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  • If there are 4 atoms in one unit cell then the packing efficiency of unit cell is:Option: 1 0.52Option:

If there are 4 atoms in one unit cell then the packing efficiency of unit cell is:

Option: 1

0.52


Option: 2

0.74


Option: 3

0.68


Option: 4

0.91


Answers (1)

best_answer

\mathrm{Packing\: Efficiency=\frac{z\times volume\: of\: one\: atom}{volume\: of\: unit\: cell}}

Since the number of atoms per unit cell is 4 that means it is a fcc unit cell. In fcc unit cell relation between the radius of atom and edge of the unit cell is given as follows: 

r=\frac{a}{2\sqrt{2}}

Thus,

\mathrm{Packing\: Efficiency=\frac{4\times\frac{4}{3}\pi r^3}{(2\sqrt{2r})^3}=\frac{\pi }{3\sqrt{2}}=0.74}

 

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