Question

The density of $KBr$ is $2.75$ g cm${}^{-3}$. The length of the unit cell is $654$ pm. This shows that $KBr$ has:

• A. face-centered cubic lattice
• B. body-centered cubic lattice
• C. simple cubic lattice
• D. none of these

Answer 1

Answer: (A)

face-centered cubic lattice

Here, we are provided with density and edge length. We need to calculate the number of atoms (and lattice-type using the number of atoms per lattice).

So, by using density, $\rho =\frac{z\times M}{N_0\times a^3}$ and putting values accordingly, we get,

$2.75=\frac{z\times 119}{(6.023\times {10}^{23})\times (654\times {10}^{-10}{)}^3};\Rightarrow z=3.89$

$⟹Z$ is approximately equal to $4$.

Hence, the above structure is the face-centered cubic lattice.