Question

200g of Nickel crystallises in cubic closed packed structure. If edge length of the unit cell is 100 pm and density of the crystal is 8.0 g/cm^3 then the number of unit cells present in the crystal is?

Answer 1

Each unit cell has:

8 corner atoms, each shared by 8 unit cells = (1/8)(8) = 1 atom

6 face atoms, each shared by 2 faces = (1/2)(6) = 3 atoms

Total: 4 atoms per unit cell

V = a3 = (200 x 10-12 m)3 = 8 x 10-30 m3 = 8 x 10-24 cm3

Now do a proportion to get the mass of the 4 atoms in a unit cell:

200 g → 24 x 1023 atoms

x → 4 atoms

Cross multiply and get

x = 4 · 200 / (24 x 1023) g ≅ 3.33 x 10-22 g

ρ = m/V = (3.33 x 10-22 g) / (8 x 10-24 cm3) ≅ 41.6 g/cm3