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Question

a. Calculate packing efficiency simple cubic lattice.

b. An element having atomic mass 107.9u has FCC lattice. The edge length of its unit cell is 408.6 pm. Calculate the density of the unit cell.

[Given, NA=6.022×1023 mol1].

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Solution

(a) In a simple cubic unit cell, atoms are located only at corners of the cube. The particles touch one another along the edge.

Then, the edge length 'a' is related to the radius 'r' by the expression a=2r.

Volume of cubic unit cell =a3=(2r)3=8r3

A simple cubic unit cell has 1 atom per unit cell.

Volume occupied by each sphere is 43πr3

Packing efficiency =Volume occupied by each atom× total number of atoms per unit cellVolume of cubic unit cell×100

=43πr3×18r3×100=52.36%

b. A fcc unit cell has 4 atoms per unit cell. Z=4

The density of the unit cell,

d=ZMa3NA=4×107.9×103(408.6×1012)3×6.022×1023

d=10.5×103 kg/m3

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