Question

A metal crystallises as body centred cubic lattice with the edge length of unit cell equal to 0.304um. If the molar mass of the metal is 50.3 gmol⁻¹,its density is

A. 5.945g cm⁻³
B. 2.9725g cm⁻³
C. 8.9175g cm⁻³
D. 4.458g cm⁻³

Answer 1

The density of the metal is approximately 8.9175 g/cm³.

How can you solve the density of the metal?

Volume of the unit cell (V cell) = a³ = (0.304 µm * 10^-6 m/µm)³ ≈ 2.712 x 10⁻²³ m³

Mass of one unit cell (m_cell) = N * M / 1000 (to convert molar mass to grams)

m cell = 2 * 50.3 g/mol * 1 g/1000 g/mol ≈ 0.1006 g

Density (ρ) = mass / volume

ρ = m cell / V cell = 0.1006 g / 2.712 x 10⁻²³ m³≈ 3.709 x 10⁻²² m³

ρ = 3.709 x 10^22 g/m² * (1 cm/10⁻² m)³ ≈ 8.9175 g/cm³

Therefore, the density of the metal is approximately 8.9175 g/cm³.