The BCC unit cell is shown below:
Atomic radius r = 0.137 nm = 0.137 x 10-9 m = 1.37 x 10-8 cm
Using Pythagoras theorem:
d2 + (d√2)2 = (4r)2
Unit cell edge length = d = (16r2/3)1/2
= (16 x (1.37 x 10-8)2/3)1/2
= 3.164 x 10-8 cm
Unit cell volume = volume of cube = d3
= (3.164 x 10-8)3
= 3.167 x 10-23 cm3
Number of tungsten atoms in unit cell = 8 x 1/8 + 1 x 1 (8 corner + 1 center atom)
= 2
Mass of tungsten atoms = number of atoms/Avogadro's number x atomic weight
= 2/6.022 x 1023 x 183.84
= 6.106 x 10-22 g
Theoretical density of tungsten = mass of tungsten atoms/volume of unit cell
= 6.106 x 10-22/3.167 x 10-23
= 19.3 g/cm3
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