Atomic number vs. other atomic properties:\nWhich property of an element is always a whole number by definition?

Introduction / Context:
Atomic properties appear frequently in chemistry and materials calculations. While many tabulated values are real numbers with decimals due to averaging or measurement, some are inherently integral by definition. Recognizing which is integral helps avoid conceptual mistakes when interpreting periodic trends and performing stoichiometric calculations.

Given Data / Assumptions:

• Atomic number (Z) counts protons in the nucleus.
• Atomic weight (relative atomic mass) is a weighted average of isotopes.
• Atomic radius and volume are experimentally derived and model-dependent.

Concept / Approach:
The atomic number is defined as the number of protons in an atom’s nucleus and therefore must be a whole number. Other quantities such as atomic weight are not whole numbers because natural elements exist as mixtures of isotopes, and the tabulated “atomic weights” are weighted averages reflecting isotopic abundance, leading to fractional values. Radii and volumes depend on bonding context and measurement methods, producing non-integer, approximate values.

Step-by-Step Solution:

Verification / Alternative check:
Any nuclide is denoted as A_ZX; Z is always an integer labeling the element identity, whereas A (mass number) is an integer for a given isotope but the periodic-table value is an average and not integral.

Why Other Options Are Wrong:

• Atomic weight/average atomic mass: fractional due to isotopic mixture.
• Atomic radius/volume: model-based and continuous values.

Common Pitfalls:
Confusing mass number (A, an integer for a specific isotope) with average atomic weight (fractional).

Final Answer:
Atomic number.