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The scientific method involves developing a hypothesis and then carrying out experiments to gather evidence to support it, however, that hasn't always been the case. The ancient Greeks, for example, did not carry out anything other than thought experiments, in other words, they imagined what would happen if they had been able to do an experiment. One of these was the beginning of the theory of atomic structure.
A philosopher (thinker) called Democritus did a thought experiment about what would happen if you hit a piece of rock with a hammer and broke it again and again. He reasoned that eventually you would end up with a piece that was so small that you could not break it into anything smaller. The Greek word for 'indivisible' is 'atomos' and that is how we get our modern word - atom. Similar ideas were developed in other civilisations, completely independently of the Greeks.
With the fall of the Greek civilization, many scientific ideas were lost, at least to the western European countries. This started to change in the seventeenth century and some very clever and well-educated people had the time and money to think about science. One of these, a man called John Dalton, revived the idea of atoms. He came up with a model that suggested that atoms were the building blocks of all chemicals and were small, hard spheres that joined together in specific proportions. As with the Greeks, there was no way of testing this or proving this at the time. But this model of atoms seemed to work quite well, especially when Italian scientist, Amedeo Avogadro, modified it slightly to apply to gasses, which was the main flaw.
During most of the 19th century, scientists believed that atoms of different elements were made up from different numbers of hydrogen atoms. We now know that it wasn't far off being the truth as a hydrogen atom is one proton with one electron. Then, at the end of the nineteenth century, a scientist called J. J. Thompson discovered the electron which was clearly a lot smaller than an atom. This showed that atoms were not the smallest particles of matter. He suggested that rather than being solid spheres, atoms were spheres of positive charge with the negatively-charged electrons spread through it. This model was replaced about a decade later when Ernest Rutherford discovered that most of the mass of an atom is contained in a small nucleus at the very center. It is still a bit strange to think of atoms being mainly empty space. Eight years later, Rutherford carried out experiments with radioactive materials that proved that the hydrogen atom was indeed present in other elements and this is regarded as being the discovery of the proton. Rutherford also suggested the idea of neutrons but it wasn't until 1932 that the neutron was finally discovered.