• # question_answer Chromium metal crystallises with a body centred cubic lattice. The length of the unit edge is found to be 287 pm. Calculate the atomic radius. What would be the density of chromium in $g/c{{m}^{3}}$? A) 7.3 B) 8.1 C) 5.1 D) 11.3

 In bcc unit cell, $4r=\sqrt{3a}$$\Rightarrow \,\,r(Cr)=\frac{\sqrt{3}a}{4}=\frac{\sqrt{3}}{4}\times 287pm$ $=124.3pm$ N = number of atoms per unit cell, M = molar mass ${{a}^{3}}$ = volume of cubic unit cell, ${{N}_{A}}$ = Avogadro's number For bcc Z = 2 $=\frac{2\times 52g}{6.023\times {{10}^{23}}}\times {{\left( \frac{1}{2.87\times {{10}^{-8}}cm} \right)}^{3}}$ $=7.3g/c{{m}^{3}}$