NEET Chemistry The Solid State Questions Solved


In a face centred cubic arrangement of metallic atoms, what is the relative ratio of the sizes of tetrahedral and octahedral voids ?

(A) 0.543                                   

 (B) 0.732

(C) 0.414                                   

(D) 0.637

(A). Consider one tetrahedral void. If the side length of the tetrahedron is l and if d is the distance from the centre to the corner, then

l2=2d2-2d2cosθ=2d21+13=43×2d2

 l=83d,  but if a is the side length of the unit cell

l=a2 and d=r1+r2, where r1 is the radius of the corner atom and r2 the radius of the void.

83r1+r2=a2,

r1+r2=a2×38=3a4

but l=2r1.    r1=l2=a22

r2=3a4-2a4=a43-2

For the octahedral void, if the radius of the void is r3, then 2r1+r3=a

r1+r3=a2,  r3=a2-r1

=a2-a22=2a4-2a4=2-2a4

ratio of the sizes of tetrahedral to octahedral voids

a43-2a42-2=1.732-1.4142-1.414=0.3180.586=0.543

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