Question

A metallic element crystallises 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 100 g of the metal?

(Molar mass of metal = 108 g/mol)

Options

• 1.33 × 10²⁰

• 2.7 × 10²²

• 2 × 10²⁴

• 5 × 10²³

Answer 1

5 × 10²³

Explanation:

Given, Edge length (a) = 3 Å = (3 × 10⁻⁸) cm ............[1 A = 1 × 10⁻⁸ cm]

Density = 8 g/cc

Volume of unit cell = (edge length)³

= (3 × 10⁻⁸ cm)³

= 27 × 10⁻²⁴ cm³

Mass of unit cell = volume × density

= 27 × 10⁻²⁴ × 8

Number of unit cell in 100 g = `100/(27 xx 10^-24 xx 8)`

= 5 × 10²³