Question

Lithium has a bcc structure. Its density is 530 kg m⁻³ and its atomic mass is 6.94 g mol⁻¹. Calculate the edge length of a unit cell of lithium metal. (N_A = 6.02 × 10²³ mol⁻¹)

Options

• 154 pm

• 352 pm

• 527 pm

• 264 pm

Answer 1

352 pm

Explanation:

Given: BCC Structure ⇒ Z = 2

Density ρ = 530 kg/m³ = 0.530 g/cm³

Atomic mass (M) = 6.94 g/mol

Avogadro’s number N_A​ = 6.02 × 10²³ mol⁻¹

To find: edge length (a) in pm = ?

`rho = (Z * M)/(a^3 * N_A)`

⇒ `a^3 = (Z * M)/(rho * N_A)`

`a^3 = (2 xx 6.94)/(0.530 xx 6.02 xx 10^23)`

= `13.88/(3.1906 xx 10^23)`

a³ = 4.35 × 10⁻²³ cm³

a = (4.35 × 10⁻²³)^1/3 cm

a = 3.52 × 10⁻⁸ cm

a = 352 pm