Question

The cubic unit cell of $ Al $ (molar mass $ 27\, g $ $ mo{{l}^{-1}} $ ) has an edge length of 405 pm. Its density is $ 2.7\text{ }g\text{ }c{{m}^{-3}} $ . The cubic unit cell is

• A. face centred
• B. body centred
• C. primitive
• D. edge centred
• E. simple

Answer 1

Answer: (A)

Density $ (\rho )=\frac{Z\times M}{{{a}^{3}}\times {{N}_{0}}} $
$ 2.7=\frac{Z\times 27}{{{(405\times {{10}^{-10}})}^{3}}\times 6.023\times {{10}^{23}}} $
$ Z=\frac{2.7\times {{(405)}^{3}}\times {{10}^{-30}}\times 6.023\times {{10}^{23}}}{27} $
$ =4 $
For face centred cubic unit cell, number of atoms are 4.