Chemistry - Solid State Question with Solution | TestHub

For cubic lattice, $\rho =\frac{Z\times A}{N_A\times V}$ or $Z=\frac{\rho \times N_A\times V}{A}$ Given that, $$\begin{array}{rl}& A=75\mathrm{g}/\mathrm{mol}\\ & V=(5\mathring{A}{)}^3={\left(5\times 10^{-8}\right)}^3{\mathrm{cm}}^3\\ & =125\times 10^{-24}{\mathrm{cm}}^3\\ & N_{\mathrm{A}}=6.02\times 10^{23}\\ & \rho =2\mathrm{gm}/\mathrm{cc}\\ & \therefore Z=\frac{2\times 6.02\times 10^{23}\times 125\times 10^{-24}}{75}\approx 2\\ & \end{array}$$ The value of $Z$ represents that element must have body centred cubic (bcc) structure. For bcc structure atomic radius $(r)=\frac{\sqrt{3}}{4}a=\frac{\sqrt{3}}{4}\times 5=2.165\mathring{A}$ $$=216.5\mathrm{pm}$$