Question

A compound having cubic structure is formed by the elements X, Y and Z.
Atoms of element X are present at corners and face centres of the cube . Atoms of element Y are present at edge centres and atoms of element Z are present at body centre.

What will be $Z_{eff}$ for the compound when all the atoms are removed from two different planes both of them individually parallel to either one of the faces of the cube and both also pass through middle of the same cube?

• A. 1
• B. 2
• C. 3
• D. 4

Answer 1

The correct option is B 2

In a cubical unit cell:

$\text{Contribution for a corner particle is}=\frac{1}{8}$
$\text{Contribution for a face centre particle is}=\frac{1}{2}$
$\text{Contribution for a edge centre particle is}=\frac{1}{4}$
$\text{Contribution for a body centre particle is}=1$
Atoms are removed from two different planes ABCD and PQRS as shown :


Atoms removed are :
8 edge centres (here Y)
6 face centres ( here X)
1 body centre (here Z)
For X :
all the face centres are removed only corners are left :
So,
$\text{Total X atoms in a unit cell}=(8\times \frac{1}{8})=1$
For Y:
Out of the 12 edges , only 4 are left.
$\text{Total Y atoms in a unit cell}=(4\times \frac{1}{4})=1$

For Z, no atom is left since body centre is removed

$Z_{eff}=1+1+0=2$