Question

A solid compound contains X,Y and Z atoms in a cubic lattice with X atoms occupying the corners, Y atoms in the body centred positions and Z atoms at the centre of the faces of the unit cell.
What are the total effective number of atoms ($Z_{eff}$) in a unit cell if all the atoms from a face diagonal of the lattice are removed?

• A. $5$
• B. $4.5$
• C. $3.75$
• D. $4.25$

Answer 1

The correct option is D $4.25$

$\text{Number of atoms of X in a unit cell}=\frac{1}{8}\times 8=1$
$\text{Number of atoms of Y in the unit cell}=1$
$\text{Number of atoms of Z in a unit cell}=\frac{1}{2}\times 6=3$
Atoms removed from a face diagonal :
2 corner atoms
1 face centre atoms
$\text{Number of atoms of X in a unit cell}=\frac{1}{8}\times 6=\frac{6}{8}=0.75$
$\text{Number of atoms of Y in the unit cell}=1$
$\text{Number of atoms of Z in a unit cell}=\frac{1}{2}\times 5=2.5$
$Z_{eff}=0.75+1+2.5=4.25$