Periodic table ordering principle:\nIn the modern periodic table, elements are arranged in increasing order of their __________.

Introduction / Context:
The modern periodic table is organized to reflect recurring chemical properties (periodicity). The key variable that correctly orders the elements and explains periodic trends in valence, electronegativity, and atomic size is not mass but a more fundamental property related to nuclear charge.

Given Data / Assumptions:

• “Modern” implies the post-Moseley arrangement that resolved anomalies in Mendeleev’s atomic-weight ordering.
• Chemical periodicity correlates with electron configurations, which follow the order imposed by nuclear charge.

Concept / Approach:
Moseley’s X-ray spectroscopy showed that the square root of the characteristic X-ray frequency varies linearly with the atomic number Z, revealing that Z (the number of protons in the nucleus) determines an element’s identity. Electron configurations, and hence chemical properties, are governed by Z, making “atomic number” the correct ordering parameter. This explains earlier anomalies (e.g., tellurium and iodine) that could not be reconciled by atomic weight alone.

Step-by-Step Solution:
Identify the property that uniquely specifies elements and controls electron configuration → atomic number Z.Recognize that the table’s rows and columns group elements by valence shell filling and periodic trends set by Z.Therefore, the correct completion is “atomic number.”

Verification / Alternative check:
Compare tellurium (Z = 52) and iodine (Z = 53): ordering by Z matches chemical properties; ordering by atomic weight would misplace them, illustrating why Z is fundamental.

Why Other Options Are Wrong:
Mass number varies among isotopes and is not unique to the element’s chemical behavior.Atomic weight is an average over isotopes and historically led to anomalies.Metallic characteristics are emergent trends, not a primary ordering index.

Common Pitfalls:
Confusing atomic weight with atomic number; overlooking isotopic variation; assuming chemical similarity derives from mass rather than electron configuration.

Final Answer:
atomic number