The atomic radius of metal x is 1.20 × 102 picometers (pm) and a crystal of metal x has a unit cell that is face-centered cubic. calculate the density of metal x? (atomic weight = 42.3 g/mol)

The density of metal X is

Explanation:

We are given:

Atomic radius of metal X =

To calculate the edge length, we use the relation between the radius and edge length for FCC lattice:

Putting values in above equation, we get:

To calculate the density of metal, we use the equation:

where,

= density

Z = number of atom in unit cell = 4  (FCC)

M = atomic mass of metal = 42.3 g/mol

= Avogadro's number =

a = edge length of unit cell =    (Conversion factor:    )

Putting values in above equation, we get:

Hence, the density of metal X is