Question

The length of a side of a unit cell of cesium chloride as determined by X ray diffraction pattern is 412.1 pm. What is the density of caesium chloride (in g/cc)? Caesium chloride crystallizes as a body centered cubic lattice. (Atomic wt. of Cs = 133). ___

Answer 1

Length of edge of the unit cell =$412.1pm,=412.1\times {10}^{-1}cm$
Volume of the unit cell =$(412.1\times {10}^{-10}{)}^3=7.00\times {10}^{-23}c{m}^3$
Formula mass of caesium chloride = 168.5 a.m.u
The number of formula units per unit cell of caesium chloride is 1 as it has body centered cubic lattice.
$\therefore$ Z = 1 formula units/unit cell
$Density=\frac{\text{Formula mass}\times Z}{\text{unit cell volume}(cm{)}^3\times N_{Avo}}$
$=\frac{168.5\times 1}{7.00\times {10}^{-23}\times 6.023\times {10}^{23}}=4g/c{m}^3$