Question

Copper crystallises in fcc unit cell with cell edge length of 3.608 × 10⁻⁸ cm. The density of copper is 8.92 g cm⁻³. Calculate the atomic mass of copper.

Options

• 31.55 u

• 60 u

• 65 u

• 63.1 u

Answer 1

63.1 u

Explanation:

Given: Fcc structure, Z = 4 atoms per unit cell

Edge length a = 3.608 × 10⁻⁸

d = 8.92 g/cm³

Formula: d = `(Z xx M)/(N_A xx a^3)`

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

a³ = (3.608 × 10⁻⁸)³

= 46.94 × 10⁻²⁴

= `(8.92 xx 6.022 xx 10^23 xx 46.94 xx 10^-24)/4`

= `(8.92 xx 6.022 xx 46.94 xx 10^-1)/4`

= `(53.72 xx 46.94 xx 10^-1)/4`

= `(2522 xx 10^-1)/4`

= `(252.2)/4`

= 63.05 ≈ 63.1