a metallic object with atoms in a face-centered cubic unit cell with an edge length of 392 pm has a density of 21.45 g/cm^3. calculate the atomic mass and radius of the metal. identify the metal.

The metal = Platinum(Pt)

FCC : Face centered cubic : the unit structures of the unit cell((other than BCC, HCP)

In FCC ⇒ atoms on every corner and side (total 4 atoms)

The length of the face diagonal (b) = 4 times the atomic radius  (r)

Formula :

Ar = atomic mass, g/mol

No = Avogadro number = 6.02.10²³

n = number of atoms

V = volume (cm³)

a = side length  

b = diagonal of the side surface  

r = atomic radius

a= 392 pm=3.92 x 10⁻⁸ cm

ρ = 21.45 g/cm³

The atomic mass :

radius :

Element with atomic mass 195 g/mol and radius = 139 pm (1.386x10⁻⁸cm) = Platinum(Pt)