Question

The density of KBr is $2.75$ g/ml. The length of the edge of the unit cell is $654$ pm. KBr has ________ centred cubic structure.

Fill in the blank.

• A. Face
• B. Body
• C. Simple
• D. None of the above

Answer 1

The correct option is A Face

Length of the edge of the unit cell $=654$ pm $=6.54\times {10}^{-4}$

Therefore, volume (V) of the unit cell $=6.54\times {10}^{-4}$ cm${}^3$

Molecular mass of KBr $=119$ g/mol

The density of KBr $=2.75$ g cm${}^2$

The formula for density is as follows:

$\rho =\frac{n\times M}{V\times N_A}$

$n=\frac{\rho \times V\times N_A}{M}$ $=\frac{2.75\times (6.54\times {10}^{-4}{)}^3\times 6.023\times {10}^{23}}{119}=3.9\approx 4$

Since the number of atoms in a unit cell is $4$, the crystal is face-centred.

Hence, the correct option is $\text{A}$