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 determine the incorrect trend among the given atomic radii, let's review the basic concept of atomic radii trends in the periodic table: 

• Atomic radius generally decreases across a period from left to right due to the increase in nuclear charge which pulls the electrons closer to the nucleus, thereby decreasing the size.
• Atomic radius generally increases down a group due to the addition of electron shells, which outweighs the effect of increased nuclear charge, resulting in a larger size.

Now, let's evaluate each option:

1. \( r_{\rm Br} < r_{\rm K} \): 
   Bromine (\( \text{Br} \)) is located to the right of Potassium (\( \text{K} \)) in the periodic table, and both elements are in the same period. Thus, \( \text{Br} \) will have a smaller atomic radius than \( \text{K} \). This trend is correct.
2. \( r_{\rm Mg} < r_{\rm Al} \): 
   Magnesium (\( \text{Mg} \)) and Aluminum (\( \text{Al} \)) are in the same period, with \( \text{Mg} \) located to the left of \( \text{Al} \). Therefore, \( \text{Al} \) should have a smaller atomic radius than \( \text{Mg} \) due to the increased nuclear charge. Thus, the given trend is incorrect.
3. \( r_{\rm Rb} < r_{\rm Cs} \): 
   Rubidium (\( \text{Rb} \)) and Cesium (\( \text{Cs} \)) are in the same group with \( \text{Cs} \) below \( \text{Rb} \). Therefore, \( \text{Cs} \) should have a larger atomic radius than \( \text{Rb} \) due to the additional electron shell. This trend is correct.
4. \( r_{\rm At} < r_{\rm Cs} \): 
   Astatine (\( \text{At} \)) is below Bromine and is a halogen, while Cesium (\( \text{Cs} \)) is an alkali metal. Despite their group differences, Cesium is known to have one of the largest atomic radii in its period and is generally larger than Astatine. This trend is correct.

The correct answer is the option where the stated trend is wrong: \( r_{\rm Mg} < r_{\rm Al} \) .

Answer 2

Step 1: Understand the trends in atomic radii in the periodic table.
Across a period (from left to right): Atomic radius generally decreases due to an increase in the effective nuclear charge. Electrons are added to the same energy level, while the number of protons in the nucleus increases, leading to a stronger attraction between the nucleus and the electrons, thus pulling them closer.
Down a group (from top to bottom): Atomic radius generally increases because electrons are added to higher energy levels (increasing the principal quantum number \( n \)), resulting in a larger electron cloud. The effect of increased nuclear charge is outweighed by the addition of electron shells and increased shielding by inner electrons. 

Step 2: Analyze each option based on the periodic trends.
(1) \( r_{Br}<r_K \) Bromine (Br) is in Period 4, Group 17, and Potassium (K) is in Period 4, Group 1. Across Period 4, atomic radius decreases from left to right. 
Therefore, \( r_K>r_{Br} \), which means \( r_{Br}<r_K \) is a correct trend. (2) \( r_{Mg}<r_{Al} \) Magnesium (Mg) is in Period 3, Group 2, and Aluminum (Al) is in Period 3, Group 13. Across Period 3, atomic radius decreases from left to right. Therefore, \( r_{Mg}>r_{Al} \), which means \( r_{Mg}<r_{Al} \) is an incorrect trend. (3) \( r_{Rb}<r_{Cs} \) Rubidium (Rb) is in Period 5, Group 1, and Cesium (Cs) is in Period 6, Group 1. Down Group 1 (alkali metals), atomic radius increases. 
Therefore, \( r_{Cs}>r_{Rb} \), which means \( r_{Rb}<r_{Cs} \) is a correct trend. (4) \( r_{At}<r_{Cs} \) Astatine (At) is in Period 6, Group 17, and Cesium (Cs) is in Period 6, Group 1. Across Period 6, atomic radius generally decreases from left to right. 
Therefore, \( r_{Cs}>r_{At} \), which means \( r_{At}<r_{Cs} \) is a correct trend. 

Step 3: Identify the incorrect trend.
Based on the analysis, the incorrect trend in atomic radii is given in option (2).