Question

The density of a uniform crystal structure can be estimated from the crystal type and information about the lattice parameter and atomic radii. Estimate the density of a material (gram/cm³) for a material with these properties:

Atomic Radius = 0.1281 nm

Crystal Type = FCC

atomic Mass = 47 grams/mol

(Note: Avogadro's Number , 6.022x10^23 atoms/mol)

Answer 1

Solutions:

1) Convert nm to cm:

0.1281 nm x (1 cm/10⁷ nm) = 0.1281 x 10¯⁷ cm = 1.281 x 10¯⁸ cm

2) Calculate the volume of the unit cell:

(1.281 x 10¯⁸ cm)³ = 2.102 x 10¯²⁴ cm³

3) Calculate the average mass of one atom :

47 g mol¯¹ divided by 6.022 x 10²³ atoms mol¯¹ = 7.805 x 10¯²³ g

4) Calculate the mass of the 4 atoms in the face-centered cubic unit cell:

7.805 x 10¯²³ g times 4 = 3.122 x 10¯²² g

5) Calculate the density (value from step 4 divided by value from step 2):

3.122 x 10¯²² g / 2.102 x 10¯²⁴ cm³ = 148.525 g/cm³