In the ccp packing, the number of lattice points per unit area in the planes is in the order

Concept:

Cubic Close Paking: 

• The cubic close packing (ccp) is the name given to a crystal structure. When we put atoms in the octahedral void, the packing is the of the form ABCABC, the packing is known as cubic close packing (ccp).  

Explanation:

• In case of (100) plane, 5 lattice points are present in the area is a². Thus, the area occupied by 1 lattice point is (a²/4)=0.20a².
• In case of (110) plane, 6 lattice points are present in the area is \(\sqrt 2 {a^2}\) Thus, the area occupied by 1 lattice point is \({{\sqrt 2 {a^2}} \over 6}\)=0.23a². 
• In case of (111) plane, 6 lattice points are present in the area \({{\sqrt 3 } \over 4} \times \sqrt 2 a \times \sqrt 2 a = {{\sqrt 3 } \over 2}{a^2}\). Thus, the area occupied by 1 lattice point is \({{\sqrt 3 } \over {12}}{a^2}\) = 0.14a².
• Thus, In the ccp packing, the number of lattice points per unit area in the planes is in the order (111) > (100) > (110).

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Conclusion:-

So, In the ccp packing, the number of lattice points per unit area in the planes is in the order (111) > (100) > (110)