A face centered cubic solid of an element ( atomic mass 60) has a cube edge of `4Å`. Calculate its density.

Explanation

Edge length `= 4 Å = 4 xx 10^(-8) cm`
Volume of unit cell = ` ( 4 xx 10^(-8) cm)^(3)`
` 64 xx 10^(-24) cm^(3)`

Mass of the unit cell = Number of atoms in the unit cell ` xx ` mass of each atom
Number of atoms in the fcc unit cell
` 8 xx 1/8 + 6 xx 1/2 = 4`
mass of one atom =` (" Atomic Mass")/( " Avogadro number") `
` = 60/( 6.023 xx 10^(23))`
Mass of the unit cell = ` ( 4 xx 60)/( 6.023 xx 10^(23))`
Density of uint cell = ` ("Mass of unit cell")/( " Volume of unit cell") `
` Rightarrow ( 4 xx 60)/( 6.023 xx 10^(23)) xx 1/(64 xx 10^(-24))`
` Rightarrow 6.2 g cm^(-3)`