Counting atoms: how many atoms are present in one gram-atom (i.e., one mole) of an element?

Introduction / Context:
The concept of the mole (historically “gram-atom” for elemental substances) is central to stoichiometry, nuclear accounting, and materials balances. It provides a bridge between microscopic particle counts and macroscopic masses measured in the laboratory.

Given Data / Assumptions:

• One mole corresponds to Avogadro’s number of entities.
• Entities can be atoms, molecules, ions, or other specified particles.

Concept / Approach:
Avogadro’s number, approximately 6.022 × 10^23 per mole, defines how many atoms are in one gram-atom of an element. In educational MCQs, it is often rounded to 6 × 10^23 for simplicity. This universal constant allows direct conversion between mass (using atomic or molar mass) and count of particles, which is essential in reaction stoichiometry and nuclear fuel calculations where atom counts determine reaction rates and activities.

Step-by-Step Solution:

Verification / Alternative check:
By definition in the SI system, one mole is the amount of substance containing exactly 6.02214076 × 10^23 specified entities. Rounding to 6 × 10^23 is acceptable for MCQ contexts.

Why Other Options Are Wrong:

• 2 × 10^23 and 3 × 10^21: incorrect magnitudes.
• 6 × 10^32 and 5 × 10^5: wildly off by many orders of magnitude.

Common Pitfalls:
Misreading exponents; confusing gram-atom with gram-mole of compounds (the concept extends but the count per mole remains the same).

Final Answer:
6 × 10^23