Copper crystallizes with face centred cubic unit cell. If the radius of copper atom is 127.8 pm, calculate the density of copper metal. (Atomic mass of Cu = 63.55 u and Avogadro’s number N_A = 6.02 x 10²³ mol^-1)
OR
Iron has a body centred cubic unit cell with the cell dimension of 286.65 pm. Density of iron is 7.87 g cm-3. Use this information to calculate Avogadro’s number. (Atomic mass of Fe = 56.0 u)

We know, no. of atoms in the unit cell of FCC lattice = Z = 4

Radius = 127.8 pm

In FCC lattice, edge length a = 2√2r, where r is the radius.

∴ a = 2(1.414)(127.8×10^-10)cm = 361.42 cm. [1pm = 10^-10cm]

Given, Atomic mass of the cell = 63.5gmol⁻¹

We know density of the unit cell =

∴ Density = = 8.946gm cm^-3.

OR

We know, no. of atoms in the unit cell of BCC lattice = Z = 2

Cell dimension a = 286.65 pm = 286.65×10^-10cm. [1pm = 10^-10cm]

Given, density of unit cell = 7.87 gm cm^-3.

We know, density =

Or, N_A = = = 6.055×10²³ mol^-1.