Question

$CsBr$ crystallises in a body centred cubic unit lattice with an edge length of $4.287\mathring{A}$ . How many molecules of $CsBr$ will be present in the unit lattice ?

• A. 1
• B. 2
• C. 3
• D. 4

Answer 1

Answer: (A)

In $CsBr$ unit cell structure $B{r}^{-}$ ions are arranged in a simple cubic arrangement. In this arrangement the $B{r}^{-}$ ions are present at all the comers of the cube. The $C{s}^{+}$ ions occupy the cubic sites i.e., $C{s}^{+}$ ions are present at the body centre of the cube. Number of $B{r}^{-}$ ions $=8\times \frac{1}{8}=1$ ions per unit cell.
There is also one $C{s}^{+}$ ion in the body centre and its contribution per unit cell is $1$.
Therefore, there is one $B{r}^{-}$ ion for each $C{s}^{+}$ ion. There is one molecule of $CsBr$ in the unit lattice.