Who established atomic numbers as the basis for organizing the periodic table?

Henry Moseley.

Explanation:

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Henry Moseley's work stated that it is better to organize the periodic table in the light of the atomic number (which accounts for the amount of protons and electrons) instead of the atomic mass, because atomic numbers are not arbitrarily assigned as long as they have the aforesaid physical basis.

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particle   p is an electron and particle q is a neutron

b. accuracy of the data matters alot more than its number of digits, organization or amount of detail. quantitative observation is more accepted than the qualitative observation.