Stark Effect: Electric Field Splitting Explained Simply

The Stark effect is the shifting and splitting of an atom's spectral lines in an electric field — the electric cousin of the Zeeman effect. Discovered by Johannes Stark in 1913, it occurs because the electric field pulls the atom's positive nucleus and negative electrons in opposite directions, changing the energies of its quantum states.

It matters because electric fields are everywhere — inside plasmas, near charged surfaces, in semiconductor devices — and the Stark effect turns atoms into tiny electric-field probes. It also revealed deep quantum details, such as the hidden degeneracy of hydrogen's energy levels.

Key Concepts

• Linear Stark effect: Energy shift proportional to the field strength (ΔE ∝ E) — occurs in hydrogen, where states of the same n but different l are degenerate.
• Quadratic Stark effect: Shift proportional to E² — occurs in most other atoms, where the field first induces a dipole moment and then interacts with it.
• Degeneracy: Hydrogen's n = 2 level has four states (2s, 2p) with identical energy; the electric field lifts this degeneracy.
• Polarizability (α): Measures how easily an atom's charge cloud is distorted; sets the size of the quadratic shift.
• Selection rules: As with Zeeman, only certain transitions (Δm = 0, ±1) appear, with characteristic polarisations.

Formulas

Linear (hydrogen, n = 2): ΔE = ±3ea₀E, where a₀ = 5.292 × 10⁻¹¹ m is the Bohr radius and E is the field in V/m — the level splits symmetrically by this amount. Quadratic (general): ΔE = −½αE², with α the polarizability. Valid for fields weak enough that higher-order terms are negligible and no ionisation occurs.

Worked Example

Hydrogen's n = 2 level sits in an electric field of 10⁵ V/m. What is the linear Stark splitting?

1. ΔE = 3ea₀E = 3 × 1.602 × 10⁻¹⁹ × 5.292 × 10⁻¹¹ × 10⁵.
2. ea₀ = 8.478 × 10⁻³⁰; × 3 = 2.543 × 10⁻²⁹; × 10⁵ = 2.543 × 10⁻²⁴ J.
3. In electron-volts: 2.543 × 10⁻²⁴ / 1.602 × 10⁻¹⁹ ≈ 1.59 × 10⁻⁵ eV.
4. As a frequency: ΔE/h = 2.543 × 10⁻²⁴ / 6.626 × 10⁻³⁴ ≈ 3.84 × 10⁹ Hz ≈ 3.8 GHz — a small but measurable split, scaling linearly with the field.

Common Misconceptions

• "The Stark effect is identical to the Zeeman effect." They are analogues, not twins: magnetic fields split via magnetic moments, electric fields via charge separation — and the Stark shift can be linear or quadratic depending on the atom.
• "Every atom shows a linear Stark effect." Only hydrogen (and hydrogen-like ions) do, thanks to their special degeneracy. Multi-electron atoms show the weaker quadratic effect.
• "Strong fields just give bigger shifts." Very strong fields rip the electron off entirely (field ionisation) — the Stark pattern breaks down.

Real-World Applications

• Plasma physicists diagnose electric fields inside fusion experiments and stellar atmospheres from Stark-broadened spectral lines.
• Semiconductor engineers account for the quantum-confined Stark effect when designing lasers and modulators.
• Stark-effect tuning is used to shift molecular energy levels in precision spectroscopy and quantum-computing schemes.

The Stark effect shifts and splits spectral lines in an electric field — linearly (ΔE = ±3ea₀E) for hydrogen's degenerate levels, quadratically (ΔE = −½αE²) for other atoms. A 10⁵ V/m field splits hydrogen's n = 2 level by about 3.8 GHz. From plasma diagnostics to semiconductor lasers, atoms in electric fields remain precise, practical field sensors.