Question

In face-centred cubic unit cell:

• A. face diagonal of the cube is $a\sqrt{2}$ or $4r$
  $(a=$ edge length, $r=$ radius of constituent units)
• B. effective number of atoms in the unit cell is $4$
• C. $8$ tetrahedral voids per unit cell
• D. rank of the unit cell is $3$

Answer 1

Answer: (A), (B), (C)

The correct options are
A face diagonal of the cube is $a\sqrt{2}$ or $4r$
$(a=$ edge length, $r=$ radius of constituent units)
B effective number of atoms in the unit cell is $4$
C $8$ tetrahedral voids per unit cell

(A) In FCC unit cell

$4r=a\sqrt{2}$ (face diagonal)

(B) $Z_{eff}=6\times \frac{1}{2}\left(Facecenters\right)+8\times 18\left(Bodycorners\right)=4$

(C)$8$ tetrahedral voids are present at a distance $\frac{a\sqrt{3}}{4}$ from each body corners.

(D) Rank of the unit cell= $Z_{effective}=4$