for spectral-line conversion, Bohr energy levels, diatomic potential curves, molecular metadata, lattice-style structure, atomic constants, SQL schemas, C/C++/Fortran/Rust examples, and reproducible atomic and molecular physics workflows.

Why Atoms and Molecules Matter

Atoms and molecules matter because they provide one of the most powerful explanatory frameworks in all of science. The color of a gas discharge, the rigidity of a crystal, the reactivity of a substance, the heat capacity of a material, the structure of a biological molecule, and the properties of an engineered semiconductor all depend on arrangements of atoms and the interactions of their electrons. Without atoms and molecules, matter would remain a descriptive category. With them, matter becomes structurally intelligible.

This is also a conceptual turning point in physics. Classical mechanics describes motion and force at macroscopic scale, but it does not by itself explain why matter has the specific forms it does. Atomic and molecular theory extends physical explanation inward. It asks how matter is built, how constituents are organized, why some combinations are stable while others are not, how spectra encode structure, and how microscopic arrangement generates macroscopic behavior.

The subject also sits at the boundary between physics and chemistry. IUPAC defines an atom as the smallest particle still characterizing a chemical element, with a positively charged nucleus carrying almost all of its mass and electrons determining its size. IUPAC defines a molecule as an electrically neutral entity consisting of more than one atom and, more rigorously, one associated with a potential-energy depression deep enough to confine at least one vibrational state. These definitions show why matter must be understood across levels: nucleus, electron cloud, atom, molecule, and material.

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From Atomic Hypothesis to Physical Reality

The atomic view of matter was not always an established scientific fact. For long periods it remained a philosophical conjecture or a useful heuristic. What changed in the modern period was not merely that scientists talked about atoms more often, but that atomic ideas became tied to lawlike chemical composition, kinetic theory, Brownian motion, spectroscopy, scattering experiments, periodic regularity, and eventually direct structural and instrumental evidence.

This matters historically because it shows that the atomic theory of matter was not accepted simply because it was elegant. It became compelling because it solved multiple problems at once. It clarified combining ratios in chemistry, explained gas behavior statistically, helped interpret diffusion and molecular motion, and later made sense of spectral regularities and nuclear scattering experiments. The strength of the atomic view came from convergence across domains.

That convergence is one of the best examples of how modern science establishes reality claims. Atoms became real not because they were directly imaged at the beginning of the theory, but because they were the most coherent explanation of a widening range of quantitative phenomena. The atomic hypothesis became physical reality through cumulative evidence, measurement, and predictive success.

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Dalton, Avogadro, and the Language of Composition

John Dalton’s atomic theory gave one of the first durable modern forms to the idea that matter is composed of discrete units combined in fixed proportions. This mattered because chemical combination laws required a language more structured than ordinary mixture. If substances combine in reproducible ratios, then matter must have a stable compositional grammar. Atomic theory made that grammar intelligible.

Avogadro’s contribution was equally important because it clarified that equal volumes of gases under the same conditions need not imply identical atoms, but could reflect equal numbers of molecules. That distinction between atoms and molecules is foundational. An atom is not simply any small unit of matter; a molecule is a bound aggregate of atoms, and the two levels of structure must be kept conceptually distinct.

This clarification made modern chemical and physical reasoning much more coherent. It allowed one to understand how elemental gases could exist as molecules, how combining ratios related to molecular composition, why molecular formulas differed from empirical ratios, and why the same atomic species could participate in different larger structures.

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The Atom: From Electron to Nucleus

The modern atom is not an indivisible billiard-ball unit. It is itself structured. The discovery of the electron showed that atoms contain smaller charged constituents, and Rutherford’s scattering interpretation then made clear that the atom contains a tiny, massive nucleus rather than being a diffuse positive medium.

This was one of the decisive turning points in the structure of matter. Most of the atom’s mass resides in a compact nucleus, while electrons occupy the surrounding region. The atom is therefore mostly empty space in geometric terms, but not empty in the physical sense: the surrounding electronic region is where charge distribution, quantum state, chemical bonding, polarizability, and spectral behavior become meaningful.

A useful scale contrast is that atomic diameters are typically on the order of:

while nuclear diameters are typically on the order of:

This immense difference in scale is one of the reasons atomic structure is so conceptually rich. Atomic size, atomic mass, nuclear charge, electron configuration, and chemical behavior all belong to related but distinct levels of physical description.

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Bohr, Spectra, and Quantized Structure

Bohr’s atomic model was historically decisive because it connected atomic structure to spectral regularity. Classical electrodynamics alone had difficulty explaining why atoms produced discrete emission lines rather than a continuum of radiated frequencies. Bohr proposed that electrons occupy quantized states and that radiation is emitted or absorbed when transitions occur between them.

This model was limited, but it was enormously fruitful. It linked the hydrogen spectrum to a simple quantum rule and showed that atomic structure could not be described adequately within a purely classical orbital picture. The atom was not merely a miniature solar system. It was a quantized system whose energies were restricted.

For the hydrogen atom, the Bohr energy levels can be written as:

where \(n = 1, 2, 3, \ldots\). This relation matters because it makes atomic discreteness calculable rather than merely suggestive. Spectra become evidence of energy-level structure, not simply colored light.

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Quantum Mechanics and Atomic Orbitals

The deeper theory of atomic structure came with quantum mechanics. Schrödinger’s wave mechanics replaced the older semiclassical orbit picture with a state-based description in which electrons are represented by wavefunctions. In this framework, atomic orbitals are not tiny literal paths but mathematically defined states characterized by quantum numbers and spatial probability structure.

This is one of the most important conceptual shifts in modern science. Atomic structure is no longer imagined primarily through miniature planetary orbits. It is described through solutions to a quantum equation under the appropriate potential. The resulting orbitals help explain shell structure, periodic trends, bonding behavior, ionization energy, spectral transitions, and the stability of matter.

The time-independent Schrödinger equation is:

For the hydrogen atom, its solutions generate the familiar quantum numbers \(n\), \(l\), and \(m\), together with orbital structures such as s, p, d, and f states. For many-electron atoms, electron-electron interaction complicates the problem, but the orbital and shell framework remains essential to explaining periodicity and bonding.

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Molecules, Bonding, and Energy Lowering

Molecules form when atoms combine in ways that lower the total energy of the system under the relevant conditions. That principle is one of the simplest and most important entry points into bonding. A stable molecule is not just an arbitrary cluster of atoms. It is a configuration whose binding arrangement is energetically favorable relative to the separated atoms, once electronic structure and nuclear positions are taken into account.

Bonding can be approached through different conceptual languages. Valence-bond reasoning emphasizes shared electron pairs and localized bonding pictures. Molecular-orbital reasoning emphasizes orbitals that extend across the whole molecule and are occupied according to quantum rules. Ionic bonding emphasizes electrostatic attraction among charged species. Metallic bonding emphasizes delocalized electrons in extended solids. Covalent bonding, ionic bonding, hydrogen bonding, van der Waals interactions, and coordination bonding each illuminate different parts of matter’s structural grammar.

The deeper point is that molecules are not an optional add-on to atomic theory. They are one of the first great tests of whether atomic structure is being understood correctly. If a theory of atoms cannot explain why atoms bind, how they bind, and why bond lengths and bond energies are what they are, then the theory remains incomplete.

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Molecular Geometry, Polarity, and Structure

Molecules are not defined only by composition. Geometry matters. The same atoms arranged differently can produce different physical and chemical behavior. Bond angles, lone-pair effects, hybridization language, molecular orbital occupancy, steric structure, and symmetry all shape molecular form. In biological and materials contexts, three-dimensional arrangement can be as important as chemical formula.

Polarity matters as well. A molecule may have polar bonds but still be nonpolar overall if the geometry causes dipole contributions to cancel. Conversely, asymmetry can make a molecule strongly polar, altering its intermolecular behavior, solubility, spectral response, dielectric behavior, and role in larger material systems.

This is where atomic theory begins to scale upward into the physical world we actually experience. Molecular geometry helps determine whether a substance is a gas or liquid under ordinary conditions, how it interacts with electric fields, how it absorbs radiation, how it packs into solids, and how it participates in larger structures such as membranes, polymers, crystals, proteins, and engineered materials.

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Matter from Atoms to Materials

Atoms and molecules are foundational, but matter at macroscopic scale also depends on how those units are organized collectively. Gases, liquids, crystals, polymers, metals, ceramics, glasses, semiconductors, biomolecules, and soft materials differ not because they escape atomic structure, but because they instantiate it differently.

Some materials are dominated by discrete molecules. Others are better described as extended networks, lattices, ionic arrays, metallic electron systems, or covalent solids. In solids, atomic arrangement and electronic structure help determine conductivity, rigidity, optical properties, thermal behavior, defects, and phase transitions. In soft matter and chemistry, molecular interaction patterns help determine fluidity, aggregation, reactivity, and self-assembly.

This is one of the reasons the phrase “structure of matter” is broader than “structure of the atom.” The subject moves from subatomic and atomic organization to bonding, then to molecular shape, then to collective material order. Each scale is distinct, but none is isolated from the others.

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Measurement, Spectra, and Evidence

The structure of matter is known through evidence-rich methods, not by conceptual preference alone. Spectroscopy is one of the most important of these methods because atomic and molecular systems interact with radiation in discrete and informative ways. Atomic spectra reveal quantized energy differences. Molecular spectra reveal rotational, vibrational, and electronic structure. Diffraction and scattering methods reveal arrangement in solids and molecules. Mass spectrometry reveals composition and isotopic structure.

NIST’s Atomic Spectra Database illustrates the importance of evaluated reference data. It provides access to critically evaluated data on atomic energy levels, wavelengths, and transition probabilities, and supports the connection between spectral measurement and atomic structure. NIST’s Chemistry WebBook plays a complementary role for chemical and molecular data, including thermochemical and spectroscopic information for chemical species.

For the photon relation linking energy and frequency, one of the most useful expressions is:

In wavelength form, the corresponding relation is:

These are among the most useful bridge equations in atomic and molecular physics because they connect measured radiation directly to quantized structure.

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Mathematical Lens

A mathematics-first treatment of atoms and molecules begins with scale, potential, quantization, and energy lowering. At the simplest level, one moves from counting constituents to describing how energy depends on configuration and state. In quantum language, allowed states are not arbitrary. They are solutions to boundary-conditioned equations, and the admissible solutions determine observables such as energy levels, orbital structure, transition frequencies, and molecular stability.

For the hydrogen-like atom, the Bohr result already suggests discrete energy structure:

Quantum mechanics generalizes this. For a bound-state problem, one solves:

with normalization condition:

Spectroscopy then links energy differences to radiation:

Molecular stability is often understood through energy curves. A schematic diatomic potential can be represented by a well-shaped function \(U(r)\) with a minimum at the equilibrium bond length \(r_e\). The qualitative lesson is that a bond exists because the combined system has a lower energy near a particular separation than at large separation.

At a more general level, this subject teaches that matter is intelligible through energy surfaces, discrete states, quantum numbers, spectra, geometry, and symmetry structure. The equations are not decorative. They define what configurations are physically allowed and why some structures are stable.

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Variables, Units, and Structural Interpretation

Atomic and molecular physics depends on variables that connect microscopic structure to measurable behavior. The table below summarizes several central quantities.

The table illustrates why the structure of matter requires both discrete and continuous descriptions. Atomic identity is indexed by integers; quantum states are discrete; spectra are measured through wavelengths and frequencies; and molecular stability is often represented through continuous energy curves.

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Worked Example: Hydrogen and H₂

A compact way to illustrate the structure of matter is to compare the hydrogen atom with the hydrogen molecule. The hydrogen atom is the simplest atomic system: one electron bound to one proton. It already reveals discrete energy levels, spectral transitions, and orbital structure. It is the great entry point into atomic quantization.

The hydrogen molecule H₂, however, adds a new question: why do two hydrogen atoms bind? In a simplified molecular-orbital picture, the electrons occupy a lower-energy bonding combination of atomic states. The molecule is stable because the total energy of the bound configuration is lower than that of two isolated atoms at large separation.

In schematic form, one can express the logic as:

That inequality is conceptually simple but physically deep. It is the heart of molecular stability. The detailed explanation requires quantum structure, electron exchange, nuclear repulsion, molecular orbitals, and energy minimization, but the general lesson is already visible: atoms form molecules when the combined arrangement lowers energy under the relevant conditions.

This example also shows why the structure of matter cannot stop at atoms alone. The physically relevant world is made not only of isolated atoms but of atoms in relation, atoms in bonds, and atoms in larger collective arrangements.

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Computational Modeling

Computational modeling helps make atomic and molecular structure concrete. A table of spectral wavelengths can be converted into photon energies. Hydrogen energy levels can be computed and compared. Energy differences can be turned into transition wavelengths. A diatomic potential can be scanned for its equilibrium separation. Molecular metadata can store formulas, bond lengths, geometries, spectra, and data provenance. Atomic constants can be preserved in reusable data tables.

The selected examples below focus on spectral-line conversion, Bohr-like energy levels, and schematic molecular potentials because they are foundational and readable. The GitHub repository extends the same logic into richer computational workflows: R spectral summaries, Python hydrogen levels and diatomic potential scans, Julia photon-energy calculations, C++ transition-energy sweeps, Fortran Bohr-level tables, SQL atomic and molecular metadata, Rust command-line utilities, C examples, documentation, and reproducible sample data.

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R Workflow: Hydrogen Spectral Lines and Photon Energies

R is especially useful for the empirical side of atomic and molecular structure: spectral datasets, repeated measurement, line fitting, uncertainty summaries, and visualization. The following workflow works with a small hydrogen-style spectral dataset, converts wavelengths to energies, and summarizes the resulting photon energies.

# Hydrogen Spectral Lines and Photon Energies
#
# This workflow converts selected hydrogen Balmer-series wavelengths
# into photon energies using:
#
#   E = h*c/lambda
#
# Variables:
#   h      = Planck constant in J*s
#   c      = speed of light in m/s
#   lambda = wavelength in meters
#   E      = photon energy in joules or electron volts
#
# The values below are illustrative and should be replaced by calibrated
# spectral measurements or evaluated line data in precision work.

library(tibble)
library(dplyr)

planck_constant_j_s <- 6.62607015e-34
speed_of_light_m_s <- 299792458
joule_per_ev <- 1.602176634e-19

spectral_lines <- tibble(
  line = c("H_alpha", "H_beta", "H_gamma", "H_delta"),
  wavelength_nm = c(656.3, 486.1, 434.0, 410.2)
) %>%
  mutate(
    wavelength_m = wavelength_nm * 1e-9,
    energy_j = planck_constant_j_s * speed_of_light_m_s / wavelength_m,
    energy_ev = energy_j / joule_per_ev
  )

summary_table <- spectral_lines %>%
  summarise(
    n_lines = n(),
    minimum_energy_ev = min(energy_ev),
    maximum_energy_ev = max(energy_ev),
    mean_energy_ev = mean(energy_ev)
  )

print(spectral_lines)
print(summary_table)

This workflow shows how R can take measured or tabulated spectral data and turn it into interpretable quantitative structure. It is especially useful when the emphasis is on data quality, repeated measurements, summary statistics, and visual comparison.

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Python Workflow: Hydrogen Levels and Diatomic Potentials

Python is especially strong for symbolic and numerical modeling of atomic and molecular structure. The following workflow computes Bohr-like hydrogen energy levels, estimates transition energies, and scans a schematic diatomic potential for an equilibrium separation.

"""
Hydrogen Energy Levels and a Schematic Diatomic Potential

This workflow demonstrates two introductory ideas in atomic and molecular
structure:

1. Hydrogen-like Bohr energy levels:
       E_n = -13.6 / n^2  eV

2. A schematic Lennard-Jones-style diatomic potential:
       U(r) = 4*epsilon*((sigma/r)^12 - (sigma/r)^6)

The potential is a teaching model. It is not a quantum-chemical
calculation for a specific molecule.
"""

import numpy as np
import pandas as pd


def hydrogen_energy_levels(n_max: int = 8) -> pd.DataFrame:
    """
    Compute Bohr-like hydrogen energy levels.

    Parameters
    ----------
    n_max:
        Maximum principal quantum number.

    Returns
    -------
    pandas.DataFrame
        Table with n and energy in electron volts.
    """
    n = np.arange(1, n_max + 1)
    energy_ev = -13.6 / n**2

    return pd.DataFrame(
        {
            "n": n,
            "energy_ev": energy_ev,
        }
    )


def transition_energy(initial_n: int, final_n: int) -> float:
    """
    Compute the photon energy for a transition between Bohr-like levels.

    Parameters
    ----------
    initial_n:
        Initial principal quantum number.
    final_n:
        Final principal quantum number.

    Returns
    -------
    float
        Transition energy in electron volts.
    """
    initial_energy = -13.6 / initial_n**2
    final_energy = -13.6 / final_n**2

    return abs(final_energy - initial_energy)


def diatomic_potential(
    r: np.ndarray,
    epsilon: float = 1.0,
    sigma: float = 1.0,
) -> np.ndarray:
    """
    Compute a schematic Lennard-Jones-style diatomic potential.

    Parameters
    ----------
    r:
        Internuclear separation in arbitrary units.
    epsilon:
        Well-depth scale in arbitrary energy units.
    sigma:
        Length scale in arbitrary distance units.

    Returns
    -------
    np.ndarray
        Potential energy in arbitrary units.
    """
    return 4.0 * epsilon * ((sigma / r) ** 12 - (sigma / r) ** 6)


def main() -> None:
    """
    Run atomic energy-level and molecular potential examples.
    """
    levels = hydrogen_energy_levels(n_max=8)

    transitions = pd.DataFrame(
        {
            "transition": ["3_to_2", "4_to_2", "5_to_2", "6_to_2"],
            "initial_n": [3, 4, 5, 6],
            "final_n": [2, 2, 2, 2],
        }
    )

    transitions["energy_ev"] = [
        transition_energy(initial_n, final_n)
        for initial_n, final_n in zip(
            transitions["initial_n"],
            transitions["final_n"],
        )
    ]

    r = np.linspace(0.75, 3.0, 1000)
    potential = diatomic_potential(r)

    potential_table = pd.DataFrame(
        {
            "r": r,
            "potential": potential,
        }
    )

    minimum_row = potential_table.loc[potential_table["potential"].idxmin()]

    print("Hydrogen-like energy levels:")
    print(levels.round(6).to_string(index=False))

    print("\nSelected transitions:")
    print(transitions.round(6).to_string(index=False))

    print("\nApproximate minimum of schematic diatomic potential:")
    print(minimum_row.round(6).to_string())


if __name__ == "__main__":
    main()

This workflow makes two important ideas visible. The first is discrete atomic energy structure. The second is molecular stabilization through an energy minimum at a preferred separation. That combination of quantized levels and energy-lowering geometry is one of the most compact computational entry points into the structure of matter.

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GitHub Repository

The article body includes only selected computational examples so the conceptual and atomic-molecular argument remains readable. The full repository contains the expanded computational infrastructure: R spectral-line workflows, Python hydrogen energy levels and diatomic potentials, Julia photon-energy models, C++ transition-energy sweeps, Fortran Bohr-level tables, SQL atomic and molecular metadata, Rust command-line utilities, C examples, documentation, and reproducible sample data.

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From Atomic Structure to Modern Physics

The study of atoms and molecules does not remain confined to introductory structure. It opens directly into spectroscopy, quantum mechanics, chemical bonding, materials science, condensed matter, photonics, molecular biology, atmospheric science, plasma physics, and much of modern technology. Atomic structure explains periodicity; molecular structure explains bonding and reaction; collective structure explains materials and phases.

This is why the subject is so central within the Physics knowledge series. It is not merely an intermediate topic between chemistry and physics. It is one of the great places where microscopic theory becomes physically vivid and materially consequential.

The next stages in this sequence naturally deepen the quantum and materials sides of the story. Quantum Mechanics and the Limits of Classical Intuition provides the formal foundation. Light, Waves, and the Physics of Radiation explains why spectra are such powerful structural evidence. Condensed Matter and the Physics of Materials shows how atoms and molecules become solids, phases, and devices. Together, these articles show that matter is not simply present. It is structured.

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Related Articles

• What Is Physics?
• Measurement, Mathematics, and the Structure of Physical Inquiry
• Light, Waves, and the Physics of Radiation
• Quantum Mechanics and the Limits of Classical Intuition
• Electromagnetism and the Unification of Fields
• Thermodynamics and the Physics of Heat
• Statistical Physics and the Emergence of Macroscopic Order
• Condensed Matter and the Physics of Materials
• Nuclear Physics and the Energetics of the Atomic Nucleus
• Chemical Bonding and Molecular Structure

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Further Reading

• Bohr, N. (1913) ‘On the Constitution of Atoms and Molecules’, Philosophical Magazine, 26(151), pp. 1–25. Available at: https://doi.org/10.1080/14786441308634955 (Accessed: 24 April 2026).
• IUPAC (2025) Atom, Compendium of Chemical Terminology. Available at: https://goldbook.iupac.org/terms/view/A00493 (Accessed: 24 April 2026).
• IUPAC (2025) Molecule, Compendium of Chemical Terminology. Available at: https://goldbook.iupac.org/terms/view/M04002 (Accessed: 24 April 2026).
• IUPAC (2025) Chemical Bond, Compendium of Chemical Terminology. Available at: https://goldbook.iupac.org/terms/view/CT07009 (Accessed: 24 April 2026).
• MIT OpenCourseWare (2010) Introduction to Solid State Chemistry. Available at: https://ocw.mit.edu/courses/3-091sc-introduction-to-solid-state-chemistry-fall-2010/ (Accessed: 24 April 2026).
• MIT OpenCourseWare (2010) Atomic Models: Rutherford and Bohr. Available at: https://ocw.mit.edu/courses/3-091sc-introduction-to-solid-state-chemistry-fall-2010/pages/structure-of-the-atom/3-atomic-models/ (Accessed: 24 April 2026).
• MIT OpenCourseWare (2010) Electron Shell Model and Quantum Numbers. Available at: https://ocw.mit.edu/courses/3-091sc-introduction-to-solid-state-chemistry-fall-2010/pages/structure-of-the-atom/5-electron-shell-model-quantum-numbers/ (Accessed: 24 April 2026).
• NIST (n.d.) Atomic Spectra Database. Available at: https://www.nist.gov/pml/atomic-spectra-database (Accessed: 24 April 2026).
• NIST (n.d.) Chemistry WebBook. Available at: https://webbook.nist.gov/chemistry/ (Accessed: 24 April 2026).
• NIST (2026) Meet the Constants. Available at: https://www.nist.gov/si-redefinition/meet-constants (Accessed: 24 April 2026).
• Rutherford, E. (1911) ‘The Scattering of α and β Particles by Matter and the Structure of the Atom’, Philosophical Magazine, 21(125), pp. 669–688.
• Schrödinger, E. (1926) ‘Quantisierung als Eigenwertproblem’, Annalen der Physik, 384(4), pp. 361–376. Available at: https://doi.org/10.1002/andp.19263840404 (Accessed: 24 April 2026).

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References

• Bohr, N. (1913) ‘On the Constitution of Atoms and Molecules’, Philosophical Magazine, 26(151), pp. 1–25. Available at: https://doi.org/10.1080/14786441308634955 (Accessed: 24 April 2026).
• IUPAC (2025) Atom, Compendium of Chemical Terminology. Available at: https://goldbook.iupac.org/terms/view/A00493 (Accessed: 24 April 2026).
• IUPAC (2025) Molecule, Compendium of Chemical Terminology. Available at: https://goldbook.iupac.org/terms/view/M04002 (Accessed: 24 April 2026).
• IUPAC (2025) Chemical Bond, Compendium of Chemical Terminology. Available at: https://goldbook.iupac.org/terms/view/CT07009 (Accessed: 24 April 2026).
• MIT OpenCourseWare (2010) Introduction to Solid State Chemistry. Available at: https://ocw.mit.edu/courses/3-091sc-introduction-to-solid-state-chemistry-fall-2010/ (Accessed: 24 April 2026).
• NIST (n.d.) Atomic Spectra Database. Available at: https://www.nist.gov/pml/atomic-spectra-database (Accessed: 24 April 2026).
• NIST (n.d.) Chemistry WebBook. Available at: https://webbook.nist.gov/chemistry/ (Accessed: 24 April 2026).
• NIST (2026) Meet the Constants. Available at: https://www.nist.gov/si-redefinition/meet-constants (Accessed: 24 April 2026).
• Rutherford, E. (1911) ‘The Scattering of α and β Particles by Matter and the Structure of the Atom’, Philosophical Magazine, 21(125), pp. 669–688.
• Schrödinger, E. (1926) ‘Quantisierung als Eigenwertproblem’, Annalen der Physik, 384(4), pp. 361–376. Available at: https://doi.org/10.1002/andp.19263840404 (Accessed: 24 April 2026).

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