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?

a = 286.65 pm = 286.65 × 10⁻¹⁰ cm
Density (ρ) = 7.874 g cm⁻³
Atomic mass of Fe = 56.0 u
Z = 2 (for body-centered cubic unit cell)
Avogadro number (N₀) = ?
ρ = Z × M / a³ × N₀
7.874 g cm⁻³ = 2 × (56.0 g mol⁻¹) / (286.65 × 10⁻¹⁰ cm)³ × N₀
N₀ = 2 × (56 g mol⁻¹) / (286.65 × 10⁻¹⁰ cm)³ × (7.874 g cm⁻³)
N₀ = 6.022 × 10²³ mol⁻¹