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Spectroscopy
Spectroscopy
Spectroscopy
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An example of spectroscopy: a prism separates white light by dispersing it into its component colors.

Spectroscopy is the field of study that measures and interprets electromagnetic spectra.[1][2] In narrower contexts, spectroscopy is the precise study of color as generalized from visible light to all bands of the electromagnetic spectrum.

Spectroscopy, primarily in the electromagnetic spectrum, is a fundamental exploratory tool in the fields of astronomy, chemistry, materials science, and physics, allowing the composition, physical structure and electronic structure of matter to be investigated at the atomic, molecular and macro scale, and over astronomical distances.

Historically, spectroscopy originated as the study of the wavelength dependence of the absorption by gas phase matter of visible light dispersed by a prism. Current applications of spectroscopy include biomedical spectroscopy in the areas of tissue analysis and medical imaging. Matter waves and acoustic waves can also be considered forms of radiative energy, and recently gravitational waves have been associated with a spectral signature in the context of the Laser Interferometer Gravitational-Wave Observatory (LIGO).[3]

Introduction

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Spectroscopy is a branch of science concerned with the spectra of electromagnetic radiation as a function of its wavelength or frequency measured by spectrographic equipment, and other techniques, in order to obtain information concerning the structure and properties of matter.[4] Spectral measurement devices are referred to as spectrometers, spectrophotometers, spectrographs or spectral analyzers. Most spectroscopic analysis in the laboratory starts with a sample to be analyzed, then a light source is chosen from any desired range of the light spectrum, then the light goes through the sample to a dispersion array (diffraction grating instrument) and captured by a photodiode. For astronomical purposes, the telescope must be equipped with the light dispersion device. There are various versions of this basic setup that may be employed.

Spectroscopy began with Isaac Newton splitting light with a prism; a key moment in the development of modern optics.[5] Therefore, it was originally the study of visible light that we call color that later under the studies of James Clerk Maxwell came to include the entire electromagnetic spectrum.[6] Although color is involved in spectroscopy, it is not equated with the color of elements or objects that involve the absorption and reflection of certain electromagnetic waves to give objects a sense of color to our eyes. Rather spectroscopy involves the splitting of light by a prism, diffraction grating, or similar instrument, to give off a particular discrete line pattern called a "spectrum" unique to each different type of element. Most elements are first put into a gaseous phase to allow the spectra to be examined although today other methods can be used on different phases. Each element that is diffracted by a prism-like instrument displays either an absorption spectrum or an emission spectrum depending upon whether the element is being cooled or heated.[7]

Until recently all spectroscopy involved the study of line spectra and most spectroscopy still does.[8] Vibrational spectroscopy is the branch of spectroscopy that studies the spectra.[9] However, the latest developments in spectroscopy can sometimes dispense with the dispersion technique. In biochemical spectroscopy, information can be gathered about biological tissue by absorption and light scattering techniques. Light scattering spectroscopy is a type of reflectance spectroscopy that determines tissue structures by examining elastic scattering.[10] In such a case, it is the tissue that acts as a diffraction or dispersion mechanism.

Spectroscopic studies were central to the development of quantum mechanics, because the first useful atomic models described the spectra of hydrogen, which include the Bohr model, the Schrödinger equation, and Matrix mechanics, all of which can produce the spectral lines of hydrogen, therefore providing the basis for discrete quantum jumps to match the discrete hydrogen spectrum. Also, Max Planck's explanation of blackbody radiation involved spectroscopy because he was comparing the wavelength of light using a photometer to the temperature of a Black Body.[11] Spectroscopy is used in physical and analytical chemistry because atoms and molecules have unique spectra. As a result, these spectra can be used to detect, identify and quantify information about the atoms and molecules. Spectroscopy is also used in astronomy and remote sensing on Earth. Most research telescopes have spectrographs. The measured spectra are used to determine the chemical composition and physical properties of astronomical objects (such as their temperature, density of elements in a star, velocity, black holes and more).[12] An important use for spectroscopy is in biochemistry. Molecular samples may be analyzed for species identification and energy content.[13]

Theory

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The underlying premise of spectroscopy is that light is made of different wavelengths and that each wavelength corresponds to a different frequency. The importance of spectroscopy is centered around the fact that every element in the periodic table has a unique light spectrum described by the frequencies of light it emits or absorbs consistently appearing in the same part of the electromagnetic spectrum when that light is diffracted. This opened up an entire field of study with anything that contains atoms. Spectroscopy is the key to understanding the atomic properties of all matter. As such spectroscopy opened up many new sub-fields of science yet undiscovered. The idea that each atomic element has its unique spectral signature enabled spectroscopy to be used in a broad number of fields each with a specific goal achieved by different spectroscopic procedures. The National Institute of Standards and Technology maintains a public Atomic Spectra Database that is continually updated with precise measurements.[14]

The broadening of the field of spectroscopy is due to the fact that any part of the electromagnetic spectrum may be used to analyze a sample from the infrared to the ultraviolet telling scientists different properties about the very same sample. For instance in chemical analysis, the most common types of spectroscopy include atomic spectroscopy, infrared spectroscopy, ultraviolet and visible spectroscopy, Raman spectroscopy and nuclear magnetic resonance.[15] In nuclear magnetic resonance (NMR), the theory behind it is that frequency is analogous to resonance and its corresponding resonant frequency. Resonances by the frequency were first characterized in mechanical systems such as pendulums, which have a frequency of motion noted famously by Galileo.[16]

Classification of methods

[edit]
A huge diffraction grating at the heart of the ultra-precise ESPRESSO spectrograph.[17]

Spectroscopy is a sufficiently broad field that many sub-disciplines exist, each with numerous implementations of specific spectroscopic techniques. The various implementations and techniques can be classified in several ways.

Type of radiative energy

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The types of spectroscopy are distinguished by the type of radiative energy involved in the interaction. In many applications, the spectrum is determined by measuring changes in the intensity or frequency of this energy. The types of radiative energy studied include:

Nature of the interaction

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The types of spectroscopy also can be distinguished by the nature of the interaction between the energy and the material. These interactions include:[2]

  • Absorption spectroscopy: Absorption occurs when energy from the radiative source is absorbed by the material. Absorption is often determined by measuring the fraction of energy transmitted through the material, with absorption decreasing the transmitted portion.
  • Emission spectroscopy: Emission indicates that radiative energy is released by the material. A material's blackbody spectrum is a spontaneous emission spectrum determined by its temperature. This feature can be measured in the infrared by instruments such as the atmospheric emitted radiance interferometer.[18] Emission can also be induced by other sources of energy such as flames, sparks, electric arcs or electromagnetic radiation in the case of fluorescence.
  • Elastic scattering and reflection spectroscopy determine how incident radiation is reflected or scattered by a material. Crystallography employs the scattering of high energy radiation, such as x-rays and electrons, to examine the arrangement of atoms in proteins and solid crystals.
  • Impedance spectroscopy: Impedance is the ability of a medium to impede or slow the transmittance of energy. For optical applications, this is characterized by the index of refraction.
  • Inelastic scattering phenomena involve an exchange of energy between the radiation and the matter that shifts the wavelength of the scattered radiation. These include Raman and Compton scattering.
  • Coherent or resonance spectroscopy are techniques where the radiative energy couples two quantum states of the material in a coherent interaction that is sustained by the radiating field. The coherence can be disrupted by other interactions, such as particle collisions and energy transfer, and so often require high intensity radiation to be sustained. Nuclear magnetic resonance (NMR) spectroscopy is a widely used resonance method, and ultrafast laser spectroscopy is also possible in the infrared and visible spectral regions.
  • Nuclear spectroscopy are methods that use the properties of specific nuclei to probe the local structure in matter, mainly condensed matter, molecules in liquids or frozen liquids and bio-molecules.
  • Quantum logic spectroscopy is a general technique used in ion traps that enables precision spectroscopy of ions with internal structures that preclude laser cooling, state manipulation, and detection. Quantum logic operations enable a controllable ion to exchange information with a co-trapped ion that has a complex or unknown electronic structure.

Type of material

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Spectroscopic studies are designed so that the radiant energy interacts with specific types of matter.

Atoms

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Atomic spectra comparison table, from "Spektroskopische Methoden der analytischen Chemie" (1922).

Atomic spectroscopy was the first application of spectroscopy. Atomic absorption spectroscopy and atomic emission spectroscopy involve visible and ultraviolet light. These absorptions and emissions, often referred to as atomic spectral lines, are due to electronic transitions of outer shell electrons as they rise and fall from one electron orbit to another. Atoms also have distinct x-ray spectra that are attributable to the excitation of inner shell electrons to excited states.

Atoms of different elements have distinct spectra and therefore atomic spectroscopy allows for the identification and quantitation of a sample's elemental composition. After inventing the spectroscope, Robert Bunsen and Gustav Kirchhoff discovered new elements by observing their emission spectra. Atomic absorption lines are observed in the solar spectrum and referred to as Fraunhofer lines after their discoverer. A comprehensive explanation of the hydrogen spectrum was an early success of quantum mechanics and explained the Lamb shift observed in the hydrogen spectrum, which further led to the development of quantum electrodynamics.

Modern implementations of atomic spectroscopy for studying visible and ultraviolet transitions include flame emission spectroscopy, inductively coupled plasma atomic emission spectroscopy, glow discharge spectroscopy, microwave induced plasma spectroscopy, and spark or arc emission spectroscopy. Techniques for studying x-ray spectra include X-ray spectroscopy and X-ray fluorescence.

Molecules

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The combination of atoms into molecules leads to the creation of unique types of energetic states and therefore unique spectra of the transitions between these states. Molecular spectra can be obtained due to electron spin states (electron paramagnetic resonance), molecular rotations, molecular vibration, and electronic states. Rotations are collective motions of the atomic nuclei and typically lead to spectra in the microwave and millimetre-wave spectral regions. Rotational spectroscopy and microwave spectroscopy are synonymous. Vibrations are relative motions of the atomic nuclei and are studied by both infrared and Raman spectroscopy. Electronic excitations are studied using visible and ultraviolet spectroscopy as well as fluorescence spectroscopy.[2][19][20][21][22]

Studies in molecular spectroscopy led to the development of the first maser and contributed to the subsequent development of the laser.

Crystals and extended materials

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The combination of atoms or molecules into crystals or other extended forms leads to the creation of additional energetic states. These states are numerous and therefore have a high density of states. This high density often makes the spectra weaker and less distinct, i.e., broader. For instance, blackbody radiation is due to the thermal motions of atoms and molecules within a material. Acoustic and mechanical responses are due to collective motions as well. Pure crystals, though, can have distinct spectral transitions, and the crystal arrangement also has an effect on the observed molecular spectra. The regular lattice structure of crystals also scatters x-rays, electrons or neutrons allowing for crystallographic studies.

Nuclei

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Nuclei also have distinct energy states that are widely separated and lead to gamma ray spectra. Distinct nuclear spin states can have their energy separated by a magnetic field, and this allows for nuclear magnetic resonance spectroscopy.

Other types

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Other types of spectroscopy are distinguished by specific applications or implementations:

Applications

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UVES is a high-resolution spectrograph on the Very Large Telescope.[31]

There are several applications of spectroscopy in the fields of medicine, physics, chemistry, and astronomy. Taking advantage of the properties of absorbance and with astronomy emission, spectroscopy can be used to identify certain states of nature. The uses of spectroscopy in so many different fields and for so many different applications has caused specialty scientific subfields. Such examples include:

  • Determining the atomic structure of a sample[32]
  • Studying spectral emission lines of the sun and distant galaxies[33]
  • Space exploration
  • Cure monitoring of composites using optical fibers.
  • Estimating weathered wood exposure times using near infrared spectroscopy.[34]
  • Measurement of different compounds in food samples by absorption spectroscopy both in visible and infrared spectrum.
  • Measurement of toxic compounds in blood samples
  • Non-destructive elemental analysis by X-ray fluorescence.
  • Electronic structure research with various spectroscopes.
  • Redshift to determine the speed and velocity of a distant object
  • Determining the metabolic structure of a muscle
  • Monitoring dissolved oxygen content in freshwater and marine ecosystems
  • Altering the structure of drugs to improve effectiveness
  • Characterization of proteins
  • Respiratory gas analysis in hospitals[7]
  • Finding the physical properties of a distant star or nearby exoplanet using the Relativistic Doppler effect.[35]
  • In-ovo sexing: spectroscopy allows to determine the sex of the egg while it is hatching. Developed by French and German companies, both countries decided to ban chick culling, mostly done through a macerator, in 2022.[36]
  • Process monitoring in Industrial process control[37]

History

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Main article: History of spectroscopy

The history of spectroscopy began with Isaac Newton's optics experiments (1666–1672). According to Andrew Fraknoi and David Morrison, "In 1672, in the first paper that he submitted to the Royal Society, Isaac Newton described an experiment in which he permitted sunlight to pass through a small hole and then through a prism. Newton found that sunlight, which looks white to us, is actually made up of a mixture of all the colors of the rainbow."[38] Newton applied the word "spectrum" to describe the rainbow of colors that combine to form white light and that are revealed when the white light is passed through a prism.

Fraknoi and Morrison state that "In 1802, William Hyde Wollaston built an improved spectrometer that included a lens to focus the Sun's spectrum on a screen. Upon use, Wollaston realized that the colors were not spread uniformly, but instead had missing patches of colors, which appeared as dark bands in the spectrum."[38] During the early 1800s, Joseph von Fraunhofer made experimental advances with dispersive spectrometers that enabled spectroscopy to become a more precise and quantitative scientific technique. Since then, spectroscopy has played and continues to play a significant role in chemistry, physics, and astronomy. Per Fraknoi and Morrison, "Later, in 1815, German physicist Joseph Fraunhofer also examined the solar spectrum, and found about 600 such dark lines (missing colors), are now known as Fraunhofer lines, or Absorption lines."[38][better source needed]

In quantum mechanical systems, the analogous resonance is a coupling of two quantum mechanical stationary states of one system, such as an atom, via an oscillatory source of energy such as a photon. The coupling of the two states is strongest when the energy of the source matches the energy difference between the two states. The energy E of a photon is related to its frequency ν by E = hν where h is the Planck constant, and so a spectrum of the system response vs. photon frequency will peak at the resonant frequency or energy. Particles such as electrons and neutrons have a comparable relationship, the de Broglie relations, between their kinetic energy and their wavelength and frequency and therefore can also excite resonant interactions.

Spectra of atoms and molecules often consist of a series of spectral lines, each one representing a resonance between two different quantum states. The explanation of these series, and the spectral patterns associated with them, were one of the experimental enigmas that drove the development and acceptance of quantum mechanics. The hydrogen spectral series in particular was first successfully explained by the Rutherford–Bohr quantum model of the hydrogen atom. In some cases spectral lines are well separated and distinguishable, but spectral lines can also overlap and appear to be a single transition if the density of energy states is high enough. Named series of lines include the principal, sharp, diffuse and fundamental series.

DIY Spectroscopy

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Spectroscopy has emerged as a growing practice within the maker movement, enabling hobbyists and educators to construct functional spectrometers using readily available materials.[39] Utilizing components like CD/DVD diffraction gratings, smartphones, and 3D-printed parts, these instruments offer a hands-on approach to understanding light and matter interactions. Smartphone applications[40][41] along with open-source tools[42] facilitate integration, greatly simplify the capturing and analysis of spectral data. While limitations in resolution, calibration accuracy, and stray light management exist compared to professional equipment, DIY spectroscopy provides valuable educational experiences[43] and contributes to citizen science initiatives, fostering accessibility to spectroscopic techniques.

See also

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Notes

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References

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[edit]
Revisions and contributorsEdit on WikipediaRead on Wikipedia

Spectroscopy

View on Grokipedia
from Grokipedia
Spectroscopy is the scientific study of the interaction between and , typically analyzed as a function of the or of the radiation emitted, absorbed, reflected, or scattered by the material. This field encompasses a wide range of techniques used to identify substances, determine their composition, and probe their physical and chemical properties by examining the unique signatures produced by atomic and molecular transitions. The history of spectroscopy traces back to the 17th century, when Sir Isaac Newton demonstrated that white light could be dispersed into a continuous of colors using a prism, laying the foundational understanding of light's composition. Significant advancements occurred in the , with Fraunhofer's identification of dark absorption lines in the solar in 1814, and and Robert Bunsen's formulation in 1859 of the principle that every element produces a unique , enabling the first spectrochemical analyses of celestial bodies. The discovery of radiation by in 1800 and ultraviolet by Johann Ritter in 1801 expanded the spectral range beyond visible light. The marked the era of modern spectroscopy, propelled by and the invention of the in 1960, which provided intense, monochromatic sources for precise measurements. At its core, spectroscopy operates on the principle that atoms and molecules absorb or emit at specific wavelengths corresponding to quantized transitions, as described by quantum theory. Common techniques include emission spectroscopy, in which excited atoms release to produce bright lines against a dark background, and , which reveals dark lines in a continuous where light is absorbed. Types of spectra include continuous spectra, produced by hot, dense objects like emitting across all wavelengths. Reflectance and processes further contribute to spectral analysis, particularly in solid or particulate materials, where and composition influence the observed signatures. Spectroscopy finds broad applications across disciplines, from determining the , temperature, and velocity of astronomical objects via and Doppler shifts in , to analyzing molecular structures in chemistry and through techniques like and . In materials science and , it identifies minerals and environmental contaminants by their reflectance properties. These methods are indispensable for non-destructive analysis, enabling insights into everything from exoplanet atmospheres to pharmaceutical .

Fundamentals

Definition and Scope

Spectroscopy is the branch of science that studies the interaction of matter with through processes such as absorption, emission, or , which produce a that provides insights into the atomic and molecular , composition, and dynamics of the under investigation. This field enables the qualitative and quantitative analysis of substances by examining how they respond to different wavelengths of , revealing unique spectral signatures that characterize their levels and chemical bonds. The term "spectroscopy" originates from the Latin word , meaning "image" or "apparition," combined with the Greek skopia, meaning "observation" or "examination," reflecting its focus on observing spectral phenomena. Although the systematic study of light dispersion began in the 17th century with Isaac Newton's work on prisms, the modern term was coined in the mid-19th century amid advances in spectral analysis by scientists like and . The scope of spectroscopy encompasses the entire , from low-energy radio waves with wavelengths on the order of meters to high-energy gamma rays with wavelengths shorter than atomic nuclei, allowing applications across diverse scales from subatomic particles to astronomical objects. It is important to distinguish spectroscopy from related terms: while spectroscopy broadly refers to the study and interpretation of spectra, spectrometry emphasizes the measurement of these spectra using instruments, spectrography is the technique of recording spectra using a spectrograph—an instrument that disperses radiation into its component wavelengths—to produce a spectrogram (a visual record of intensity versus wavelength, historically photographic and now often digital), and specifically involves the quantitative measurement of light absorption or transmission as a function of for analytical purposes. Central to spectroscopic analysis are different types of spectra: a continuous spectrum appears as a smooth distribution of wavelengths, like that from a hot incandescent source; an features bright lines or bands against a dark background, indicating wavelengths emitted during electronic transitions; and an absorption spectrum shows dark lines superimposed on a continuous spectrum, corresponding to wavelengths absorbed by the sample. Two fundamental metrics in spectroscopy are and (SNR). , often quantified as R=λΔλR = \frac{\lambda}{\Delta \lambda}, where λ\lambda is the and Δλ\Delta \lambda is the smallest resolvable difference, determines the instrument's ability to distinguish closely spaced spectral features, such as fine atomic lines. SNR, defined as the ratio of the signal intensity to the noise level (typically the root-mean-square of background fluctuations), assesses the quality and reliability of spectral data, with higher values enabling clearer detection of weak signals amid noise. These metrics are crucial for ensuring the precision and interpretability of spectra across the field's interdisciplinary applications in chemistry, physics, , and astronomy.

Basic Principles of Radiation-Matter Interaction

, the basis of all spectroscopic techniques, is characterized by its λ\lambda, ν\nu, and energy EE. The and are inversely related through the cc in , given by ν=c/λ\nu = c / \lambda. The energy of a , the quantum of electromagnetic radiation, is directly proportional to its via Planck's relation E=hνE = h\nu, where hh is Planck's constant (6.626×10−346.626 \times 10^{-34} J s), highlighting the quantized nature of . This relation underscores the wave-particle duality of radiation, which behaves as both waves (exhibiting interference and ) and particles (photons with discrete energy packets) depending on the experimental context. The primary mechanisms of interaction between and matter in spectroscopy are absorption, emission, and . Absorption occurs when a is taken up by an atom or , promoting an to a higher or exciting a vibrational mode, provided the 's matches the difference between states. Emission is the reverse process, where an excited species relaxes to a lower state, releasing a of corresponding ; this is observed in techniques like or . involves the redirection of without net absorption, divided into elastic scattering (e.g., , where the 's remains unchanged) and inelastic scattering (e.g., , where the scattered gains or loses due to vibrational or rotational transitions in the ). For absorption processes, the extent of through a medium is quantified by the Beer-Lambert law, which describes the of intensity. The law derives from considering the incremental loss of photon flux dIdI over a path length dzdz due to absorption by NN absorbers each with cross-section σ\sigma, yielding dI/dz=−σNIdI / dz = -\sigma N I, or integrated form I=I0e−αlI = I_0 e^{-\alpha l} where α=σN\alpha = \sigma N is the absorption coefficient and ll is the path length. In terms of concentration cc (moles per unit ), this becomes the A=−log⁡10(I/I0)=ϵclA = -\log_{10}(I / I_0) = \epsilon c l, where ϵ\epsilon is the molar absorptivity (a measure of the absorber's efficiency at a given ). This linear relationship enables quantitative analysis of concentrations in spectroscopic measurements. Not all transitions between energy states are equally probable; selection rules dictate which interactions are allowed based on quantum mechanical constraints. These rules arise from the properties of the wavefunctions and the interaction operator in time-dependent , requiring the integral ⟨ψ2∣μ^∣ψ1⟩\langle \psi_2 | \hat{\mu} | \psi_1 \rangle to be non-zero for observable transitions. For electric transitions, common in UV-Vis and IR spectroscopy, allowed changes in quantum numbers include Δl=±1\Delta l = \pm 1 for orbital and specific parity or matches (e.g., gerade to ungerade for homonuclear diatomics). Vibrational selection rules, such as Δv=±1\Delta v = \pm 1 for harmonic oscillators, further restrict observations to modes that alter the molecular dipole moment. These rules ensure that only certain spectral lines appear, providing insights into molecular structure and .

Theoretical Foundations

Quantum Mechanical Basis

The quantum mechanical foundation of spectroscopy rests on the time-independent , which describes the stationary states of bound . For a particle in a potential V(r)V(\mathbf{r}), the equation takes the form H^ψ=[E](/page/E!)ψ\hat{H} \psi = [E](/page/E!) \psi, where H^=−ℏ22m∇2+V(r)\hat{H} = -\frac{\hbar^2}{2m} \nabla^2 + V(\mathbf{r}) is the Hamiltonian operator, ψ\psi is the wave function, and [E](/page/E!)[E](/page/E!) is the eigenvalue. This yields discrete levels for bound systems, such as electrons in atoms or nuclei, enabling the prediction of spectral transitions between these levels when the system interacts with . In atomic systems, solving the Schrödinger equation for hydrogen-like atoms produces quantized energy levels given by En=−13.6 eVn2E_n = -\frac{13.6 \, \mathrm{eV}}{n^2}, where nn is the principal quantum number; this formula arises from the Coulomb potential and spherical symmetry, with higher-ZZ atoms scaled by Z2Z^2. For molecules, the Born-Oppenheimer approximation separates the fast electronic motion from slower nuclear vibrations and rotations, leading to discrete vibrational energy levels approximated as Ev=ℏω(v+12)E_v = \hbar \omega (v + \frac{1}{2}) for harmonic oscillators (with quantum number vv and frequency ω\omega), combined with rotational levels EJ=ℏ22IJ(J+1)E_J = \frac{\hbar^2}{2I} J(J+1) (where JJ is the rotational quantum number and II the moment of inertia). These quantized levels underpin the discrete spectral features observed in absorption and emission spectra. Spectroscopic transitions occur via time-dependent perturbations from the , treated using first-order . In the electric , valid for wavelengths much larger than the system size, the interaction Hamiltonian is H^′=−μ⋅E\hat{H}' = -\mathbf{\mu} \cdot \mathbf{E}, where μ\mathbf{\mu} is the dipole moment operator and E\mathbf{E} the . The transition rate from initial state ∣i⟩|i\rangle to final state ∣f⟩|f\rangle is given by : Γ=2πℏ∣⟨f∣H^′∣i⟩∣2ρ(Ef−Ei)\Gamma = \frac{2\pi}{\hbar} |\langle f | \hat{H}' | i \rangle|^2 \rho(E_f - E_i), with ρ(E)\rho(E) the density of final states; this yields the probability per unit time for absorption or emission when is conserved. The strength of such dipole-allowed transitions is quantified by the fij=8π2mν3he2∣μij∣2f_{ij} = \frac{8\pi^2 m \nu}{3 h e^2} |\mu_{ij}|^2, where ν\nu is the transition frequency, mm the , ee the charge, and μij=⟨i∣μ∣j⟩\mu_{ij} = \langle i | \mathbf{\mu} | j \rangle; this dimensionless measure relates quantum probabilities to classical oscillator models and determines line intensities in spectra.

Spectral Lines and Transitions

Spectral lines arise from quantum mechanical transitions between discrete levels in atoms or molecules, where the emission or absorption of photons at specific frequencies corresponds to the difference ΔE = hν between the levels, as predicted by quantum theory. These lines are not infinitely sharp but exhibit finite widths and shapes due to various physical processes that perturb the ideal delta-function response. The observed line profile reflects the of multiple broadening mechanisms, influencing the resolution and interpretation of spectra in experimental settings. The primary intrinsic broadening is natural broadening, stemming from the finite lifetime τ of the due to . According to the time-energy , this leads to an energy uncertainty ΔE ≈ ħ / τ, manifesting as a Lorentzian line shape in the with (FWHM) Γ = 1/τ in angular frequency units, or Δν = 1/(2πτ) in frequency units. This Lorentzian profile is symmetric and has extended wings, described by the function L(ν) = (Γ / 2π) / [(ν - ν₀)² + (Γ / 2)²], where ν₀ is the central ; it dominates in low-pressure environments where other effects are minimal. Thermal motion of atoms or molecules in a gas introduces , arising from the relativistic frequency shift δν / ν = v / c along the , where v is the component. The Maxwell-Boltzmann distribution yields a Gaussian line shape with FWHM Δν = (ν / c) √( (8 k T ln 2) / M ), where k is Boltzmann's constant, T is , and M is the atomic or . This broadening increases with and decreases with mass, often convolving with the Lorentzian to form a in real spectra. The intensity of spectral lines, quantified by the integrated absorption coefficient ∫ α(ν) dν, is proportional to the transition dipole moment squared |μ_{if}|² and the population difference between initial and final states, as given by the Einstein coefficients for absorption. For molecular spectra involving vibrational changes, the Franck-Condon principle governs the overlap of vibrational wavefunctions between electronic states, determining relative intensities through factors |⟨χ_v' | χ_v'' ⟩|², where χ denotes vibrational wavefunctions; vertical transitions with maximal overlap yield the strongest lines, explaining progressions in band spectra. External fields further modify line positions and structures. The causes splitting in a B due to the interaction of the with the field, with energy shift ΔE = μ_B g m_j B, where μ_B is the , g is the , and m_j is the ; this results in linearly or circularly polarized components, enabling diagnostics. Similarly, the in an E induces splitting via the quadratic Stark shift ΔE ∝ α E² (for non-degenerate states, with α) or linear shifts in degenerate cases like , altering line positions and widths proportionally to E. Hyperfine structure emerges from the magnetic dipole and electric quadrupole interactions between the nuclear spin I and the total electron angular momentum J, forming total angular momentum F = I + J with energy shifts A [F(F+1) - I(I+1) - J(J+1)] / 2, where A is the hyperfine coupling constant. This fine splitting, typically on the order of MHz to GHz, arises primarily from the Fermi contact term for s-electrons and dipolar interactions, resolving nuclear properties in high-resolution spectra.

Classification of Methods

By Radiative Energy Type

Spectroscopic methods are classified by the type of radiative energy employed, which corresponds to distinct regions of the . Each region targets specific energy differences in matter, from low-energy spin and rotational transitions to high-energy core and nuclear excitations. This classification highlights how the matches the scale of intramolecular or atomic processes, enabling selective probing of , electronic structures, and nuclear properties. In the radio and microwave regions (frequencies typically 10 MHz to 300 GHz, corresponding to energies of approximately 4 \times 10^{-8} to 10^{-3} eV), spectroscopy focuses on low-energy transitions involving nuclear and spins as well as molecular rotations. (NMR) spectroscopy uses radio-frequency pulses to induce transitions between nuclear spin states in a , providing detailed information on molecular connectivity and environments. spin resonance (ESR), also known as (EPR), employs radiation to excite spin transitions, particularly useful for studying paramagnetic and free radicals. in the microwave domain measures pure rotational transitions, yielding molecular moments of inertia that reveal bond lengths and angles in gas-phase molecules. Infrared (IR) spectroscopy utilizes mid- to far-IR (wavelengths 2.5–50 μm, energies ~0.025–0.5 eV), which matches the energy scale of molecular vibrational modes. Absorption or emission in this region excites , , and other , allowing identification of functional groups through characteristic band positions. The region, spanning 400–1500 cm⁻¹, is particularly diagnostic as it encodes unique patterns of molecular , enabling compound identification akin to a "molecular ." Visible and ultraviolet (UV-Vis) spectroscopy covers wavelengths from 10–780 nm (energies ~1.6–124 eV), aligning with electronic transitions in valence shells. These methods probe promotions of electrons between molecular orbitals, such as π–π* or n–π* transitions in organic compounds. In transition metal complexes, d–d bands arise from splitting of d-orbitals in ligand fields, providing insights into coordination geometry and oxidation states. X-ray and gamma-ray spectroscopy employs high-energy photons (energies >100 eV for X-rays and >100 keV for gamma rays), targeting inner-shell processes. X-ray absorption spectroscopy excites core electrons to higher levels, revealing local electronic structure and oxidation states around atoms. Mössbauer spectroscopy, using gamma rays, examines recoilless nuclear transitions in solids, sensitive to the nuclear environment and isomer shifts indicative of chemical bonding. These radiative energy regions correspond to hierarchical energy scales in : rotational and spin transitions at micro- to milli-electronvolt (μeV–meV) levels (radio/), vibrational modes at milli- to fraction-of-electronvolt (meV–~0.5 eV) (IR), valence electronic transitions at (eV) scales (UV-Vis), core-level excitations at kiloelectronvolt (keV) (X-rays), and nuclear levels at higher keV (gamma rays). This matching ensures specificity in probing different physical phenomena.

By Interaction Nature

Spectroscopic methods can be classified by the primary interaction mechanism between and , encompassing absorption, emission, , and coherence-based processes. This categorization emphasizes the fundamental physical processes involved, such as energy transfer or phase alterations, rather than the specific energy range of the . These interactions enable the probing of molecular, atomic, or material properties through distinct signatures in the detected signals. Absorption spectroscopy measures the intensity of light transmitted through a sample after interaction with matter, where the reduction in transmitted light intensity quantifies the absorption at specific wavelengths. This technique directly probes transitions from ground to excited states, with the absorbed intensity proportional to the population in the lower energy state, governed by the Beer-Lambert law: A=ϵclA = \epsilon c l, where AA is , ϵ\epsilon is the , cc is concentration, and ll is path length. Emission spectroscopy involves exciting a sample to higher states and analyzing the emitted as it relaxes back to lower states, providing information on excited-state dynamics. The emitted reveals levels and transition probabilities, often through or . A key parameter is the fluorescence lifetime τ\tau, defined as the average time a spends in the before emission, given by τ=1kr+knr\tau = \frac{1}{k_r + k_{nr}}, where krk_r is the radiative decay rate and knrk_{nr} is the non-radiative decay rate; this lifetime is sensitive to environmental factors like . Scattering spectroscopy distinguishes elastic and inelastic processes based on energy exchange with matter. Rayleigh scattering is elastic, where incident photons are redirected without frequency change (Δν=0\Delta \nu = 0), arising from temporary polarization of the sample. In contrast, is inelastic, with scattered light shifted by Δν=νvib\Delta \nu = \nu_{vib}, corresponding to molecular vibrational frequencies, enabling vibrational spectroscopy without absorption. Brillouin scattering, another inelastic variant, involves interactions with acoustic phonons, producing frequency shifts on the order of GHz that probe sound velocities and elastic properties in materials. Coherence methods, such as , exploit phase relationships in the radiation-matter interaction for enhanced detection. By superimposing reference and sample beams in a Michelson or Mach-Zehnder interferometer, phase shifts induced by the sample's or dispersion are measured, enabling high-resolution, phase-sensitive spectroscopy. This approach improves signal-to-noise ratios for weak interactions, as seen in where interferograms are transformed to reveal spectral details. Detection limits in these methods are fundamentally tied to the interaction cross-sections, which quantify the probability of photon-matter events per molecule. Larger cross-sections, as in vibrational transitions, enhance sensitivity for trace analytes, achieving limits down to parts-per-billion in optimized setups; for instance, IR absorption can detect sub-μg/mL concentrations via pathlength scaling. Noise sources like detector limit ultimate sensitivity, but cross-section-driven signal strength allows selective tracing of analytes in complex matrices.

Spectroscopic Techniques by Target

Atomic Spectroscopy

Atomic spectroscopy examines the spectra produced by free atoms and ions in the gas phase, where interactions with electromagnetic radiation reveal the electronic structure through discrete transitions between quantized energy levels. These transitions generate sharp, well-defined spectral lines, each corresponding to a specific energy difference unique to the element, enabling precise identification and quantification without the broadening effects from molecular vibrations or rotations. The simplicity of atomic spectra arises from the isolated nature of atoms, making this branch essential for analyzing gaseous samples and vaporized materials. In , energy levels are classified using spectroscopic s under the LS (Russell-Saunders) coupling approximation, suitable for lighter atoms where orbital and spin angular momenta couple separately before combining. The is denoted as 2S+1LJ^{2S+1}L_J, where LL represents the total orbital angular momentum (with letters S for L=0L=0, P for L=1L=1, D for L=2L=2, etc.), SS is the total , 2S+12S+1 is the multiplicity indicating spin degeneracy, and JJ is the total angular momentum ranging from ∣L−S∣|L - S| to L+SL + S. Transitions between these levels obey selection rules, such as ΔL=±1\Delta L = \pm 1 for electric dipole radiation, producing the observed sharp lines in emission or absorption spectra. This notation facilitates the prediction of spectral patterns and intensities for multi-electron atoms. A foundational technique in atomic spectroscopy is atomic absorption spectroscopy (AAS), which quantifies elements by measuring the absorption of resonant light by ground-state atoms in a vaporized sample. The process involves atomization—typically via flame or graphite furnace—to produce free atoms, followed by passage through a hollow cathode lamp emitting element-specific wavelengths; the degree of absorption follows Beer's law, where intensity is proportional to atomic concentration. AAS excels in trace elemental analysis, detecting metals at parts-per-billion levels in environmental, clinical, and industrial samples, though interferences from molecular species or matrix effects require corrections like background subtraction. Flame photometry, a form of , is optimized for and alkaline metals, exploiting their low excitation energies to produce intense emission lines when aspirated into a . In this method, the sample solution is nebulized into a propane-air or acetylene-air , where evaporates, and atoms are thermally excited; emitted is isolated via filters and measured photometrically, with curves linking intensity to concentration. It is particularly sensitive for sodium (589 nm doublet) and (766 nm), achieving detection limits around 0.1 ppm, and finds routine use in , , and biological fluid analysis for these ions. For simultaneous multi-element detection, optical emission spectroscopy (ICP-OES) employs a high-temperature plasma (around 6000–10,000 K) generated by radio-frequency induction to fully atomize and ionize samples, exciting atoms to emit characteristic lines across the UV-visible range. The plasma's robustness allows analysis of complex matrices like geological waters or digests, detecting over 70 elements at trace levels (e.g., 1–10 ppb for many metals) using axial or radial viewing configurations for optimal signal-to-noise. interferences, where overlapping emissions from different elements obscure signals (e.g., iron lines near ), are resolved through high-resolution echelle gratings, background correction algorithms, and inter-element correction factors derived from standard additions. Official methods like EPA 6010C standardize ICP-OES for , emphasizing matrix matching and quality controls to ensure accuracy. In astrophysics, atomic spectroscopy underpins elemental abundance determinations in stellar atmospheres, exemplified by the Fraunhofer absorption lines in the Sun's visible spectrum, which arise from cooler gas layers absorbing continuum radiation at atomic transition wavelengths. These dark lines, cataloged extensively since the 19th century, match laboratory spectra of elements like hydrogen (Balmer series at 656 nm, 486 nm), calcium (K line at 393 nm), and iron, revealing the solar photosphere's composition (e.g., ~74% hydrogen by mass). Advances in solar spectroscopy, including ultraviolet observations, have refined these identifications, confirming atomic processes dominate the line formation in low-density plasmas.

Molecular Spectroscopy

Molecular spectroscopy probes the energy levels associated with vibrational, rotational, and electronic motions in molecules, providing insights into their structure, bonding, and dynamics. These introduce complexity beyond atomic systems, as molecular spectra often exhibit from coupled transitions. Vibrational and rotational spectra appear in the and regions, while electronic spectra dominate the ultraviolet-visible range, with overlaps enabling detailed characterization of polyatomic and diatomic in isolation or dilute phases. Rovibrational spectra, observed primarily in the , arise from simultaneous changes in vibrational and rotational quantum numbers, resulting in banded structures. For diatomic molecules, the fundamental vibrational transition (Δv = +1) is accompanied by rotational changes governed by selection rules ΔJ = ±1 or 0, producing distinct P, , and R branches. The P branch (ΔJ = -1) appears at lower frequencies than the band origin, corresponding to transitions from higher initial rotational levels to lower final levels; the R branch (ΔJ = +1) shifts to higher frequencies; and the branch (ΔJ = 0), when allowed, forms a central line, though it is often absent in simple diatomics due to restrictions. These branches enable of rotational constants B and vibrational frequencies from spacing and band contours. Real molecular vibrations deviate from the model due to in the , leading to non-equispaced energy levels and observable . The anharmonic oscillator energy levels are approximated by Ev=hν(v+12)−hνxe(v+12)2E_v = h\nu \left( v + \frac{1}{2} \right) - h\nu x_e \left( v + \frac{1}{2} \right)^2 where vv is the vibrational , ν\nu is the harmonic frequency, and xe>0x_e > 0 is the anharmonicity constant (small, typically 0.01-0.03). This negative correction accounts for weaker higher (Δv > 1) and interactions between levels, improving spectral predictions for polyatomics. Electronic spectroscopy in the UV-Vis region excites valence electrons between molecular orbitals, often revealing conjugation and functional groups. The π → π* transition, prominent in unsaturated hydrocarbons and aromatics, involves promotion from a bonding π orbital to an antibonding π* orbital, absorbing around 200–400 nm depending on conjugation length; for example, shows a strong band near 175 nm./New_Page/4%3A_Structure_Determination_I-_UV-Vis_and_Infrared_Spectroscopy_Mass_Spectrometry/4.4%3A_Ultraviolet_and_visible_spectroscopy) The depicts these processes, mapping singlet (S) and triplet (T) states with vertical electronic transitions and horizontal non-radiative relaxations. Singlet-triplet (ISC) from S₁ to T₁ occurs via spin-orbit coupling, enabling or energy transfer, with rates enhanced in heavy-atom substituted molecules. Fourier transform infrared (FTIR) spectroscopy is a cornerstone technique for rovibrational analysis, offering high sensitivity and resolution for gas-phase studies like atmospheric monitoring and liquid-phase identification of solvents or biomolecules. In gases, long path lengths exploit weak absorptions for trace detection; in liquids, (ATR) modes minimize preparation. , based on changes, complements FTIR by providing orthogonal selection rules and is particularly suited to aqueous environments, where water's weak scattering avoids the strong IR absorption bands that interfere with studies. Isotopic substitution alters spectral features through changes in the μ = m₁m₂/(m₁ + m₂), scaling vibrational frequencies as ν ∝ √(k/μ), where k is the force constant. Heavier isotopes increase μ, lowering band positions; for instance, replacing ¹H with ²H in HCl shifts the fundamental from ~2990 cm⁻¹ to ~2145 cm⁻¹, aiding mode assignment and confirming molecular identity in complex mixtures. These shifts are more pronounced for vibrations involving the substituted atom, enabling for dynamic studies.

Condensed Matter Spectroscopy

Condensed matter spectroscopy investigates the electronic, vibrational, and structural properties of solids and extended materials, emphasizing collective excitations such as phonons and plasmons, as well as band structures that arise from periodic lattices. Unlike isolated systems, these materials exhibit delocalized states and interactions that lead to emergent phenomena observable through spectroscopic probes. This field is crucial for understanding semiconductors, metals, and insulators, where spectroscopy reveals how atomic orbitals form energy bands influencing conductivity and optical responses. In band theory, the periodic potential of a crystal lattice causes wavefunctions to form Bloch states, resulting in bands separated by s. Semiconductors feature a small , typically 0.1 to 4 eV, where the valence band (filled with s) and conduction band (empty) play key roles in charge transport. Direct s occur when the valence band maximum and conduction band minimum align at the same wavevector k in the , enabling efficient radiative recombination, as in GaAs with a gap of 1.42 eV at . In contrast, indirect s, like in (1.12 eV), require assistance for momentum conservation during transitions, reducing luminescence efficiency. Excitons in semiconductors are bound electron-hole pairs formed when an is excited from the valence to the conduction band, held together by attraction with binding energies of 10-100 meV in typical materials. These quasi-particles behave like atoms but are influenced by the screening of the host lattice, leading to Wannier-Mott excitons in three-dimensional semiconductors with large radii (up to hundreds of angstroms). In direct-gap materials, excitons manifest as sharp absorption lines below the band edge, enhancing in devices like LEDs. X-ray photoelectron spectroscopy (XPS) probes surface composition in condensed matter by measuring the kinetic energy of photoelectrons emitted from core levels under irradiation, with penetration depths of 1-10 nm. Binding energy shifts, arising from chemical environment changes (e.g., oxidation states), allow identification of elemental ; for instance, carbon 1s peaks shift by 1-5 eV depending on bonding. This technique is essential for analyzing surface oxides or interfaces in materials like thin films. Ultraviolet photoelectron spectroscopy (UPS) examines valence band structures in solids using helium discharge lamps (photon energies 21.2-40.8 eV), ejecting electrons from occupied states near the . It maps the , revealing band dispersions and work functions; for example, in metals, it shows a broad valence band width of 5-10 eV. UPS complements XPS by focusing on delocalized electrons critical for electronic properties in semiconductors and organics. Phonon spectroscopy in solids uses (IR) absorption and to probe lattice vibrations, which are collective modes representing quantized displacements of atoms. IR spectroscopy detects polar phonons that couple to electromagnetic fields, exciting transverse optical (TO) modes at frequencies around 10-15 THz in ionic crystals like NaCl. , involving inelastic light scattering, reveals both optical and acoustic phonons through changes in , often showing longitudinal optical (LO) modes split from TO by the Lyddane-Sachs-Teller relation. These techniques identify lattice symmetries and in materials. Phonon dispersion relations describe how vibrational frequencies depend on wavevector, given by ω(k)\omega(\mathbf{k}), where acoustic branches start at zero frequency at the Brillouin zone center (k=0) and flatten near zone boundaries due to short-range forces. In one-dimensional chains, the relation is ω(k)=2Km∣sin⁡(ka2)∣\omega(k) = 2\sqrt{\frac{K}{m}} \left| \sin\left(\frac{ka}{2}\right) \right|
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