The Elements on the periodic table cannot be arranged in Alphabetical order because doing that will not order the elements based on their chemical properties.
Recall that, the modern periodic law states that, the Chemical properties of elements are a periodic function of their atomic numbers.
Elements must be arranged based on the trends of their chemical properties and arranging alphabetically will not follow this trend.
Also, the major difference between the modern perodic table and an Alphabetical periodic table is that the modern periodic table contains elements arranged according to their atomic numbers which determine the Chemical properties (modern periodic law) while an Alphabetical periodic table contains elements arranged based on their initial letters in an Alphabetical order (from A to Z). This is inappropriate because it doesn't obey the modern perodic law.
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