The modern periodic table is based on:
A. Atomic weight
B. Atomic size
C. Atomic number
D. Recurrence of chemical properties

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Hint: Think about the various ways in which people have tried to arrange the periodic table and classify the elements. Consider all the fallacies they came across due to their chosen method of classification.

Complete step by step answer:
We know that almost all the people that tried to classify the elements so that some trend could be seen in their properties arranged the elements according to their atomic weight. Doberiener, Newlands, Mendeleev, all of them arranged the elements according to their atomic weights. Mendeleev could not explain the presence of isotopes and thus his periodic table was later discarded when Mosely found a better way to classify the elements, which was the atomic size.
Mosely arranged the elements in such a way that took care of all the problems that people were facing up until then. He classified the elements based on their atomic numbers. This took care of the isotopes as they have the same atomic number but different atomic mass.
The size of the atom is not taken into consideration since it changes at the slightest disturbance like the shielding effect, the effective nuclear charge, and even ionization. Thus, this is not considered a reliable way for classification. Although recurrence of chemical properties is seen, they are not what the modern periodic table is based on

Hence, the answer is ‘C. Atomic number’.

Note: Remember that the recurrence of chemical properties is a consequence of arranging the elements in the order of their atomic number. Please do not get confused due to the fact that similarities in chemical properties is also seen in the modern periodic table.