Absorption Spectrum
An absorption spectrum is produced when a continuous (white-light) source passes through a cool gas or solid, and atoms absorb photons at specific wavelengths that correspond exactly to allowed upward transitions between energy levels. The result is a continuous spectrum crossed by dark lines — each dark line marking a wavelength absorbed by a particular element. Absorption spectra are complementary to emission spectra and are used in stellar spectroscopy (Fraunhofer lines in sunlight), remote chemical analysis, and atmospheric science.
Key Formula
E_photon = E₂ − E₁ = hf = hc/λ
LaTeX: E_{\text{photon}} = E_2 - E_1 = h f = \frac{hc}{\lambda}
| Symbol | Meaning | Unit |
|---|---|---|
| E_photon | Energy of absorbed photon | J (or eV) |
| E₂ | Energy of higher level (excited state) | J (or eV) |
| E₁ | Energy of lower level (initial state) | J (or eV) |
| h | Planck's constant = 6.626 × 10⁻³⁴ J·s | J·s |
| f | Frequency of absorbed photon | Hz |
| c | Speed of light = 3 × 10⁸ m/s | m/s |
| λ | Wavelength of absorbed photon | m |
Worked Example
Problem
The D-lines in the solar absorption spectrum (Fraunhofer lines) are due to sodium absorbing at λ = 589 nm. Calculate the energy of the photon absorbed and identify which energy transition is responsible.
Solution
Step 1: Calculate photon energy. E = hc/λ = (6.626×10⁻³⁴ × 3×10⁸) / (589×10⁻⁹) E = 1.988×10⁻²⁵ / 5.89×10⁻⁷ E = 3.375×10⁻¹⁹ J Step 2: Convert to eV. E = 3.375×10⁻¹⁹ / 1.6×10⁻¹⁹ = 2.11 eV Step 3: Identify transition. For sodium, the 3s → 3p transition has ΔE ≈ 2.10 eV, corresponding to the famous yellow D-lines of sodium.
Answer
Photon energy ≈ 2.11 eV, corresponding to the sodium 3s → 3p electronic transition.
Comparison: Emission vs. Absorption Spectrum
| Feature | Emission Spectrum | Absorption Spectrum |
|---|---|---|
| Appearance | Bright lines on dark background | Dark lines on continuous rainbow |
| Cause | Electrons drop to lower levels | Electrons jump to higher levels |
| Light source needed | Hot/excited gas only | Continuous (white) light behind cool gas |
| Wavelengths | Same as absorption lines | Same as emission lines for same element |
| Example | Neon sign glow | Fraunhofer lines in sunlight |
Interactive Tools
PhET Neon Lights and Other Discharge Lamps
Compare emission and absorption spectra for common elements.
Open ToolNIST Atomic Spectra Database
Reference for measured absorption line wavelengths of elements.
Open ToolKhan Academy — Absorption and Emission Spectra
Video explanations and worked problems on atomic spectra.
Open Tool
Wikimedia Commons, CC BY-SA
Related Terms
Emission Spectrum
An emission spectrum is the set of discrete wavelengths (spectral lines) of electromagnetic radiation emitted by an atom or molecule when its electrons transition from higher to lower energy levels, releasing photons. Each element produces a unique pattern of spectral lines that serves as its "fingerprint," allowing identification of elements in distant stars, gas clouds, and laboratory samples. The energy of each emitted photon equals exactly the energy difference between the two levels involved in the transition: E = hf = hc/λ.
Energy Level
An energy level is one of the discrete, quantized values of energy that a bound quantum system (such as an electron in an atom or a molecule) is permitted to have. Unlike classical systems where energy can take any continuous value, quantum mechanics constrains bound particles to specific allowed states, each characterized by a set of quantum numbers. Transitions between energy levels result in the absorption or emission of photons with energies exactly equal to the difference between the two levels, producing the characteristic spectral lines used in atomic spectroscopy.
Excited State
An excited state is any quantum state of an atom, molecule, or nucleus in which one or more particles occupy energy levels higher than the ground state, having absorbed energy from a photon, collision, or thermal source. Excited states are inherently unstable — atoms typically remain in an excited state for about 10⁻⁸ seconds (nanosecond timescale) before spontaneously returning to a lower energy state by emitting a photon. The controlled management of excited states is fundamental to lasers (population inversion), fluorescence microscopy, and phosphorescence.
"Absorption" is from the Latin absorptio, derived from absorbere (to swallow up), from ab- (away) + sorbere (to suck in). In spectroscopy, the term was popularized after Gustav Kirchhoff and Robert Bunsen's systematic study of spectral lines in 1859–1860. The Fraunhofer lines (named for Joseph von Fraunhofer, 1814) were the first absorption lines identified in the solar spectrum.