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The discovery of \[\_\_\_\_\_\_\] showed that an atom is divisible?

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Hint: Dalton studied the atom very keenly and after a series of experiments and researches, he discovered the facts about the atom and declared that the matter are composed of several similar atoms of the elements and the smallest particle of element is atom.

Complete answer:
Dalton gave Dalton's atomic theory, in which he stated that all matter is made up of atoms and the atoms are the smallest indivisible particle.
Dalton’s theory was believed for a long time that an atom is indivisible. But later in \[1897\] when J.J Thomson discovered cathode rays, Dalton’s theory was disapproved.
In \[1897\] J.J Thomson discovered electrons while working on the gas discharge tube. And this discovery led to the fact that atoms are further divisible.
He stated that may be atoms are divisible as he claimed that cathode rays are made up of negatively charged atoms that move towards the positively charged anodes. And these negatively charged electrons may be the part of the atom.
Later on it is found that electrons revolve around the nucleus of the atom in the separate energy level shells.
So, the answer to the question is: The discovery of J.J Thomson showed that an atom is divisible.

Note:
Later on , the divisibility of an atom is also proved by the discovery of the proton by Ernest Rutherford. He is also known as the father of the proton. Unlike electrons, protons bear a positive charge. The discovery of neutrons as a subatomic particle also suggested the divisibility of the atom. So, we can say the discovery of the subatomic particles with time like electron, proton, and neutron strengthened the fact that an atom is not indivisible as suggested by Dalton’s atomic theory. But the important point to keep in mind is that it was J.J. Thomson’s discovery of electrons that first challenged Dalton's atomic theory.