Solid State - Result Question 25

####25. The correct statement(s) for cubic close packed (ccp) three dimensional structure is (are)

(2016 Adv.)

(a) The number of the nearest neighbours of an atom present in the topmost layer is 12

(b) The packing efficiency of atom 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

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Answer:

Correct Answer: 25. (b,c,d)

Solution:

  1. (a) Nearest neighbour in the topmost layer of ccp structure is 9 thus, incorrect.

(b) Packing efficiency is 74 thus, correct.

(c) Tetrahedral voids =2

Octahedral voids =1 per atom thus, correct.

(d) Edge length, a=42r=22r

thus, correct

Explanation Edge length =a

Radius =r

AC2=AB2+BC2 (4r)2=a2+a2=2a2 4r=2a r=24a=a22a=22r

In ccp structure, number of spheres is 4 .

Hence, volume of 4 spheres =4(43πr3)

Total volume of unit cell =a3=(22r)3

of packing efficiency

= Volume of 4 spheres  Volume of unit cell =4(43πr3)[2(2r)]3×100 =74.05



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