CBSE Class 12-science Answered
An element A has a ccp arrangement of atoms. The radius of A is equal to 143.2pm. Calculate the lattice parameter of the unit cell and the density of solid Al if its atomic weight = 30u.
Asked by Topperlearning User | 01 Apr, 2014, 03:37: PM
Expert Answer
Because A is ccp we have an fcc unit cell. Cell contents: 4 atoms/cell [8 at corners (each 1/8), 6 in faces (each 1/2)]
Lattice parameter: atoms in contact along face diagonal, therefore 4rAl = a(2)1/2
a = 4(1.432Å)/(2)1/2 = 4.050Å.
Density = Mass/Volume = Mass per unit cell/Volume per unit cell g/cm3
Mass of unit cell = mass of 4 Al atoms = (30g/mol)(1mol/6.022x1023atoms)(4 atoms/unit cell) = 1.992 x 10-22 g/unit cell
Volume unit cell = a3 = (4.05x10-8cm)3 = 66.43x10-24 cm3/unit cell
Density= {1.992x10-22g/unit cell}/{66.43x10-24 cm3/unit cell} = 2.998 g/cm3
Answered by | 01 Apr, 2014, 05:37: PM
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