Glossary

22.1 The Structure of the Atom

3 min read•june 25, 2024

Atomic structure is the foundation of modern physics. From to the , our understanding of atoms has evolved dramatically. These insights explain emission spectra, energy levels, and the behavior of electrons in atoms.

Quantum mechanics takes atomic theory further, describing electron transitions and characteristics. The quantum mechanical model, with its and , provides a more accurate picture of electron behavior. This knowledge is crucial for understanding atomic interactions and chemical properties.

Atomic Structure

Rutherford's gold foil experiment

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  • Fired positively charged at thin gold foil expected most to pass through with minimal deflection
  • Observations showed most particles passed through undeflected, some deflected at large angles, and a few deflected back towards source
  • Implications revealed atom is mostly empty space with positive charge and mass concentrated in small, dense and electrons orbiting at relatively large distance

Atomic spectra significance

  • appears as bright lines on dark background when electrons transition from higher to lower energy levels, each element has unique spectrum (hydrogen, helium)
  • appears as dark lines on bright background when electrons transition from lower to higher energy levels, corresponds to same wavelengths as emission spectrum
  • Spectra provide evidence for discrete energy levels in atoms and are used to identify elements and compositions in various substances (stars, gases)

Bohr model vs quantum model

  • has electrons orbiting nucleus in fixed, circular orbits transitioning between specific energy levels with emission and absorption of photons during transitions
  • Quantum model has electrons existing in probability distributions called orbitals described by quantum numbers (n, l, m, s) with quantized energy levels not always in circular orbits
  • Both models account for discrete energy levels and explain emission and absorption spectra
  • Quantum model is more accurate accounting for sublevels and orbitals while Bohr model is simpler but limited in describing complex atoms

Quantum Mechanics and Atomic Transitions

Electron energy transitions

  • Energy change calculated as ΔE=Ef−Ei\Delta E = E_f - E_i where EfE_f is final energy level and EiE_i is initial energy level
  • Bohr model calculates energy as En=−13.6eVn2E_n = -\frac{13.6 eV}{n^2} where nn is
  • Quantum model calculates energy as En=−13.6eVn2+correction termsE_n = -\frac{13.6 eV}{n^2} + \text{correction terms} accounting for electron-electron interactions and relativistic effects

Photon characteristics in transitions

  • Photon energy calculated as E=hν=hcλE = h\nu = \frac{hc}{\lambda} where hh is (6.626×10−346.626 \times 10^{-34} J⋅s), ν\nu is frequency, cc is speed of light (2.998×1082.998 \times 10^8 m/s), and λ\lambda is wavelength
  • Frequency calculated as ν=ΔEh\nu = \frac{\Delta E}{h} and wavelength calculated as λ=hcΔE\lambda = \frac{hc}{\Delta E}

Quantum mechanical model features

  • Electrons exist in probability distributions called orbitals described by four quantum numbers:
    1. Principal quantum number (n) determines main energy level and size of orbital
    2. (l) determines shape of orbital (s, p, d, f)
    3. (m) determines orientation of orbital in space
    4. (s) describes intrinsic angular momentum of electron (up or down)
  • states no two electrons in an atom can have same set of quantum numbers
  • states electrons fill orbitals in order of increasing energy (1s, 2s, 2p, 3s)
  • states electrons occupy orbitals of same energy singly before pairing up

Wave function and electron behavior

  • The (ψ) describes the quantum state of an electron in an atom
  • The is used to solve for the wave function and determine allowed energy states
  • The square of the wave function (|ψ|²) gives the , which represents the likelihood of finding an electron in a particular region of space
  • Atomic orbitals are three-dimensional representations of electron probability distributions
  • describes the arrangement of electrons in atomic orbitals, following the aufbau principle, Pauli exclusion principle, and Hund's rule

Key Terms to Review (29)

Absorption Spectrum: An absorption spectrum is the unique pattern of dark absorption lines or bands observed in the continuous spectrum of light that has passed through a gaseous medium. This phenomenon occurs when atoms or molecules in the gas absorb specific wavelengths of light, leaving gaps or dark lines in the otherwise continuous spectrum.
Alpha Particles: Alpha particles are a type of ionizing radiation consisting of two protons and two neutrons, which are emitted from the nucleus of certain radioactive elements during radioactive decay. They are the largest and most highly charged type of particle emitted during radioactive processes.
Angular Momentum Quantum Number: The angular momentum quantum number is a fundamental quantum number that describes the angular momentum of an electron in an atom. It is a quantized value that represents the orbital angular momentum of an electron and is a key characteristic in understanding the structure of an atom.
Atomic Orbital: An atomic orbital is a mathematical function that describes the wave-like behavior of an electron in an atom. It is the quantum mechanical model that defines the wave-like behavior of an electron in an atom's nucleus.
Atomic Spectra: Atomic spectra refer to the unique patterns of light emitted or absorbed by atoms when their electrons transition between different energy levels. This phenomenon provides valuable insights into the internal structure and properties of atoms, which is a fundamental aspect of understanding the nature of matter and energy.
Aufbau Principle: The Aufbau principle is a fundamental concept in quantum mechanics that describes the way electrons occupy energy levels within an atom. It states that electrons will fill the available energy levels of an atom in order of increasing energy, starting from the lowest energy level and progressively filling higher levels.
Bohr Model: The Bohr model is a representation of the atom that was developed by Danish physicist Niels Bohr in 1913. It describes the structure of an atom, depicting electrons orbiting the nucleus in discrete, fixed energy levels or shells. This model helped explain the observed spectral lines emitted by atoms and laid the foundation for the modern understanding of atomic structure.
D Orbital: The d orbital is one of the five principal electron orbitals in an atom. It is characterized by a more complex spatial distribution of electron density compared to the s and p orbitals, allowing for a greater variety of possible electron configurations and energy levels within the atom.
Electron Configuration: Electron configuration is the arrangement of electrons in an atom's orbitals, which determines the atom's chemical properties and behavior. It describes how electrons are distributed among the various energy levels and sublevels within the atom.
Electron Energy Transitions: Electron energy transitions refer to the movement of electrons between different energy levels or orbitals within an atom. This process is fundamental to understanding the structure and behavior of atoms, as it governs the absorption and emission of electromagnetic radiation by atoms.
Electron Probability Density: Electron probability density is a fundamental concept in quantum mechanics that describes the likelihood of finding an electron in a specific region of space around an atom. It is a crucial aspect of understanding the structure of atoms and the behavior of electrons within them.
Emission Spectrum: An emission spectrum is the series of discrete wavelengths of electromagnetic radiation emitted by an atom or molecule when it transitions from a higher energy state to a lower energy state. This phenomenon is a fundamental characteristic of the structure of atoms and is used to identify the composition of matter.
F Orbital: The f orbital is one of the five main types of atomic orbitals, which are regions in an atom where an electron is likely to be found. The f orbital is characterized by a higher angular momentum quantum number (l = 3) and a more complex spatial distribution compared to the s, p, and d orbitals.
Hund's Rule: Hund's rule is a fundamental principle in quantum mechanics that describes the electronic configuration of atoms. It explains the preferred arrangement of electrons in atomic orbitals based on the concept of electron spin and the minimization of electron-electron repulsion.
Magnetic Quantum Number: The magnetic quantum number is a quantum number that describes the orientation of an atomic orbital with respect to an external magnetic field. It is one of the four quantum numbers that define the state of an electron in an atom, along with the principal quantum number, angular momentum quantum number, and spin quantum number.
Nucleus: The nucleus is the central and most essential part of an atom, containing protons and neutrons, and is responsible for the atom's overall stability and characteristics. It is the core of the atom, where the majority of its mass and positive charge are concentrated.
Orbitals: Orbitals are regions in an atom where electrons are most likely to be found. They are the fundamental building blocks that describe the distribution and behavior of electrons within an atom's structure.
P Orbital: The p orbital is one of the four fundamental types of atomic orbitals, along with s, d, and f orbitals. It is a higher-energy orbital that can hold up to six electrons and has a more complex, three-dimensional shape compared to the spherical s orbital.
Pauli Exclusion Principle: The Pauli exclusion principle is a fundamental principle in quantum mechanics that states that two identical fermions (particles with half-integer spin, such as electrons) cannot occupy the same quantum state simultaneously. This principle is a key concept in understanding the structure of atoms and the behavior of electrons within them.
Photon: A photon is the fundamental particle that makes up light and other forms of electromagnetic radiation. It is a discrete packet of energy that exhibits both particle-like and wave-like properties, serving as the basic unit of all light and other electromagnetic phenomena.
Planck's Constant: Planck's constant is a fundamental physical constant that represents the smallest possible change in energy or action. It is a crucial parameter in quantum mechanics and is denoted by the symbol 'h'. Planck's constant is essential in understanding the quantum nature of light, the structure of the atom, and various other quantum phenomena.
Principal Quantum Number: The principal quantum number, denoted as $n$, is a fundamental concept in quantum mechanics that describes the energy levels of an atom. It is a positive integer that represents the shell or energy level in which an electron resides within an atom's structure.
Quantum Model: The quantum model, also known as the quantum mechanical model, is a fundamental theory in physics that describes the behavior and properties of matter and energy at the atomic and subatomic scale. It provides a comprehensive understanding of the structure and dynamics of atoms, molecules, and other microscopic systems, challenging the classical, deterministic view of the physical world.
Quantum Numbers: Quantum numbers are a set of discrete values that describe the state of an electron within an atom. They are fundamental to understanding the structure of atoms and the behavior of electrons in quantum mechanics.
Rutherford's Gold Foil Experiment: Rutherford's gold foil experiment was a groundbreaking experiment that provided crucial evidence for the existence of the atomic nucleus and the plum pudding model of the atom. It helped pave the way for the development of the modern atomic theory.
S Orbital: An s orbital is a type of atomic orbital that has a spherical shape and represents the lowest energy level or shell in an atom. It is the simplest and most fundamental of the atomic orbitals and is designated by the quantum number n = 1, with a total angular momentum quantum number l = 0.
Schrödinger equation: The Schrödinger equation is a fundamental equation in quantum mechanics that describes the wave-like behavior of particles and how they evolve over time. It is a central concept in understanding the structure of atoms and the behavior of subatomic particles.
Spin Quantum Number: The spin quantum number is a fundamental property of subatomic particles, such as electrons, that describes the intrinsic angular momentum or 'spin' of the particle. It is a quantized value that determines the particle's magnetic moment and behavior in magnetic fields.
Wave Function: The wave function is a mathematical description of the quantum state of an object or particle. It provides a complete description of the particle's behavior and evolution over time, and its square gives the probability density of the particle's position in space.
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