Question

The ratio of co-ordination number of Al and number of Al atoms per unit cell in fcc lattice is :

• A. $3:1$
• B. $2:1$
• C. $1:1$
• D. $4:1$

Answer 1

Answer: (A)

$3:1$

Number of Al atoms per unit cell of Al in its crystal lattice is 4.

Al has fcc unit cell with Al atoms at 8 corners and 6 face centres of a cubic.

Each corner atom contributes one eight to the unit cell and each face centre atom contributes one half to the unit cell.

Total number of Al atoms in one unit cell $=8\times \frac{1}{8}+6\times \frac{1}{2}=1+3=4$

In fcc unit cell, the coordination number is 12.

Hence, the ratio of co-ordination number of Al and number of Al atoms per unit cell in fcc lattice is $\frac{12}{4}=3:1$