Chemistry - Solid State Question with Solution | TestHub

Given:

$a=5\text{ A˚}=5\times 10^{-8}\text{ cm}$

$\rho =4{\text{ g cm}}^{-3}$

$M=149{\text{ g mol}}^{-1}$

$N_A=6.022\times 10^{23}{\text{ mol}}^{-1}$

The density of the unit cell is given by the formula:

$\rho =\frac{Z\times M}{a^3\times N_A}$

Rearranging for the number of atoms per unit cell ($Z$):

$Z=\frac{\rho \times a^3\times N_A}{M}$

Substituting the given values:

$Z=\frac{4\times (5\times 10^{-8}{)}^3\times 6.022\times 10^{23}}{149}$

$Z=\frac{4\times 125\times 10^{-24}\times 6.022\times 10^{23}}{149}$

$Z=\frac{500\times 10^{-1}\times 6.022}{149}$

$Z=\frac{301.1}{149}\approx 2$

Since $Z=2$, the crystal structure is body centred cubic.

Answer: Body centred cubic