2.1 Atomic structure and spectroscopy

Atoms are the building blocks of matter, with unique structures and electron configurations. Understanding these basics is crucial for grasping how atoms interact with light, forming the foundation of spectroscopy in astrochemistry.

Atomic spectroscopy reveals the chemical makeup and physical conditions of celestial objects. By studying the absorption and emission of light by atoms, scientists can identify elements, measure abundances, and uncover properties of distant stars and galaxies.

Atomic Structure and Electronic Configurations

Composition and Structure of Atoms

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• Atoms consist of a positively charged nucleus containing protons and neutrons, surrounded by negatively charged electrons in quantized energy levels or shells
• The number of protons in the nucleus determines the atomic number and the element (hydrogen has 1 proton, helium has 2 protons)
• The number of neutrons can vary, resulting in different isotopes of the same element (carbon-12 and carbon-14 are isotopes of carbon with 6 and 8 neutrons, respectively)
• Electrons occupy specific energy levels (shells) and sublevels (orbitals) around the nucleus, following the Pauli exclusion principle and Hund's rule

Electronic Configurations and Chemical Properties

• The electronic configuration of an atom describes the arrangement of electrons in shells and subshells, using notation such as 1s², 2s², 2p⁶, etc.
  • For example, the electronic configuration of carbon is 1s² 2s² 2p², indicating 2 electrons in the 1s subshell, 2 in the 2s subshell, and 2 in the 2p subshell
• The valence electrons, those in the outermost shell, determine an atom's chemical properties and its ability to form bonds with other atoms
  • Atoms with a complete outer shell (such as noble gases) are generally less reactive, while those with incomplete outer shells (such as alkali metals) are more reactive
• The arrangement of electrons in an atom follows the aufbau principle, which states that electrons fill orbitals in order of increasing energy (1s, 2s, 2p, 3s, 3p, 4s, 3d, etc.)
• The Pauli exclusion principle states that no two electrons in an atom can have the same set of quantum numbers, limiting the number of electrons in each orbital to two with opposite spins

Principles of Atomic Spectroscopy

Interaction of Electromagnetic Radiation with Atoms

• Atomic spectroscopy is the study of the interaction between electromagnetic radiation and atoms, specifically the absorption, emission, or scattering of photons by atoms
• Atoms can absorb photons with specific energies, causing electrons to transition from lower to higher energy levels (excitation)
  • For example, a hydrogen atom can absorb a photon with a wavelength of 121.6 nm, causing an electron to transition from the 1s orbital to the 2p orbital
• Conversely, electrons can emit photons when transitioning from higher to lower energy levels (de-excitation)
  • The emission of a photon with a wavelength of 656.3 nm occurs when an electron in a hydrogen atom transitions from the 3d orbital to the 2p orbital
• The energy of the absorbed or emitted photons corresponds to the difference between the energy levels involved in the transition, as described by the Bohr model and quantum mechanics

Types of Atomic Spectra and Their Formation

• Atomic spectra can be emission spectra (bright lines on a dark background) or absorption spectra (dark lines on a bright background), depending on the source and the medium through which the light passes
  • Emission spectra are produced when atoms are excited by heat, electrical discharge, or other means, causing electrons to emit photons as they return to lower energy levels
  • Absorption spectra are produced when light from a continuous source passes through a cooler gas, causing atoms in the gas to absorb photons at specific wavelengths corresponding to their energy level transitions
• The wavelengths and intensities of the spectral lines depend on the electronic structure of the atoms and the conditions (temperature, density, etc.) of the emitting or absorbing medium
• The Doppler effect can cause spectral lines to be shifted in wavelength if the emitting or absorbing atoms are moving relative to the observer (redshift for receding motion, blueshift for approaching motion)

Atomic Spectra for Astronomical Analysis

Element Identification and Abundance Determination

• Each element has a unique set of spectral lines corresponding to the specific energy transitions allowed by its electronic structure, serving as a "fingerprint" for identification
  • For example, the presence of strong absorption lines at 589.0 nm and 589.6 nm in the spectrum of a star indicates the presence of sodium in the star's atmosphere
• The wavelengths (or frequencies) of the spectral lines can be measured and compared to known laboratory values to identify the elements present in an astronomical object
• The intensity of the spectral lines is related to the abundance of the corresponding element, with stronger lines indicating a higher abundance
  • The ratio of the strengths of spectral lines from different elements can be used to determine the relative abundances of those elements in the object
• Spectral analysis techniques, such as equivalent width measurements and curve of growth analysis, are used to quantify elemental abundances from the observed spectra

Spectral Line Profiles and Physical Conditions

• The width and shape of the spectral lines can provide information about the temperature, pressure, and velocity of the emitting or absorbing material
  • Thermal broadening of spectral lines occurs due to the random motions of atoms in a gas, with higher temperatures resulting in broader lines
  • Pressure broadening occurs when collisions between atoms perturb their energy levels, causing the spectral lines to widen
  • Rotational broadening occurs when a rapidly rotating object (such as a star) produces a range of Doppler shifts across its surface, resulting in broader spectral lines
• The presence of magnetic fields can cause spectral lines to split into multiple components (the Zeeman effect), providing information about the strength and orientation of the magnetic field
• The polarization of spectral lines can also provide information about the presence and orientation of magnetic fields or the geometry of the emitting or absorbing material

Atomic Transitions and Spectral Lines

Energy Levels and Selection Rules

• Atomic transitions occur when electrons move between different energy levels within an atom, either by absorbing or emitting photons
• The energy of the photon involved in a transition is equal to the difference between the energy levels, as described by the Planck-Einstein relation: $E = hν$, where $E$ is the energy, $h$ is Planck's constant, and $ν$ is the frequency of the photon
• Allowed transitions are those that satisfy the selection rules based on quantum mechanical principles, such as the conservation of angular momentum and parity
  • For example, in a hydrogen atom, transitions between states with the same principal quantum number (Δn = 0) are forbidden, while transitions with Δn = ±1 are allowed
• Forbidden transitions, which violate the selection rules, can still occur but with much lower probabilities than allowed transitions

Transition Probabilities and Spectral Line Intensities

• The probability of a transition occurring depends on factors such as the population of the energy levels involved, the transition probability (Einstein coefficients), and the availability of photons with the appropriate energy
• The Einstein coefficients (A, B) describe the rates of spontaneous emission, stimulated emission, and absorption for a given transition
  • The A coefficient represents the probability per unit time of an electron spontaneously transitioning from a higher to a lower energy level, emitting a photon
  • The B coefficients represent the probabilities per unit time per unit energy density of an electron being stimulated to emit or absorb a photon by the ambient radiation field
• The relative populations of the energy levels involved in a transition are described by the Boltzmann distribution, which depends on the temperature and the energy difference between the levels
• The strength and shape of spectral lines are influenced by various factors, including the temperature, density, and velocity distribution of the emitting or absorbing atoms, as well as the presence of magnetic or electric fields
  • Higher temperatures lead to a greater population of higher energy levels, increasing the intensity of emission lines from those levels
  • Higher densities can cause collisional de-excitation, reducing the intensity of emission lines and enhancing the intensity of absorption lines
  • The motion of atoms relative to the observer can cause Doppler broadening and shifting of spectral lines, as well as changes in their intensities due to the dependence of the Einstein coefficients on the radiation field