# Spectroscopy **Spectroscopy** is the study of how matter absorbs, emits and scatters [[Electromagnetic_radiation|electromagnetic radiation]] as a function of the radiation's wavelength, frequency or [[Photon|photon]] energy. A spectrum is the record of that interaction — intensity against wavelength — and because every [[Atom|atom]] and [[Molecule|molecule]] has its own ladder of [[Energy_level|energy levels]], its spectrum is a fingerprint: the same set of lines appears bright when the substance emits and dark when it absorbs. Spectroscopy is how the composition of the [[Sun|Sun]] was read from ninety million miles away, how a chemist confirms the structure of a new compound, and how the [[Redshift|expansion of the universe]] was discovered. In the microsim below the reader works the simplest spectrum there is, the hydrogen-like atom. Three controls set the upper level n_i (3 to 12), the lower level n_f (1, 2 or 3, which selects the Lyman, Balmer or Paschen series) and the nuclear charge Z (1 for [[Hydrogen|hydrogen]], 2 for He⁺, 3 for Li²⁺); the Rydberg formula 1/λ = R·Z²·(1/n_f² − 1/n_i²) places each line on a spectrum strip, and a toggle switches between emission, bright lines on a dark strip, and absorption, dark lines cut from a continuum, to show that they are the same lines. As n_i climbs the lines crowd toward the series limit, and the hydrogen 5→2 line lands at 434 nm, the violet Balmer line the Portal Book's Bohr exercise derives. On the [[Chemistry]] flagship this article is the child of Part V — Energy, section *Spectral lines* (row K30), a section shared with the [[Physics]] flagship, where the same Rydberg strip is the C23 embed. ## Introduction Light of a single colour is light of a single wavelength, and a prism or a [[Diffraction_grating|diffraction grating]] spreads a beam into its wavelengths the way [[Isaac_Newton|Newton]]'s prism spread sunlight into a [[Rainbow|rainbow]]. A spectroscope adds a narrow slit, so that each wavelength forms its own image of the slit — a line — and a scale or a detector to record where the lines fall. The relation between the position of a line and the energy it carries is Planck's, E = h·ν = h·c/λ, with h = 6.6262×10⁻³⁴ J·s and c = 2.998×10⁸ m/s, so that a violet photon at 435.8 nm carries 4.56×10⁻¹⁹ J and a red one at 660 nm 3.01×10⁻¹⁹ J; a photon of 1 eV, which is 1.602×10⁻¹⁹ J, has a wavelength of 1,240 nm (derived).[^cboc-photon] The [[Electromagnetic_spectrum|electromagnetic spectrum]] runs from radio waves, whose photons carry microelectronvolts, to gamma rays carrying megaelectronvolts, and each band probes a different kind of motion in matter: radio and microwave photons flip nuclear and electron spins and turn molecules; infrared photons make bonds vibrate; visible and ultraviolet photons move valence [[Electron|electrons]] between orbitals; X-rays reach the core electrons and gamma rays the nucleus. The spectroscopist therefore chooses the band for the question, and the article below classifies the methods by the radiation used, by the kind of interaction and by the kind of sample. ## Theory A line appears where the photon energy matches the difference between two energy levels of the atom or molecule. For a hydrogen-like atom — one electron bound to a nucleus of charge Z — the [[Bohr_model|Bohr model]] gives the levels exactly: E_n = −2.179×10⁻¹⁸·Z²/n² J, so that a jump from n_i to n_f releases or absorbs ΔE = 2.179×10⁻¹⁸·Z²·(1/n_f² − 1/n_i²) J.[^cboc-bohr][^boyd-hydrogenic] Dividing by h·c turns this into the Rydberg formula the sim draws, 1/λ = R·Z²·(1/n_f² − 1/n_i²), with R = 2.179×10⁻¹⁸ J/(h·c) = 1.097×10⁷ m⁻¹ (derived), which agrees with the CODATA Rydberg constant 1.0973731568×10⁷ m⁻¹ to the four figures the Bohr constant carries.[^codata] The constant 2.179×10⁻¹⁸ J is half the Hartree energy E_h = 4.360×10⁻¹⁸ J of the hydrogenic solution to the [[Schrödinger_equation|Schrödinger equation]], which reproduces the Bohr energies but, in the Portal Book's phrase, gets them for the right reasons, with the electron in an [[Atomic_orbital|orbital]] rather than on a ring.[^boyd-hydrogenic][^cboc-wrong-reasons] The sim's worked line is the hydrogen 5→2 transition: ΔE = 2.179×10⁻¹⁸·(1/4 − 1/25) J = 4.576×10⁻¹⁹ J = 2.856 eV, and λ = h·c/ΔE = 434 nm (derived), the violet Hγ line of the [[Balmer_series|Balmer series]].[^cboc-bohr] Setting n_f = 1 moves every line into the ultraviolet — Lyman-α, 2→1, is at 122 nm (derived) — and n_f = 3 moves them into the infrared, so the strip shows the visible band in colour and marks ultraviolet and infrared lines as labelled ticks. As n_i increases the spacing shrinks as 1/n_i², and the lines pile up against the series limit at λ = n_f²/(R·Z²): 91 nm for Lyman, 365 nm for Balmer and 820 nm for Paschen in hydrogen (derived). Raising Z multiplies every energy by Z²: the 2→1 jump in Li²⁺ carries 1.471×10⁻¹⁷ J, nine times hydrogen's, and its photon sits at 13.5 nm (derived).[^cboc-bohr] The He⁺ ion at Z = 2 has its ground state at −8.716×10⁻¹⁸ J, four times deeper than hydrogen's, which is why the helium ion's lines fall in the ultraviolet where hydrogen's are visible.[^cboc-bohr] The emission–absorption toggle is Kirchhoff's law in a picture: a gas absorbs at exactly the wavelengths at which it emits.[^kirchhoff1860] Which lines actually show depends on which levels are occupied. In cold hydrogen every atom sits in n = 1, so the gas absorbs only the Lyman series; the Balmer lines appear in absorption only where the n = 2 level is thermally populated, and since the [[Boltzmann_distribution|Boltzmann factor]] for that 10.2 eV excitation is of order 10⁻⁵ even at 10,000 K (derived), Balmer absorption is a signature of hot gas, while Balmer emission needs only that excited atoms fall back down. The sim draws all the lines of the chosen series in either mode (an ILLUSTRATIVE choice) and leaves the populations to the reader. Real lines are not infinitely sharp. An excited state that lives for a time τ has a natural width γ = 1/(2π·τ), so a 6.25 ns lifetime gives a Lorentzian line 25 MHz wide (derived), and the [[Uncertainty_principle|uncertainty relation]] ΔE·Δt ≈ ħ is the same statement.[^raven-linewidth] In a gas the thermal motion of the atoms Doppler-shifts each one's line by −v/λ, and the sum over a Maxwell–Boltzmann distribution of velocities is a Gaussian of full width (2.355/λ)·√(k_B·T/m); for nitrogen atoms at 400 K observed at 940 nm that is 1.2 GHz, some 240 natural widths (derived from the book's figure parameters).[^raven-doppler] Intense light broadens a line further by saturating the transition, as γ·√(1 + s), where s is the intensity over the saturation intensity.[^raven-saturation] These widths are why high-resolution [[Atomic_physics|atomic]] spectroscopy is done on cold or laser-selected atoms. ## Classification of methods Spectroscopic methods are sorted in three independent ways: by the radiation or particle that probes the sample, by the nature of the interaction measured, and by the kind of material. A technique is a cell in that three-way table — [[Nuclear_magnetic_resonance|NMR]] is radio-frequency, resonant absorption, of nuclei in molecules; [[Ultraviolet–visible_spectroscopy|UV–visible spectroscopy]] is optical absorption by the valence electrons of molecules or ions — and the same physics of levels and line shapes runs through every cell. ### Type of radiative energy Most spectroscopy uses electromagnetic radiation, and the band names the method: radio-frequency for NMR and electron spin resonance, microwave for the rotational spectra of gas-phase molecules, infrared for vibrations, visible and ultraviolet for electronic transitions, X-rays for core levels and gamma rays for nuclear transitions. [[Infrared_spectroscopy|Infrared spectroscopy]] alone identifies most functional groups in an organic molecule from the wavenumbers at which its bonds stretch and bend. Other probes carry the same information in different currency: electrons scattered from a surface lose energy in quantised steps, ions sorted by mass in [[Mass_spectrometry|mass spectrometry]] give a spectrum of mass rather than of wavelength, and acoustic and mechanical spectroscopies measure how a material answers a sweep of frequencies of [[Sound|sound]]. ### Nature of the interaction The measured quantity can be absorption, the fraction of incident light removed at each wavelength; emission, the light a sample gives off when excited by heat, an electric discharge, a flame or a laser; elastic scattering or reflection, which returns the wavelength unchanged and probes structure and surfaces; inelastic scattering, in which the light exchanges a quantum of vibration or rotation with the molecule and comes back shifted, as in the Raman effect; and resonance, in which the sample is driven at a frequency that matches a level spacing and the response is read through the absorption or the re-radiated field. [[Absorption_spectroscopy|Absorption]] and [[Emission_spectrum|emission]] are the two faces the sim toggles between, and Kirchhoff's law is the statement that the wavelengths of the two coincide.[^kirchhoff1860] ### Type of material Atoms give line spectra, sharp and few, because an isolated atom has only electronic levels; molecules add rotational and vibrational ladders on top of each electronic level, so their spectra are bands of closely spaced lines that merge in liquids and solids; crystals and [[Semiconductor|semiconductors]] absorb across a continuum above the [[Band_gap|band gap]] rather than at lines, and nuclei have their own gamma-ray and radio-frequency spectra. Plasmas and stars show the atomic lines of their elements, ionised to a degree that reports their temperature. ## Other types Beyond the three-way classification lie methods that use the same idea in other currencies. Time-resolved spectroscopy follows a spectrum as it changes after a flash of light on scales down to femtoseconds; Doppler-free laser methods pick out atoms moving at a chosen velocity and so remove the thermal width described above; imaging spectroscopy records a full spectrum at every pixel of a picture, which is how satellites map minerals and vegetation and how [[Magnetic_resonance_imaging|magnetic resonance imaging]] maps water in tissue. [[Spectrophotometry|Spectrophotometry]] is the quantitative branch: the [[Beer–Lambert_law|Beer–Lambert law]] makes the [[Absorbance|absorbance]] at a chosen wavelength proportional to concentration, so a calibrated absorption spectrum is a measurement of how much, not only of what. ## Applications In [[Analytical_chemistry|analytical chemistry]] a spectrum is the standard evidence of identity and purity: an infrared spectrum confirms functional groups, an NMR spectrum maps the carbon and hydrogen skeleton, a UV–visible spectrum quantifies a coloured species, and an atomic emission or absorption line quantifies a metal at trace levels. In [[Astrophysics|astrophysics]] spectroscopy is nearly the whole of the evidence, since a star cannot be sampled. The dark lines Fraunhofer catalogued in sunlight are the absorption lines of the elements in the solar atmosphere, and the strength of a star's Balmer absorption lines, which the Boltzmann argument above ties to the population of n = 2, reports the temperature of its atmosphere. A shift of the whole line pattern measures motion along the line of sight: an atom receding at speed v emits at λ_obs = λ_em·(1 + z) with z = v/c, so that all four visible hydrogen lines of a galaxy slide by the same fraction, which is the [[Doppler_effect|Doppler]] measurement behind [[Hubble's_law|Hubble's law]].[^raven-redshift] In [[Materials_science|materials science]] the absorption edge of a semiconductor gives its band gap, and in medicine the radio-frequency spectroscopy of protons became, once gradients were added, magnetic resonance imaging. Every one of these is the microsim's picture again: a ladder of levels, a set of lines, and a physical quantity read from where the lines fall and how strong they are. ## History Newton showed in 1666, and published in the *Opticks* of 1704, that a prism separates white light into colours that a second prism cannot split further, and he gave the word spectrum its scientific meaning.[^newton1704] William Hyde Wollaston noticed dark lines in the solar spectrum in 1802, and Joseph von Fraunhofer, using a slit and better glass, catalogued hundreds of them between 1814 and 1817 and labelled the strongest with the letters still used, the D lines of sodium among them.[^wollaston1802][^fraunhofer1817] In 1860 Gustav Kirchhoff and Robert Bunsen showed that each element emits a characteristic set of bright lines, that a cooler gas absorbs at the same wavelengths, and that spectrum analysis could identify elements in a flame or in the Sun; within a year they had discovered [[Caesium|caesium]] and [[Rubidium|rubidium]] by their lines, and Kirchhoff had stated the law that ties emission to absorption.[^kirchhoff-bunsen1860][^kirchhoff1860] Anders Ångström measured the four visible hydrogen lines to a precision that let Johann Balmer, a Swiss schoolteacher, find in 1885 that their wavelengths fit λ = B·n²/(n² − 4) for n = 3, 4, 5, 6.[^angstrom1868][^balmer1885] Johannes Rydberg generalised the formula to other series and other elements in 1890, writing it in wavenumbers as the difference of two terms, and [[Niels_Bohr|Niels Bohr]] explained why in 1913: the terms are energy levels, quantised by his rule, and the lines are jumps between them.[^rydberg1890][^bohr1913] Bohr's model gave the Rydberg constant from h, e, m and c and was recognised with the 1922 Nobel Prize in Physics.[^bohr-nobel] The twentieth century widened the subject in every direction: Raman's discovery of inelastic light scattering in 1928, nuclear magnetic resonance in 1946, and the [[Laser|laser]] after 1960, whose narrow, tunable lines made it possible to resolve structure finer than the Doppler width; the hydrogen 1S–2S interval has been measured with lasers to a few parts in 10¹⁵.[^raman1928][^nmr-nobel][^parthey2011] ## Hobbyist Spectroscopy is one of the few branches of physics an amateur can practise with a few dollars of equipment. A compact disc or DVD is a reflection grating with thousands of lines per millimetre, and a slit cut in card, the disc and a phone camera make a spectroscope that shows the two yellow D lines of a sodium street lamp at 589.0 and 589.6 nm, the green 546.1 nm line of mercury in a fluorescent tube, the continuous rainbow of an incandescent bulb and the Fraunhofer lines in daylight reflected from a wall.[^nist-asd] Amateur astronomers put a transmission grating in front of a telescope camera and record the Balmer lines of bright stars, the emission lines of nebulae and the redshifts of the brighter quasars; open software calibrates the wavelength scale against the same reference lines the professionals use, published in the NIST Atomic Spectra Database.[^nist-asd] The microsim's strip is the calibrated picture such a setup produces for hydrogen. ## See also - [[Rydberg_formula]] - [[Hydrogen_spectral_series]] - [[Balmer_series]] - [[Emission_spectrum]] - [[Absorption_spectroscopy]] - [[Spectral_line]] - [[Ultraviolet–visible_spectroscopy]] - [[Infrared_spectroscopy]] - [[Nuclear_magnetic_resonance]] - [[Hydrogen_line]] - [[Bohr_model]] - [[Beer–Lambert_law]] ## References [^cboc-photon]: Blackstock, Lindsay; Brewer, Sharon; Cinel, Bruno (2022). *Chemical Bonding and Organic Chemistry*. Chapter 2 "Quantum Theory and Electronic Structure of Atoms", pp. 176–181 (E = hν = hc/λ; h, c and the electronvolt; photon energies at 435.8 nm and 660 nm). Portal Book 054, https://open.umn.edu/opentextbooks/textbooks/chemical-bonding-and-organic-chemistry [^cboc-bohr]: Blackstock, Brewer and Cinel (2022), *Chemical Bonding and Organic Chemistry*, Chapter 2, pp. 181–182 (E_n = −2.179×10⁻¹⁸/n² J; H 5→2: 4.576×10⁻¹⁹ J = 2.856 eV; Li²⁺ 2→1: 1.471×10⁻¹⁷ J; He⁺ n = 1: −8.716×10⁻¹⁸ J). Portal Book 054. [^cboc-wrong-reasons]: Blackstock, Brewer and Cinel (2022), *Chemical Bonding and Organic Chemistry*, Chapter 2, p. 183 (the Bohr model gives the right energies "for the wrong reasons"). Portal Book 054. [^boyd-hydrogenic]: Boyd, W. Christopher (2025). *Exploring Inorganic and Organometallic Chemistry*. Chapter 1, pp. 27–28 (E_n = −(Z²/2n²)E_h with E_h = 4.360×10⁻¹⁸ J; the Bohr radius a₀ = 5.292×10⁻¹¹ m). Portal Book 052, https://open.umn.edu/opentextbooks/textbooks/exploring-inorganic-and-organometallic-chemistry [^codata]: NIST. "CODATA Internationally Recommended Values of the Fundamental Physical Constants" — Rydberg constant R∞. https://physics.nist.gov/cuu/Constants/ [^raven-linewidth]: Raven, Will (2025). *Atomic Physics for Everyone*. Chapter 3 "Atoms at Rest", pp. 55–60 (Lorentzian lineshape; N(t) = N₀e^(−t/τ); τ = 1/Γ = 1/(2πγ); the 6.25 ns example), and Chapter 11, pp. 230–231 (ΔE·Δt from the uncertainty relation). Portal Book 046, https://open.umn.edu/opentextbooks/textbooks/atomic-physics-for-everyone-an-introduction-to-atomic-physics-quantum-mechanics-and-precision-spectroscopy-with-no-college-level-prerequisites [^raven-doppler]: Raven (2025), *Atomic Physics for Everyone*, Chapter 4 "Atoms in Motion", pp. 78–86 (Doppler shift −v/λ; the Maxwell–Boltzmann velocity distribution; Doppler width (2.355/λ)√(k_BT/m); Fig. 4.7 parameters). Portal Book 046. [^raven-saturation]: Raven (2025), *Atomic Physics for Everyone*, Chapter 3, pp. 63–66 (saturation intensity; power-broadened width γ√(1 + s)). Portal Book 046. [^raven-redshift]: Raven (2025), *Atomic Physics for Everyone*, Chapter 4, pp. 88 and 91 (f_obs = f_em/(1 + z), z = v/c; the Balmer lines of a receding galaxy). Portal Book 046. [^kirchhoff1860]: Kirchhoff, G. (1860). "Ueber das Verhältniss zwischen dem Emissionsvermögen und dem Absorptionsvermögen der Körper für Wärme und Licht." *Annalen der Physik und Chemie* 185 (2): 275–301. [^kirchhoff-bunsen1860]: Kirchhoff, G.; Bunsen, R. (1860). "Chemische Analyse durch Spectralbeobachtungen." *Annalen der Physik und Chemie* 186 (6): 161–189. [^newton1704]: Newton, Isaac (1704). *Opticks: or, a Treatise of the Reflexions, Refractions, Inflexions and Colours of Light*. London: Smith and Walford. [^wollaston1802]: Wollaston, W. H. (1802). "A Method of Examining Refractive and Dispersive Powers, by Prismatic Reflection." *Philosophical Transactions of the Royal Society of London* 92: 365–380. [^fraunhofer1817]: Fraunhofer, J. (1817). "Bestimmung des Brechungs- und des Farbenzerstreuungs-Vermögens verschiedener Glasarten, in Bezug auf die Vervollkommnung achromatischer Fernröhre." *Denkschriften der Königlichen Akademie der Wissenschaften zu München* 5: 193–226. [^angstrom1868]: Ångström, A. J. (1868). *Recherches sur le spectre solaire*. Uppsala: W. Schultz. [^balmer1885]: Balmer, J. J. (1885). "Notiz über die Spectrallinien des Wasserstoffs." *Annalen der Physik und Chemie* 261 (5): 80–87. [^rydberg1890]: Rydberg, J. R. (1890). "Recherches sur la constitution des spectres d'émission des éléments chimiques." *Kungliga Svenska Vetenskaps-Akademiens Handlingar* 23 (11): 1–155. [^bohr1913]: Bohr, N. (1913). "On the Constitution of Atoms and Molecules." *Philosophical Magazine*, Series 6, 26 (151): 1–25. [^bohr-nobel]: Nobel Prize Outreach. "The Nobel Prize in Physics 1922 — Niels Bohr." https://www.nobelprize.org/prizes/physics/1922/summary/ [^raman1928]: Raman, C. V.; Krishnan, K. S. (1928). "A New Type of Secondary Radiation." *Nature* 121: 501–502. [^nmr-nobel]: Nobel Prize Outreach. "The Nobel Prize in Physics 1952 — Felix Bloch and Edward Mills Purcell" (nuclear magnetic precision measurements). https://www.nobelprize.org/prizes/physics/1952/summary/ [^parthey2011]: Parthey, C. G.; Matveev, A.; Alnis, J.; et al. (2011). "Improved Measurement of the Hydrogen 1S–2S Transition Frequency." *Physical Review Letters* 107 (20): 203001. https://doi.org/10.1103/PhysRevLett.107.203001 [^nist-asd]: Kramida, A.; Ralchenko, Yu.; Reader, J.; and the NIST ASD Team. *NIST Atomic Spectra Database*. National Institute of Standards and Technology (sodium D lines 588.995 and 589.592 nm; mercury 546.074 nm; hydrogen Balmer lines). https://www.nist.gov/pml/atomic-spectra-database ## Further reading - Blackstock, Brewer and Cinel, *Chemical Bonding and Organic Chemistry* (2022), Chapter 2 "Quantum Theory and Electronic Structure of Atoms", pp. 125–192 — Portal Book 054. - Raven, *Atomic Physics for Everyone* (2025), Part I "Atom–Light Interactions", pp. 13–117 — Portal Book 046. - Averill and Eldredge, *General Chemistry: Principles, Patterns, and Applications* (2011), Chapter 6 "The Structure of Atoms", pp. 497–589 (line spectra and the Rydberg equation; page to pin) — Portal Book 050, https://open.umn.edu/opentextbooks/textbooks/general-chemistry-principles-patterns-and-applications - Boyd, *Exploring Inorganic and Organometallic Chemistry* (2025), Chapter 1 — Portal Book 052. - Flowers, Neth, Robinson et al., *Chemistry: Atoms First 2e* (OpenStax, 2019), Chapter 3 "Electronic Structure and Periodic Properties of Elements", pp. 115–184 — Portal Book 051, https://open.umn.edu/opentextbooks/textbooks/chemistry-atoms-first ## External links - [NIST Atomic Spectra Database](https://www.nist.gov/pml/atomic-spectra-database), reference wavelengths and energy levels - [CODATA fundamental constants](https://physics.nist.gov/cuu/Constants/) at NIST, the Rydberg constant - The Wikipedia pair's external links list further open resources <!-- MATTERSIM:BEGIN g33 — Matter & Energy Cluster microsim (framework build, specs/sims/Spectroscopy.json); do not hand-edit inside --> **Microsim — three.js (Wikitube framework):** *Spectroscopy* <div class="wt-sim" data-src="https://wikitube-3d-microsims.netlify.app/matter/Spectroscopy.html" data-title="Spectroscopy"></div> *Built from `MICROSIM_GUIDE/specs/sims/Spectroscopy.json`; part of the [[PORTAL_Matter|Matter portal]] spine (section sims and See-also variants).* <!-- MATTERSIM:END --> ## Wikipedia : Wikitube **Strict pair:** [Wikipedia](https://en.wikipedia.org/wiki/Spectroscopy) : [Wikitube](https://en.wikitube.io/wiki/Spectroscopy) · pinned revision [1373528125](https://en.wikipedia.org/w/index.php?oldid=1373528125) · 2026-09-11 ## Previous hub tags Hubs: `Life_Physics`. Portals: [[PORTAL_Chemistry]], [[PORTAL_Physics]]. --- *Matter & Energy Cluster child articles, wave 1 · 2026-09-11 · drafted · Chemistry row K30 · sim pending (matter/Spectroscopy).*