Question:
Which of the following statement is not correct?
Which of the following statement is not correct?
Show Hint
Both \(fcc\) and \(ccp\) represent the same type of close packing and have packing efficiency:
\[
74\%
\]
Updated On: Jun 25, 2026
- Packing efficiency of hcp and ccp lattices are identical
- Packing efficiency of fcc lattice \(\gt \) Packing efficiency of ccp lattice
- Packing efficiency of fcc lattice \(=\) Packing efficiency of ccp lattice
- Packing efficiency of hcp lattice \(=\) Packing efficiency of fcc lattice
Show Solution
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The Correct Option is B
Solution and Explanation
Step 1: Recall packing efficiencies of common lattices.
The packing efficiencies of: \[ hcp,\ ccp,\ \text{and}\ fcc \] structures are all: \[ 74\% \]
Step 2: Understand the relation between fcc and ccp.
The cubic close packing \((ccp)\) arrangement is actually represented by the face centered cubic \((fcc)\) lattice.
Thus, \[ fcc \equiv ccp \] Hence, both have identical packing efficiency: \[ 74\% \]
Step 3: Check each option.
Option (1): Packing efficiency of hcp and ccp are identical This is correct.
Option (2): \[ \text{Packing efficiency of fcc}\gt \text{Packing efficiency of ccp} \] This is incorrect because: \[ fcc = ccp \] Option (3): \[ \text{Packing efficiency of fcc}=\text{Packing efficiency of ccp} \] This is correct.
Option (4): \[ \text{Packing efficiency of hcp}=\text{Packing efficiency of fcc} \] This is also correct.
Step 4: Final conclusion.
Hence, the incorrect statement is \[ \boxed{ \text{Packing efficiency of fcc lattice}\gt \text{Packing efficiency of ccp lattice} } \]
The packing efficiencies of: \[ hcp,\ ccp,\ \text{and}\ fcc \] structures are all: \[ 74\% \]
Step 2: Understand the relation between fcc and ccp.
The cubic close packing \((ccp)\) arrangement is actually represented by the face centered cubic \((fcc)\) lattice.
Thus, \[ fcc \equiv ccp \] Hence, both have identical packing efficiency: \[ 74\% \]
Step 3: Check each option.
Option (1): Packing efficiency of hcp and ccp are identical This is correct.
Option (2): \[ \text{Packing efficiency of fcc}\gt \text{Packing efficiency of ccp} \] This is incorrect because: \[ fcc = ccp \] Option (3): \[ \text{Packing efficiency of fcc}=\text{Packing efficiency of ccp} \] This is correct.
Option (4): \[ \text{Packing efficiency of hcp}=\text{Packing efficiency of fcc} \] This is also correct.
Step 4: Final conclusion.
Hence, the incorrect statement is \[ \boxed{ \text{Packing efficiency of fcc lattice}\gt \text{Packing efficiency of ccp lattice} } \]
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