• # question_answer Pottasium has a bcc structure with nearest neighbour distance $4.52\overset{\text{o}}{\mathop{\,\text{A}}}\,$. Its atomic weight is 39. Its density (in kg ${{m}^{-3}}$) will be A) 454 B) 804 C) 852       D) 910

 For $bcc,$ $d=\frac{\sqrt{3}}{2}a\,\text{or}\,a=\frac{2d}{\sqrt{3}}=\frac{2\times 4.52}{1.732}=5.219\overset{\text{o}}{\mathop{\text{A}}}\,=522pm$$\rho =\frac{\operatorname{Z}\times M}{{{\operatorname{a}}^{3}}\times {{\operatorname{N}}_{A}}\times {{10}^{-30}}}$$=\frac{2\times 39}{{{\left( 522 \right)}^{3}}\times \left( 6.023\times {{10}^{23}} \right)\times {{10}^{-30}}}$ $=0.91g/c{{m}^{3}}=910kg\,{{m}^{-3}}$