The Zeeman effect — spectral lines in a magnetic field

What is the Zeeman effect?

You switched on field B, and one sharp spectral line broke into three closely spaced components. That is the Zeeman effect: the magnetic field splits the atom's energy levels, so instead of one transition the electron can make several transitions of slightly different energy — and you see several very closely spaced lines instead of one.

Energy splitting:

— μ_B is the Bohr magneton (a constant tied to the electron's magnetic moment), g_L is the Landé factor (≈1 for the normal Zeeman effect), and m_l numbers the allowed levels. The stronger the field B, the larger the energy difference ΔE between the components.

Why study atomic spectra in a magnetic field?

The line spacing translates into a wavelength spacing: $\Delta\lambda \approx \dfrac{\mu_B \lambda^2}{h c}\, B$. For the yellow sodium line (λ ≈ 589 nm) this is only about 16 pm per 1 T — which is why the splitting is so hard to observe and requires very sensitive instruments (an interferometer) rather than an ordinary prism. By measuring this tiny spacing precisely, physicists read off the strength of the magnetic field in which the emitting atom was located.

How was it discovered?

In 1896 Pieter Zeeman observed that the spectral lines of sodium in a flame split into several components under a strong magnetic field. Hendrik Lorentz — based on his newly developed theory of the electron — gave the phenomenon a detailed theoretical interpretation. For their joint research on the influence of magnetism on radiation, both received the Nobel Prize in Physics in 1902.

What are its applications today?

The Zeeman effect was one of the first experimental proofs that an atom's energy levels are tied to the magnetic moment of the electrons orbiting the nucleus — that is, to the structure of the atom, later described by quantum mechanics. Today astronomers use it to measure the magnetic fields of stars and sunspots: by analysing the spacing of the split lines in the spectrum of light from a given region, one can calculate how strong the magnetic field is there.

Why you need this for the exam:

Remember the direction of the dependence: no field — one line; with a field — several lines, and their spacing grows with B. This is a classic proof of the quantisation (splitting) of an atom's energy levels under an external factor.

Remember: a magnetic field splits a spectral line into several closely spaced components, and their spacing grows linearly with the field strength B — that is the Zeeman effect.