# In a face centred cubic lattice, atom A occupies the corner positions and atom B occupies the face centre positions. If one atom of B is missing from one of the face centred points, the formula of the compound is Option 1) $A_{2}B\;$ Option 2) $\; AB_{2}\;$ Option 3) $\; A_{2}B_{3}\;$ Option 4) $\; A_{2}B_{5}$

As we learnt in

No. of atoms(z) for face centered unit cell -

Lattice points: at corners and face centers of unit cell.

For face centered cubic (FCC), z=4.

- wherein

No. of atoms(z) for simple cubic unit cell -

Lattice points: at corners

For simple cubic (SC), z=1

- wherein

Number of atom A per unit cell $=8\times \frac{1}{8}=1$

Number of atom B per unit cell $=5\times \frac{1}{2}=\frac{5}{2}$

AB5/2 i.e. A2B5

Correct option is 4.

Option 1)

$A_{2}B\;$

This is an incorrect option.

Option 2)

$\; AB_{2}\;$

This is an incorrect option.

Option 3)

$\; A_{2}B_{3}\;$

This is an incorrect option.

Option 4)

$\; A_{2}B_{5}$

This is the correct option.

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