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Democritus was the first person to come up with the concept of "the atom". Democritus believed that everything in the universe is made up of atoms and that they were both microscopic and indestructible.
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In 1803, John Dalton develops a theory which states that elements consist of indivisible particles (atoms), all atoms of the same element are identical, and most importantly, that atoms cannot be created or destroyed. This theory of his would lay the bases for future discoveries and studies of atoms.
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In 1866, Goldstein discovered the "canal rays" also known as positive rays. These rays are positively charged ions which we know know to be protons. He discovered them through an experiment using a cathode and a tube.
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In 1897, Thomson announced his discovery of smaller components within atoms. These components being electrons. Not long after he announced his discovery, he came up with a visual representation to match titled "The Plum Pudding Model" which displayed electrons (negatively charged" floating around within a positively charged atom (this would be the actual "pudding" of the model).
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In 1910, Millikan was able to accurately determine the magnitude of an electrons charge. He discovered this by using charges oil drops which he used to determine the mass of an electron.
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During an experiment, Rutherford noticed that alpha particles were seemingly repelled by gold foil. Rutherford eventually concluded that this repulsion of particles was due to a dense and powerful core at the center of the atom which we now know to be the nucleus.
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In 1913 Niels Bohr proposed a theory for the hydrogen atom stating that electrons orbit the nucleus in specific orbitals that have a specific size and energy level. To support this theory, Niels Bohr came up with the "Bohr Model" which visualizes how the electrons were only able to occupy certain orbits around the nucleus.
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Using Niels Bohr's atomic theory, Schrodinger concluded that matter (specifically electrons) could be in the form of both particles and waves. This conclusion allowed Schrodinger to procure a mathematic formula rooted in Bohr's theory which could calculate the different energy levels of electrons within an atom. With his equation, Schrodinger created a visual to go with it known as the "Quantum Mechanical Model" which shows the probability of finding an electron in any region of an atom.