Question

Copper crystallises into a fcc lattice with edge length 3.61 × 10⁻⁸ cm. Show that the calculated density is in agreement with its measured value of 8.92 g cm⁻³.

Answer 1

Given : fee structure = 1 + 3 = 4 atoms.

Edge length, a= 3.61 x 10^-8 cm,

Atomic mass of Cu = 63.4 gm mo1^-1.

Density of Cu=?

Mass of one Cu atom

`= ("Atomic mass")/N_A`

`= 63.4/(6.022 xx 10^23)`

= 1.0539 x 10^-22 gm

Mass of one unit cell

= 4 x 1.0539 x 10^-22

= 4.215 x 10^-22 gm

Volume a³

= (3.61 x 10^-8)³

= 4.699 x 10^-23 cm³.

Density of cell

`ρ = "Mass"/"Volume"`

`= (4.215 xx 10^-22)/(4.699 xx 10^-23) `

∴ ρ = 8.965 g cm^-1.

∴  The density of copper is 8.965 g / cm.