Question:
For the given close packed structure of a salt made of cation $X$ and anion $Y$ shown below (ions of only one face are shown for clarity), the packing fraction is approximately (packing fraction $=\frac{\text { packing efficiency }}{100}$ )
For the given close packed structure of a salt made of cation $X$ and anion $Y$ shown below (ions of only one face are shown for clarity), the packing fraction is approximately (packing fraction $=\frac{\text { packing efficiency }}{100}$ )
Updated On: June 02, 2025
0.74
0.63
0.52
0.48
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The Correct Option is B
Solution and Explanation
Step 1: Understanding the Close-Packed Structure
The structure is a close-packed arrangement, which suggests we are dealing with a face-centered cubic (FCC) structure or cubic close packing (CCP) structure.
In FCC, ions are packed in such a way that the packing efficiency is maximum.
Step 2: Packing Efficiency in FCC Structure
In a face-centered cubic structure, the packing efficiency is approximately 63%, meaning 63% of the total volume is occupied by the ions.
Step 3: Calculating the Packing Fraction
The packing fraction is defined as the ratio of the packing efficiency to 100:
Step 4: Considering the Ionic Size Ratio
When the cation is significantly smaller than the anion, the packing efficiency can decrease from the typical FCC value of 74%. In this case, the packing fraction is given as 0.63, which is consistent with this situation.
Final Result
The packing fraction for the given close-packed structure is approximately 0.63.
The structure is a close-packed arrangement, which suggests we are dealing with a face-centered cubic (FCC) structure or cubic close packing (CCP) structure.
In FCC, ions are packed in such a way that the packing efficiency is maximum.
Step 2: Packing Efficiency in FCC Structure
In a face-centered cubic structure, the packing efficiency is approximately 63%, meaning 63% of the total volume is occupied by the ions.
Step 3: Calculating the Packing Fraction
The packing fraction is defined as the ratio of the packing efficiency to 100:
Packing fraction = Packing efficiency / 100Substituting the packing efficiency:
Packing fraction = 63 / 100 = 0.63However, in this case, the packing fraction is 0.63, which suggests that the cation and anion sizes differ, and this lower packing fraction reflects this discrepancy.
Step 4: Considering the Ionic Size Ratio
When the cation is significantly smaller than the anion, the packing efficiency can decrease from the typical FCC value of 74%. In this case, the packing fraction is given as 0.63, which is consistent with this situation.
Final Result
The packing fraction for the given close-packed structure is approximately 0.63.
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