**Quantum mechanics** is a set of principles underlying the most fundamental known description of all physical systems at the submicroscopic scale (at the atomic level). Notable among these principles are simultaneous wave-like and particle-like behavior of matter and radiation ("Wave–particle duality"), and the prediction of probabilities in situations where classical physics predicts certainties. Classical physics can be derived as a good *approximation* to quantum physics, typically in circumstances with large numbers of particles. Thus quantum phenomena are particularly relevant in systems whose dimensions are close to the atomic scale, such as molecules, atoms, electrons, protons and other subatomic particles. Exceptions exist for certain systems which exhibit quantum mechanical effects on macroscopic scale; superfluidity is one well-known example. Quantum theory provides accurate descriptions for many previously unexplained phenomena such as black body radiation and stable electron orbits. It has also given insight into the workings of many different biological systems, including smell receptors and protein structures.