Explain how chemists can state with
certainty that no one will discover an element
that would appear on the periodic table
between sulfur (S) and chlorine (Cl)

The nucleus of a sulfur atom contains 16 protons.

The nucleus of a chlorine atom contains 17 protons.

Explanation:

Atoms are arranged in the Periodic Table according to the number of protons in their nuclei — their atomic numbers.

A proton is an integral particle —  you can't have half a proton.

S and Cl are adjacent in the Periodic Table, so it is impossible to find an element that will fit between them.

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