Question

1. Unit Cells

i. A certain metal crystallizes in a face-centered cubic unit cell. If the atomic radius is 150 pm, calculate the edge length (cm) and volume of the unit cell (cm3)?

ii. If said metal is Gold (Au), calculate the density.

Answer 1

Solution:

1) Convert pm to cm: 150 pm*(1cm/10^10pm) = 1.5*10^-8 cm =r

2) Edge length of the cell: From pythogorean theorm; r = a ÷ 2(√2)

1.5*10^-8 cm = a ÷ 2(√2)

a = 4.242*10^-8 cm

3) Volume of cell: V = a^3 = (4.242*10^-8 cm)^3 = 7.633*10^-23 cm^3

4) Mass of 4 unit cells in a unit cell:

At. wt of Au = 197g/mol

197g/mol/6.023x 10²³ atoms/mol = 3.27*10^-22 g/atom

3.27*10^-22 g/atom times 4 atoms = 1.308*10^-21 g

5) Density of element= mass of unit cell/volume = 1.308*10^-21 g / 7.633*10^-23 cm^3 = 17.13 g/cm^3