Question

A metallic element crystallizes in simple cubic lattice. If edge length of the unit cell is 3Å, with density 8 g/cc, what is the number of unit cells in 108 g of the metal?
(Molar mass of metal = 100 g/mol)

Options

• 2 × 10²⁴

• 2 × 10²³

• 2.7 × 10²²

• 1.33 × 10²⁰

Answer 1

2 × 10²³ 

Explanation:

a = 3 Å = 3 × 10^-8 cm

Volume of the unit cell (a³) = (3 × 10^-8)³ cm³ = 27 × 10^-24 cm³

Mass of unit cell = 27 × 10^-24 cm³ × 8 g cm^-3

= 216 × 10^-24 g

216 × 10^-24 g = 1 unit cell

∴ 180 g = `108/(216 xx 10^-24) = 5 xx 10^23` unit cells.