Question

The number of atoms contained in a fcc unit cell of a monoatomic substance is

• A. 1
• B. 2
• C. 4
• D. 6

Answer 1

Answer: (C)

Face centred cubic is also called cubic close packed arrangement. It has points at all the comers as well as at the centre of each of the six faces. In this arrangement, there is one atom at each of the eight comers.
The number of atoms present at comers per unit cell $=8\times \frac{1}{8}=1.$
The number of atoms present at faces per unit cell$=6\times \frac{1}{2}=3$
$\therefore$ Total number of atoms in ccp or fee arrangement =1+3 = 4 The no. of atoms is a unit cell may be calculated by the the formula
$Z=\frac{n_c}{8}+\frac{n_b}{1}+\frac{n_f}{2}+\frac{n_e}{4}$
Where nc = no. of atom at the corner
$n_b$ = no. of atoms at body centre
$n_f$ = no. of atoms at face centre
$n_e$ = no. of atoms at edge centre.
An Fcc crystal contains
$=\frac{8}{8}+\frac{6}{2}=4$ atoms in a unit cell.