Atomic spectra

Line spectra instead of a continuous rainbow

A hot dense object can produce a broad continuous spectrum, but a low-density excited atomic gas produces sharp emission lines. When continuous light passes through cooler atomic gas, the same allowed transitions appear as dark absorption lines.

Emission and absorption are two directions of the same energy-level system.

Hydrogen and the Rydberg relation

For hydrogen, wavelengths can be predicted by:

The Balmer Hα line at about 656 nm comes from n=3 → 2; Hβ near 486 nm comes from n=4 → 2.

Spectra of multi-electron atoms

Atoms with many electrons have far more transitions because subshell energies, electron–electron interactions, spin–orbit coupling and selection rules create many states. Each element therefore has a characteristic forest of lines rather than a simple hydrogen-like sequence.

Line intensity also contains information: it depends on transition probabilities and the populations of the initial states, not only on the existence of two energy levels.

From wavelength to chemical identification

Spectroscopy can identify atoms in flames, plasmas, stars and laboratory discharges. Calibration is essential: measured wavelengths are compared with known standards, and resolving power must be high enough to separate nearby lines.

A spectral line is not a literal colored electron. It is a photon produced or absorbed when the atomic quantum state changes.

Hydrogen transition calculator

Broadening and real measurements

Real lines have finite width. Thermal motion produces Doppler broadening; collisions cause pressure broadening; finite excited-state lifetime creates natural broadening. Instruments add their own resolution function.

Those widths are not merely imperfections. They can reveal temperature, pressure, velocity and local environment.

Series limits reveal ionization energies

Within a hydrogen series, lines become progressively closer together as n_high increases. At the series limit, the upper state has reached the continuum: the atom has been ionized.

For transitions starting from the hydrogen ground state, the Lyman-series limit therefore corresponds to 13.6 eV. Spectral convergence is direct evidence that bound levels accumulate toward a finite ionization threshold rather than continuing at equal spacing forever.

Reading a spectrum as data

A spectrum is therefore much more than a barcode for identifying an element. It can diagnose temperature, density, velocity and local fields.

Spectrometers, calibration and resolving power

A spectrometer separates wavelengths using a diffraction grating, prism or interferometric method and records intensity as a function of wavelength or frequency. Calibration against known lines converts detector position into wavelength.

Resolving power determines whether two nearby spectral features appear as separate lines. Better resolution can reveal isotope shifts, fine structure or pressure-broadened components that a lower-resolution instrument merges together.

In astronomy, the same principles allow identification of elements in stellar atmospheres without collecting a physical sample. The atoms announce their energy structure through the light they absorb and emit.

Atomic spectra versus molecular spectra

Atoms have electronic transitions but no molecular rotation or vibration. Molecules add rotational and vibrational degrees of freedom, so one electronic transition can be accompanied by many vibrational and rotational changes. Molecular spectra therefore often form bands with much richer internal structure.

This distinction matters when interpreting a flame or discharge spectrum. Sharp isolated atomic lines may coexist with broader molecular bands from transient species in the same source.

Flame tests and laboratory identification

Heating a salt in a flame excites some atoms or ions, which can emit characteristic visible light. Sodium’s strong yellow emission is so intense that trace sodium contamination can dominate a flame color.

A spectrometer is more reliable than the eye because it separates wavelengths and can distinguish overlapping emitters. Qualitative flame color is useful as a demonstration; line positions provide the actual analytical fingerprint.

Quantitative spectroscopy requires more than identifying a line. Detector response, source intensity, self-absorption and calibration all affect measured intensity.

Exercises

Balmer identification

Which series contains the H transition 4 → 2?

Emission versus absorption

Why can the same wavelength appear bright in one spectrum and dark in another?

Line width

Name one physical cause of spectral broadening.