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This article is about the structure of an atom. For the particle accelerator phenomenon, see Electron Cloud (Particle Accelerator).

Electron cloud is a confusing word, if not originally coined, by the Nobel Prize laurate and acclaimed educator Richard Feynman in The Feynman Lectures on Physics for discussing "exactly what is an electron?". This intuitive model provides a simplified way of visualizing an electron as a solution of the Schrödinger equation. In the electron cloud analogy, the probability density of an electron, or wavefunction, is described as a small cloud moving around the atomic or molecular nucleus, with the thickness of the cloud proportional to the probability density.

The model evolved from the earlier Bohr model, which likened an electron orbiting an atomic nucleus to a planet orbiting the sun. The electron cloud formulation better explains many observed phenomena, including the double slit experiment, the periodic table and molecular bonding, and atomic interactions with light. Although lacking in certain details, the intuitive model roughly allows for wave-particle duality, for electron behaviour that is both "wavy" as per the left side of E=mc² and "lumpy" as per the right side.

Experimental evidence suggests that the probability density is not just a theoretical model for the uncertainty in the location of the electron, but rather that it reflects the actual state of the electron. This carries an enormous philosophical implication, that the universe's evolution is fundamentally uncertain. What drives this randomness in the motion of an electron is a question that has seen little advancement since its discovery in the early 20th century, although the answer, written in the fine print of the universe, has the prospect of being among the greatest breakthroughs of all time. Certainly the physicists of the time appreciated its significance, readily seen in the Copenhagen Interpretation.

In the electron cloud model, rather than following fixed orbits, electrons bound to an atom are observed more frequently in certain areas around the nucleus called orbitals. The electron cloud can transition between electron orbital states, and each state has a characteristic shape and energy, all predicted as the Schrödinger equation has infinitely many solutions. Experimental results motivated this conceptual refinement of the Bohr model. The famous double slit experiment demonstrates the random behaviour of electrons, as free electrons shot through a double slit are seen to materialize at random locations with wavelike interference. Heisenberg's uncertainty principle accounts for this and, taken together with the double slit experiment, implies that an electron behaves more like a smear of infinitesimal pieces, or "cloud", each piece moving somewhat independently as in a churning cloud. These pieces can be forced to coincide at an isolated point in time, but then they all must move relative to each other at an increased spread of rates to conserve the "uncertainty". Certain physical interactions of this wave-like electron, such as observing which slit an electron passes through in the double-slit experiment, require this coincidence of pieces into a lump-like particle. In such an interaction the electron "materializes", "lumps", or "is observed" at the location of one of the infinitesimal pieces, apparently randomly chosen. Although the cloud shrinks to the accuracy of the observation (if observed by light for example the wavelength of the light limits the accuracy), its momentum spread increases so that Heisenberg's uncertainty principle is still valid.

Unlike the fixed orbit conceptualization, the electron cloud is not predicted to collapse into a proton while emitting a photon to minimize the sum of electric potential and kinetic energies, since the "cloud" would gain too much kinetic energy, as required to conserve uncertainty. The smear obeys Schrödinger's equation (see also Erwin Schrödinger), which has discrete solutions at differing energy levels. Each of these solutions can be depicted in gray scale, loosely resembling a cloud. This predicts light interactions with an atom, as electrons transition between these cloud states by absorbing or emitting photons equivalent to the difference, or quantum, in their energy. Also, the periodic table is predicted as an electron is added to the lowest unoccupied energy orbital in progressing from hydrogen to helium, and to subsequent elements, with properties that match those predicted by the orbital solutions to Schrödinger's equation.

The term "electron cloud" carries a connotation that simple language facilitates progress especially in areas such as small scale physics where everyday experience does not extrapolate well. Additional experiments, such as the behaviour of electrons in high speed accelerators, have resulted in more sophisticated models including quantum electrodynamics and superstring theories, although the most exciting discoveries are certainly ahead of us in, as Feynman put it, "the greatest adventure that the human mind has ever begun".

• Atomic orbital
• Chemical bond
• Computational chemistry
• Density functional theory
• Electron configuration
• Electron density
• Molecular orbital
• Probability amplitude
• Quantum chemistry
• Slater determinant