235. The compound CuCl has the ZnS (Cubic) structure. Its density is 3.04 g cm^–3. What is the length of the edge of unit cell? (At. mass of Cu = 63.5, CI = 35.5) 

Formula mass of CuCl =63.5 +35.5

                                      =  99.0

The number of formula units per cell of ZnS is 4. It has face centred cubic structure.

$$\begin{gathered} we have \\ Z =4 \\ density \left(d\right) =3.4 g C{m}^{-3} \\ {N}_0 (Avogadro\text{'}s number) =6.023 x{10}^{23} \\ Mass =99.0 gram \\ Therefore u\sin g formula \\ density =\frac{Mass x Z}{unit cell volume(Cm{)}^3 x{N}_{avod.no.}} \\ d =\frac{M x Z}{a^3 x N_0} \\ {a}^3 =\frac{99 x4}{3.4 x6.023 x{10}^{23}} \\ {a}^3 =1.932 x{10}^{-22}c{m}^3 \\ unit cell length a= (1.932 x{10}^{-22}{)}^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$3$}\right.} \\ takinig \log both side \\ \log a =\frac{1}{3}\log 1.932 x{10}^{-22} \\ =\frac{1}{3}(0.2860-22) =\frac{1}{3}(-21.7140) \\ = -7.238 =0.762 x{10}^{-8} \\ taking anti\log \\ a =anti\log 0.762 x{10}^{-8} =5.758 x{10}^{-8} cm \\ = 5.758 x {10}^{-8}cm \end{gathered}$$