In the 5th cent. B.C. the Greek philosophers Democritus and Leucippus proposed that matter was made up of tiny, indivisible particles they called atom, or in Greek "a-tomos". The reason why they assumed this is because nothing can come from nothing.
Around 1803, John Dalton (1766-1844) developed the first useful atomic theory of matter. He imagined the atom as a sphere full of an electrically positive substance mixed with negative electron.
Then in 1897, Thompson discovered the first component part of the atom: the electron, a particle with a negative electric charge.
Discovery of the Atom
By the 19th century, technology had advanced greatly and many elements had been discovered to work with.
Using the available elements scientist such as John Dalton and Amedeo Avogadro forced them to interact with one another. From these interactions they were able to prove the existence of the atom.
That depends on exactly what you mean by "discovered."
Jainism had a concept of small particles similar to atoms in the 6th millennium BC, and either Democritus or his mentor Leucippus (or possibly both together) independently came up with the idea (and the word "atomos", which is Greek for "uncuttable") in the 5th century BC.
However, these were essentially lucky guesses; there was no real scientific basis behind them, so saying these people "discovered" atoms is a pretty big stretch.
The best candidate is probably John Dalton, who in the early 19th century proposed (based this time on experiments) that substances were composed of atoms, and even assigned relative weight values to several types of atom.
John Dalton was the first who introduced the idea of atom. Atom, the very word, means inseparable or indivisible.
Based on that idea in chemistry many laws have been stated such as, law of conservation of mass, law of multiple proportions etc etc.
Who discovered Neutron, Proton, and Electron?
Electron: J. J. Thomson
Neutron: James Chadwick
Proton: Ernest Rutherford
Rutherford model
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A stylised representation of the Rutherford model of a lithium atom (nuclear structure anachronistic)
The Rutherford model or planetary model is a model of the atom devised by Ernest Rutherford. Rutherford directed the famous Geiger-Marsden experiment in 1909, which suggested on Rutherford's 1911 analysis that the so-called "plum pudding model" of J. J. Thomson of the atom was incorrect. Rutherford's new model for the atom, based on the experimental results, had the new features of a relatively high central charge concentrated into a very small volume in comparison to the rest of the atom and containing the bulk of the atomic mass (the nucleus of the atom).
Rutherford's model did not make any new headway in explaining the electron-structure of the atom; in this regard Rutherford merely mentioned earlier atomic models in which a number of tiny electrons circled the nucleus like planets around the sun, or a ring around a planet (such as Saturn). However, by implication, Rutherford's concentration of most of the atom's mass into a very small core made a planetary model an even more likely metaphor than before, as such a core would contain most of the atom's mass, in an analogous way to the Sun containing most of the solar system's mass.