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

Answer in Brief
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)

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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

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