When comparing the atomic sizes of chlorine and argon, it's essential to consider several factors, including their positions on the periodic table and the concept of atomic radius. While your use of the z/e ratio (the effective nuclear charge divided by the number of electrons) is a valid approach, it’s important to clarify how atomic size is generally understood in the context of periodic trends.

Understanding Atomic Size

Atomic size, or atomic radius, typically refers to the distance from the nucleus of an atom to the outermost shell of electrons. This size can vary based on several factors, including the number of electron shells and the effective nuclear charge experienced by the outer electrons.

Periodic Trends

To grasp why argon is larger than chlorine, let’s look at their positions in the periodic table:

• Chlorine (Cl) is located in Group 17 (the halogens) and Period 3.
• Argon (Ar) is in Group 18 (the noble gases) and also in Period 3.

Both elements are in the same period, which means they have the same number of electron shells. However, the key difference lies in their nuclear charge:

• Chlorine has an atomic number of 17, meaning it has 17 protons and 17 electrons.
• Argon has an atomic number of 18, giving it 18 protons and 18 electrons.

Effective Nuclear Charge and Atomic Radius

The effective nuclear charge (Z_eff) increases as you move across a period from left to right. This increase in positive charge pulls the electrons closer to the nucleus, resulting in a smaller atomic radius. Therefore, even though chlorine has a lower nuclear charge than argon, it has a higher effective nuclear charge compared to its electron shielding, which causes its atomic radius to be smaller.

Comparing Atomic Radii

In terms of actual measurements, the atomic radius of chlorine is approximately 99 picometers, while argon has an atomic radius of about 188 picometers. This indicates that argon is indeed larger than chlorine. The discrepancy in your findings may stem from a misunderstanding of how atomic size is defined and measured.

Conclusion

In summary, while your reasoning using the z/e ratio is insightful, the overall atomic size comparison between chlorine and argon shows that argon is larger due to its higher nuclear charge and the resulting electron interactions. It's always beneficial to cross-reference with reliable sources or atomic radius tables to clarify such concepts. If you have any further questions or need more clarification, feel free to ask!