Question

The solid having the least packing efficiency is _ _ _.

• A. caesium chloride
• B. cadmium iodide
• C. zinc sulfide (wurtzite form)
• D. zinc sulfide (zinc blende form)

Hint:

Close-packed structures (FCC/HCP) have highest packing efficiency (~74\%), while BCC-type structures have lower (~68\%)

Answer 1

The Correct Option is A

Step 1: Understand packing efficiency.
Packing efficiency refers to the fraction of space occupied by particles in a crystal structureHigher coordination number generally leads to higher packing efficiency

Step 2: Analyze CsCl structure.
CsCl has a body-centered cubic type arrangement with coordination number 8Although coordination number is high, the packing efficiency is about $68\%$ which is lower than close-packed structures

Step 3: Analyze CdI$_2$ structure.
CdI$_2$ has a layered hexagonal close-packed arrangement with cations occupying alternate layersThe packing is derived from close-packed arrangement, giving higher efficiency

Step 4: Analyze ZnS (wurtzite).
Wurtzite structure is based on hexagonal close packing with tetrahedral voids occupiedThis leads to relatively high packing efficiency

Step 5: Analyze ZnS (zinc blende).
Zinc blende has a cubic close-packed arrangement (face-centered cubic)Again, packing efficiency is high (about $74\%$)

Step 6: Compare all structures.
\[ \text{ZnS (blende)} \approx 74\% > \text{ZnS (wurtzite)} \approx 74\% > \text{CdI}_2 > \text{CsCl} \approx 68\% \]

Step 7: Conclusion.
Thus, the solid with the least packing efficiency is
\[ \boxed{\text{caesium chloride}} \]