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Question

Chemistry Question on Unit Cells

The density of a metal which crystallises in bccbcc lattice with unit cell edge length 300pm300\,pm and molar mass 50gmol150 \,g \,mol^{-1} will be

A

10gcm310\, g\,cm^{-3}

B

14.2gcm314.2\, g\,cm^{-3}

C

6.15gcm36.15\, g\,cm^{-3}

D

9.32gcm39.32\, g\,cm^{-3}

Answer

6.15gcm36.15\, g\,cm^{-3}

Explanation

Solution

d=Z×Ma3×NAd=\frac{Z\times M}{a^{3}\times N_{A}} For bccbcc structure, Z=2Z = 2 d=2×506.023×1023×(300×1010)3d=\frac{2\times50}{6.023\times10^{23}\times\left(300\times10^{-10}\right)^{3}} =6.15gcm3=6.15\,g\,cm^{-3}