Short description: Change of an electron between energy levels in an atom

A transition is a change of an electron between different energy levels in an atom. Such transitions occur when energy is absorbed or emitted, typically in the form of a photon.

Description

In quantum mechanics, electrons in atoms occupy discrete quantized energy levels. An atomic electron transition (also called a quantum jump or quantum leap) occurs when an electron changes from one energy level to another within an atom or artificial atom.^[6]^[7]

These energy levels are unique to each atom and produce characteristic spectral fingerprints. Techniques such as energy-dispersive X-ray spectroscopy and X-ray photoelectron spectroscopy rely on these characteristic transitions to identify atomic composition.^[8]

When an electron moves to a higher energy level, it absorbs energy. When it falls to a lower level, it emits energy. These processes are governed by quantum-mechanical selection rules and conservation of energy.

Transitions between energy levels produce discrete spectral features and are fundamental to atomic spectroscopy.

Photon absorption and emission

An electron transition from ${{{1}}}$ to ${{{1}}}$ accompanied by photon emission.

Electrons can relax into lower-energy states by emitting electromagnetic radiation in the form of photons. Conversely, they can absorb photons and become excited into higher-energy states.

The energy of the photon must exactly match the energy difference between the two states. Larger energy gaps correspond to shorter photon wavelengths.^[9]

The relation between photon energy and frequency is:

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where $h$ is the Planck constant, $ν$ is frequency, $c$ is the speed of light, and $λ$ is wavelength.

Quantum theory

An atom interacting with electromagnetic radiation experiences an oscillating electric field:

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where $ω$ is the angular frequency and $ĕ rad$ is the polarization vector.^[10]

The interaction Hamiltonian for an atomic dipole in an electric field is:

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Using time-dependent perturbation theory and Fermi’s golden rule, the stimulated transition probability depends on the dipole matrix element:

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The angular part of this expression leads directly to the quantum-mechanical selection rules for atomic transitions.

Electromagnetic radiation interactions

To excite an electron into a higher energy level, incident radiation must have energy equal to the energy gap between the levels. Because atomic energy differences are often on the scale of ultraviolet and X-ray photons, these wavelengths are widely used in spectroscopy.^[8]

The Franck–Condon principle states that electronic transitions occur much faster than nuclear motion. As a result, transitions occur essentially instantaneously compared to atomic vibrations and are only likely if the initial and final wavefunctions overlap significantly.^[11]

Radiative relaxation produces photons with wavelengths characteristic of the atom and transition involved.

Spectroscopy techniques

Several experimental methods use electron transitions:

Ultraviolet–visible spectroscopy uses visible or ultraviolet light to probe absorption and transmission spectra.^[12]

Energy-dispersive X-ray spectroscopy excites inner-shell electrons using high-energy electrons and measures emitted X-rays characteristic of the atom.^[13]

X-ray photoelectron spectroscopy uses incident X-rays to eject electrons from surfaces and determine elemental composition from their binding energies.^[14]

History

Danish physicist Niels Bohr first proposed quantum jumps in 1913.^[15] Shortly afterward, the Franck–Hertz experiment by James Franck and Gustav Hertz experimentally confirmed that atoms possess quantized energy states.^[16]

In 1975, Hans Dehmelt predicted that individual quantum jumps could be observed directly. In 1986, quantum jumps were experimentally observed using trapped ions of barium and mercury.^[9]

Recent discoveries

In 2019, experiments with superconducting artificial atoms demonstrated that some quantum jumps evolve continuously and can even be reversed during the transition.^[17]

Other quantum jumps remain fundamentally unpredictable due to the probabilistic nature of quantum measurement.^[18]