Question

Tungsten has a BCC structure, an atomic radius of 0.137 nm and an atomic weight of 183.84 g/mol. Compute its theoretical density.

Answer 1

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