How do we know that atoms are divisible?

What experiments were conducted or what was observed or discovered to prove this?

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Atoms are divisible contrary to the early beliefs that the smallest "indivisible" matter is an atom. When an atom loses its identity it means that they are divisible. Atoms chemically react with other kinds of atoms thus changing their activity. During a chemical reaction, there is an exchange of electrons. When electrons are transferred, that is the very first evidence that an atom is divided: electron is detached to the entire atom. Secondly, nuclear reaction is another proof that atoms are divisible. During nuclear reactions, atoms are either combined (fusion) or separated (fission) to form another kind of element. 

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