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Democritus, a Greek philosopher, co-originated the thought (with his teacher, Leucippus) that all matter is composed of indivisible elements.
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John Dalton, a British chemist and physicist, developed a theory that matter is simply composed of atoms of different weights and is combined in ratios by weight. Also proposed that these atoms are spherical, and are in motion.
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JJ Thomson discovers the electron, using properties of cathode rays.
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Albert Einstein, creates special and general theories of relativity, and hypothesizes about the particle nature of light. This was the basis of nuclear energy.
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Ernest Rutherford known as the father of nuclear physics, developed the theory for the structure of the atom. He used a gold foil experiment, observing the scattering of alpha particles, and demonstrated for the first time the existence of the atomic nucleus.
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Neils Bohr developed the Bohr atomic model, with electrons travelling in orbits around the nucleus, and chemical properties being determined by how many electrons are in the outer orbits. He also integrated the Planck quantum theory, stating that when electrons change orbits they emit a quantum of discrete energy.
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James Chadwick discovers the neutron component of the atomic nucleus, explaining the nuclear fission of uranium 235. This also made it possible to produce elements heavier than uranium in the lab.
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Mann proposes the quark model (independently George Zweig does as well), which describes elementary particles that have no substructure (and therefore can't be split).