How an electric field splits hydrogen’s spectral lines

Try an electric field as well

A magnetic field could change the colours emitted by atoms. Could an electric field do the same? In 1913, Johannes Stark reported that a strong electric field separated hydrogen lines into several components. Tiny changes inside the atom became neighbouring bright lines in a spectrum.

Stark also observed their polarization, the direction in which the light vibrates. Looking across the electric field, he found components with definite polarizations relative to it. The spectrum offered several things to compare: the positions of the lines and the vibration direction of each component.

Read the evidence: J. Stark (1913), Observation of the Separation of Spectral Lines by an Electric Field, Nature 92, 401 Nobel Prize in Physics 1919 — official award record

A colour compares two atomic energies

Electrons in atoms can occupy certain energy states. An electron dropping from a higher state to a lower one gives the difference to a photon. A larger difference means a higher light frequency and a shorter wavelength.

An electric field changes the energies of those states. What happens to a line depends on both ends of its transition. If both energies rise by the same amount, the colour hardly changes. If states that once shared an energy separate, several colours may become possible. Which transitions emit light, and with which polarization, also depends on how the atomic states interact with the light.

Read the evidence: J. Stark (1913), Observation of the Separation of Spectral Lines by an Electric Field, Nature 92, 401 J. A. Sherman et al. (2012), High accuracy measure of atomic polarizability in an optical lattice clock

A shift can follow the field or its square

Some excited states of ideal hydrogen share the same energy. An electric field mixes and separates them. Within the appropriate approximation, the separation can grow in proportion to field strength. This linear effect is an important starting point for the early hydrogen spectra.

An isolated state without such an equal-energy partner often behaves differently in a weak field. Its leading energy change grows with the square of field strength, so reversing the field leaves that change unchanged. The equation describes this simpler quadratic case. F is field strength, and the polarizability describes how readily the electron distribution responds. Here the state is isolated from equal-energy partners and has no permanent electric dipole, or a permanent separation of positive and negative charge. The expression keeps the direction-independent response; the detailed conditions appear in the reading note.

\Delta E=-\frac{1}{2}\alpha F^2

Read the evidence: J. A. Sherman et al. (2012), High accuracy measure of atomic polarizability in an optical lattice clock NIST TN 1524, Trapped ions and laser cooling V — quadratic Stark shifts and polarizability

Use the field as a measuring tool

Modern optical clocks must also account for this shift. Sherman and colleagues measured the static electric response of a clock transition: the difference between the responses of its two levels. Electrode spacing and voltage needed calibration. Stray fields could move the centre of a voltage scan away from zero, and an uneven field could make atoms at different positions emit slightly different frequencies.

An electric field can also mix a long-lived atomic state with a short-lived one and change how long the atom survives. That interaction needs control in a Lamb-shift experiment and can become a deliberate probe in spectroscopy. Stark received the 1919 prize; its citation also recognized his canal-ray Doppler work, which used spectral shifts to study the motion of the emitters.

Read the evidence: J. A. Sherman et al. (2012), High accuracy measure of atomic polarizability in an optical lattice clock Lamb and Retherford (1947), original paper scan hosted by the University of Maryland, pp. 241–243 Nobel Prize in Physics 1919 — official award record

Sources and reading notes

Stark’s short 1913 announcement is available as an indexed publisher abstract; direct links redirected while this article was prepared. We keep his observations of line components and polarization separate from later perturbation theory. Sherman and collaborators supply a modern, independent measurement of a quadratic Stark shift. No early plate or field map is reconstructed. The quadratic expression assumes an isolated, nondegenerate state of definite parity with no permanent electric dipole, retains scalar polarizability and omits tensor and hyperfine contributions; the hydrogen linear splitting uses different assumptions.