# Gold Occurs as Face Centred Cube and Has a Density of 19.30 Kg Dm-3. Calculate Atomic Radius of Gold - Chemistry

Sum

Gold occurs as face centred cube and has a density of 19.30 kg dm-3. Calculate atomic radius of gold (Molar mass of Au = 197)

#### Solution

Unit cell of FCC =1/8xx8+6xx1/2

=4 atoms

Mass of unit cell of FCC  =4xx197/(6.022xx10^23)

=130.85 x 10-23g

rho=19.3 g/cm-3

Volume of unit cell=(130.85xx10^-23)/19.3

=6.78x10-23 cm3

a3=6.78x10-23

a is edge of unit cell

a= root(3)(6.78xx10^(-23)

=4.08x10-8 cm

For FCC

a=sqrt8.r

r=a/sqrt8=(4.08xx10^(-8))/sqrt8

r=1.44x10-8 cm

r=144 pm

Concept: Number of Atoms in a Unit Cell
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