Question

Choose the incorrect trend in the atomic radii (r) of the elements :

• A. \( r_{Br}<r_K \)
• B. \( r_{Mg}<r_{Al} \)
• C. \( r_{Rb}<r_{Cs} \)
• D. \( r_{At}<r_{Cs} \)

Hint:

To determine the relative atomic radii of elements, locate their positions in the periodic table and apply the general trends: atomic radius decreases across a period and increases down a group. Be mindful of any exceptions to these general trends, although they are not relevant in this specific question.

Answer 1

The Correct Option is B

To identify the incorrect atomic radius trend among the provided options, let's first review the fundamental principles governing atomic radii in the periodic table:

• Across a period from left to right, atomic radius generally diminishes. This is attributed to an increasing nuclear charge that exerts a stronger pull on electrons, drawing them closer to the nucleus.
• Down a group, atomic radius generally increases. The addition of electron shells results in a larger atomic size, outweighing the effect of increased nuclear charge.

Now, let's examine each given option:

1. \( r_{\rm Br} < r_{\rm K} \): 
   Bromine (\( \text{Br} \)) and Potassium (\( \text{K} \)) are in the same period, with \( \text{Br} \) situated to the right of \( \text{K} \). Consequently, \( \text{Br} \) exhibits a smaller atomic radius than \( \text{K} \). This trend is accurate.
2. \( r_{\rm Mg} < r_{\rm Al} \): 
   Magnesium (\( \text{Mg} \)) and Aluminum (\( \text{Al} \)) belong to the same period, with \( \text{Mg} \) positioned to the left of \( \text{Al} \). Due to the enhanced nuclear charge, \( \text{Al} \) is expected to have a smaller atomic radius than \( \text{Mg} \). Therefore, the stated trend is inaccurate.
3. \( r_{\rm Rb} < r_{\rm Cs} \): 
   Rubidium (\( \text{Rb} \)) and Cesium (\( \text{Cs} \)) are in the same group, with \( \text{Cs} \) located below \( \text{Rb} \). The presence of an additional electron shell in \( \text{Cs} \) leads to a larger atomic radius compared to \( \text{Rb} \). This trend is accurate.
4. \( r_{\rm At} < r_{\rm Cs} \): 
   Astatine (\( \text{At} \)) is positioned below Bromine and is classified as a halogen, whereas Cesium (\( \text{Cs} \)) is an alkali metal. Notwithstanding their differing group classifications, Cesium possesses one of the largest atomic radii within its period and generally exceeds that of Astatine. This trend is accurate.

The correct response corresponds to the option presenting an erroneous trend: \( r_{\rm Mg} < r_{\rm Al} \) .