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In body-centred cubic structure,

The no. of atoms per unit cell

= 2

Volume of 2 atoms (spherical)

=2

*

(4/3)

Ï€r

3

We know the radius of atom in BCC is

r = a√

3

4

Volume occupied by the atoms per unit cell

(v) = 8Ï€

a

√

33 4

v =

= 8Ï€

a

3

3

√

3------- ---------3 4

*

4

*

4

Volume occupied by the atoms per unit cell

(v) =

Ï€a

3

√3----8

Volume of the unit cell for a cubic system

(V) = a

3

Atomic packing factor (APF) =

(

Ï€a

3

√

3

/

8

)

--------------a

3

√

3(or) APF =

Ï€

---------

8

APF = 0.68

Therefore, we can say that 68% volume of the unit cell of BCC is occupied by atoms and remaining 32%volume is vacant.

Thus the packing density is 68%.

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