Q.

The CORRECT statement(s) for cubic close packed (ccp) three dimensional structure is (are)

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a

The number of the nearest neighbors of an atom present in the topmost layers is 12

b

The efficiency of atom packing is 74%

c

The number of octahedral and tetrahedral voids per atom are 1 and 2, respectively

d

The unit cell edge length is 22  times the radius of the atom

answer is B.

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Detailed Solution

In the middle layer, an atom present at the center has 6 neighboring atoms, 3 neighboring atoms in the top layer and 3 neighboring atoms in the bottom layer. Total 12 neighboring atoms. The top-most layer will have 9 nearest neighbors.

Packing efficiency=volume occupies by 4 spheres in unit cell total volume of unit cell ×100=4×43πr3a3×100=4×43πr3(22r)3×100=74%

In CCP,  number of octahedral voids = 1 × no. of atom
Number of tetrahedral voids = 2 × no. of atom 
Hence, the number of octahedral and tetrahedral voids per atom are 1 and 2, respectively.
For edge length:

4r=2a a=22r

Where ‘a’ is edge length of unit cell and ‘r’ is radius of atom.

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The CORRECT statement(s) for cubic close packed (ccp) three dimensional structure is (are)