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Calculate the number of atoms per unit cell of a metal having the lattice parameter 2.9 A and density 7.87 gm/cm3.

Atomic weight of metal is 55.85. Avogadro number is 6.023×1023/gm mole.

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Let a=edge of unit cell

=lattice parameter of a cubic cell

 

M= mass of element per mole

= atomic weight of the element

 

ρ= density of the metal

 

NA= Avogadro's number

n= number of atoms per unit cell

 

Thus

a=2.9˙A=2.9×108cm

M=55.85

ρ=7.87 gm/cc

NA=6.023×1023

Number of atoms per unit cell,n:

Using the relation

ρ a3=nMNA

or n=ρ a3NAM

=7.87×(2.9×108)3×6.0238×102355.85=2

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