Question

According to radius ratio rule if R$'$ is radius of anion and r is the radius of cation then for an atom to occupy octahedral hole, the possible relation between R and r is

• A. r = 2.25 R
• B. r = 0.514 R
• C. r = 0.225 R
• D. r = 0.314 R

Hint:

For octahedral coordination, the radius ratio between the cation and anion must fall between 0.414 and 0.732. The value of 0.514 R is optimal for octahedral coordination.

Answer 1

The Correct Option is B

Step 1: Understanding the radius ratio rule.
The radius ratio rule helps in determining the stability of an ionic structure. For an atom to occupy an octahedral hole, the radius ratio (r/R) must fall within a certain range. The typical value for this range is \( r/R \approx 0.414 \) to \( r/R \approx 0.732 \). Based on this, the relation \( r = 0.514 R \) is the correct one.
Step 2: Analyzing the options.
(A) r = 2.25 R: This is incorrect, as this ratio is far too large for the octahedral hole.
(B) r = 0.514 R: This is the correct ratio, as it is within the acceptable range for an atom to fit into the octahedral hole.
(C) r = 0.225 R: This ratio is too small for an atom to occupy an octahedral hole.
(D) r = 0.314 R: While close, this is still not the ideal ratio for an octahedral hole.
Step 3: Conclusion.
The correct relation is r = 0.514 R, which corresponds to option (B).