Question

Obtain the relationship between density of a substance and the edge length of unit cell

Answer 1

The density of a substance is given as d = zM/a³NA.

- Let:

d = density

a = edge length

z = no of atoms per unit cell

M = molar mass

NA = Avogdro no.

- The volume of 1 unit cell = a³

- The mass of one atom, m = M/NA

- Mass of one unit cell = no of atoms per unit cell × Mass of each atom = z × m = z × M / NA

- Now, density = mass of one unit cell/volume of one unit cell

⇒ d = (z × M)/ (a³ × NA)

- This is the required relationship.