Q.

The percentage of void space of a metallic element crystallising in a ABCABC ..... type lattice pattern is

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a

24%

b

34%

c

74%

d

26%

answer is B.

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Detailed Solution

The ABCABC type of arrangement leads to a face-centered cubic structure that is similar to a cubic close packing in general. Atoms can be found on the cube's corners and face centres in FCC.
Consequently, a cubic unit cell has a total of, n=8×18+6×12=4

Atoms on face diagonals will now come into contact with one another in FCC. So, 4r=2a
r=a22(r is radius of each atom ) Currently, cubic unit cell volume by edge length a=a3 Vol. occupied = 4×34π(r)3  =4×43×πa223=163×π×a3162=πa332→ Volume occupied =πa3a3a3×100=74%→ Void =(100-74)%=26%
 

Therefore, the correct option is B 26%

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