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Dalton's atomic theory was based on the idea that all atoms of the same element are identical in all their properties. This means that he believed elements were comprised of uniform particles with the same size, mass, and chemical behavior.

The discovery of isotopes invalidated Dalton's assumption about atoms of the same element being identical. Isotopes are atoms of the same element that have varying numbers of neutrons in their nuclei, creating differences in their atomic mass while still possessing the same atomic number (number of protons). This gives isotopes different physical properties while largely maintaining similar chemical properties.

A classic example of isotopes is hydrogen, which has three main isotopes named protium, deuterium, and tritium. All three isotopes have one proton, but they have different numbers of neutrons: protium has 0 neutrons, deuterium has 1 neutron, and tritium has 2 neutrons. This difference in the number of neutrons leads to different atomic masses for each isotope. Consequently, their physical properties, such as boiling and melting points, differ.

Nowadays, it is widely accepted that atoms of the same element are not identical in every aspect, as isotopes demonstrate the variance in neutron count and atomic mass. Despite this, isotopes still possess the same chemical properties, validating Dalton's theory that atoms of the same element behave similarly during chemical reactions. However, his assumption about identical properties does not hold true due to these observable differences among isotopes. In conclusion, Dalton's assumption about all atoms of the same element being identical is not valid because isotopes exist and demonstrate that atoms of the same element can have different properties due to the variation in their neutron count and atomic mass.