atomic orbital

Where exactly is the electron in an atom? The honest answer is that you cannot pin it down to a point and a speed at the same time — that is a rule of quantum mechanics. Instead we describe where it is likely to be found, as a sort of fuzzy cloud of probability around the nucleus. An atomic orbital is the name for one of these clouds: a region of space, with a particular shape and energy, that can hold up to two electrons.

Orbitals come in families with characteristic shapes. An s orbital is a sphere centred on the nucleus. The three p orbitals look like dumbbells pointing along the x, y, and z axes. The five d orbitals have more elaborate four-lobed (and one doughnut-shaped) forms — these are the workhorses of transition-metal chemistry. The seven f orbitals are more intricate still and matter for the lanthanides and actinides. Each orbital is labelled by quantum numbers that fix its size (which shell, like 1s, 2s, 3d), its shape (s, p, d, f), and its orientation in space. The squared height of the orbital's wavefunction at any point tells you the probability of finding the electron there.

Orbitals are the alphabet of inorganic chemistry. Their shapes explain why molecules adopt the geometries they do, why transition-metal complexes are coloured, and why magnetism appears. A crucial caveat: an orbital is a mathematical solution for a single electron around one nucleus; in a real many-electron atom or a bonded molecule the picture is an approximation, useful and accurate but not literally a tiny tunnel the electron travels through. The electron is not orbiting like a planet — it is delocalised across the whole cloud at once.