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Quantum mechanics provided justification for a number of practical observations that could not be explained by classical mechanics.
A number of brilliant scientists of the twentieth century, including Rutherford, Planck, Einstein, Bohr, de Broglie, Thomson, Schrodinger and Heisenberg (among others) contributed to the development of quantum mechanics.
The basic idea of quantum mechanics is that certain physical quantities can only change in discrete amounts (so called quanta) and not in a continuous fashion; hence the name quantum. Operating on a nanoscale, on the order of atoms and subatomic particles, this fundamental branch of physics provides an explanation for the particle-wave duality of matter and atomic behavior during chemical bonding. It also presents a unified view of photons, electrons, and other subatomic particles.
Among the fundamental issues with the atomic model (which provided earliest explanation for atoms), the most important was the rotating electrons that release energy as they accelerate around the nucleus, yet do not fall into it, thereby neutralizing the protons. This was explained by the wave-like behavior of electrons, rather than particle behavior as per classical mechanics. This also explained the diffraction patterns observed when an incident beam of electrons passed through a crystal.
Another achievement in the understanding of atoms and subatomic particles is the Heisenberg uncertainty principle, which states that the precise location and momentum of an electron cannot be simultaneously known; thus the term "uncertainty."
The quantum theory describes atoms as having complex orbitals (regions with a certain probability of electron presence, rather than a certainty as per classical mechanics). The electrons and orbitals are explained by a set of 4 quantum numbers: principle, angular momentum, magnetic, and spin. These numbers determine the average distance of the orbital from the nucleus, the shape of the orbital, the orientation of the orbital, and electron spin (clockwise or counterclockwise). No two electrons can have the same set of these quantum numbers, i.e. the same energy levels, leading to the famous Exclusion Principle.
There are a number of other achievements of quantum mechanics or quantum theory or quantum physics. It suffices to say that it provided a better description of atoms and subatomic particles and has been able to provide logical explanations for practical observations.
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