Question

Calculate the radius of copper atom. The atomic weight of copper is 63.55 g mol⁻¹. It crystallises in face-centred cubic lattice and has density of 8.93 g cm⁻³ at 298 K.

(N_A = 6.023 × 10²³ mol⁻¹)

Answer 1

Given: Atomic mass of copper (M) = 63.55 g/mol

Density (ρ) = 8.93 g/cm³

Face-centred cubic (fcc) structure ⇒ Z = 4 atoms/unit cell

Avogadro’s number, N_A = 6.023 × 10²³ mol⁻¹

Formula: We are to calculate the atomic radius of copper.

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

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

`a^3 = (4 xx 63.55)/(8.93 xx 6.023 xx 10^23)`

`a^3 = 254.2/(53.78 xx 10^23)`

a³ = 4.73 × 10⁻²³ cm³

∴ a = `(4.73 xx 10^(−23))^(1/3)`

a = 3.60 × 10⁻⁸ cm

a = 3.60 Å

In fcc,

∴ Face diagonal = `sqrt 2 a = 4 r`

`r = (sqrt 2 * a)/4`

Substitute a = 3.60 Å

r = `(1.414 xx 3.60)/4`

r = `5.0904/4`

∴ r = 1.2726 Å ≈ 1.28 Å