Final answer:
The false statement is that atoms of any one element are identical to those of any other element. Dalton's theory clearly differentiates atoms of different elements by size, mass, and other properties.
Step-by-step explanation:
The component of Dalton's Atomic Theory which was NOT true is 'The atoms of any one element are identical to those of any other element'. This is incorrect because Dalton's theory stated that atoms of a given element are identical in size, mass, and other properties, but they are different from atoms of any other element in size, mass, and other properties. Therefore, atoms of different elements have distinct properties. The other statements provided align with Dalton's theory, which posits that elements consist of indivisible atoms, atoms from different elements can combine in whole number ratios to form compounds, and atoms are not converted into different element atoms during chemical reactions.