Ahypothetical metal has the bcc crystal structure, a density of 7.24 g/cm3, and an atomic weight of 48.9 gmol. a) sketch a bcc unit. b) cell determine the atomic radius of this metal. c) calculate the side length of the bcc unit cell

Answer :

(a) The sketch of BCC unit cell is shown below.

(b) The atomic radius of this metal is,

(c) The side length of the BCC unit cell is,

Solution : Given,

Number of atom in unit cell of BCC (Z) = 2

Atomic mass (M) = 48.9 g/mole

Density =

Avogadro's number

First we have to calculate the edge length of unit cell.

Formula used :  

     .............(1)

where,

= density  =

Z = number of atom in unit cell  = 2

M = atomic mass  = 48.9 g/mole

= Avogadro's number  =

a = edge length of unit cell  or the side length of the BCC unit cell =?

Now put all the values in above formula (1), we get:

The edge length of unit cell is,

Now we have to determine the atomic radius of this metal.

Formula used :

where,

a = edge length of unit cell

r = nearest neighbor distance  or atomic radius of metal

Now put all the given values in this formula, we get :

The atomic radius of this metal is,

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