Question

Iron crystallises in a bcc system with a lattice parameter of $ \text{2}\text{.861}\,\overset{\text{o}}{\mathop{\text{A}}}\,. $ Calculate the density of iron in the bcc system (atomic weight of $ \text{Fe}=56,{{\text{N}}_{\text{A}}}=6.02\times {{10}^{23}}\,\text{mo}{{\text{l}}^{-1}} $ ).

• A. $ 7.94g\,m{{L}^{-1}} $
• B. $ 8.96\text{g}\,\text{m}{{\text{L}}^{-1}} $
• C. $ 2.78\text{g}\,\text{m}{{\text{L}}^{-1}} $
• D. $ 6.72\text{g}\,\text{m}{{\text{L}}^{-1}} $

Answer 1

Answer: (A)

$ d=\frac{ZM}{{{N}_{A}}{{a}^{3}}} $ (for bcc, $ Z=2 $ )
$ {{d}_{Fe}}=\frac{(2)\times 56.0\,g\,mo{{l}^{-1}}}{(6.02\times {{10}^{23}}mo{{l}^{-1}}){{(2.861\times {{10}^{-8}})}^{3}}c{{m}^{3}}} $
$ =7.94\,g\,M{{L}^{-1}} $