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

Explanation

Edge length `= 4Å = 4.00 xx 10^(-10) cm`
Volume of unit cell `= ( 400 xx 10^(-10) cm ) `
`= 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 unit cell `= (" Mass of unit cell")/( "Volume of unit cell")`
`rArr ( 4 xx 60)/( 6.023 xx 10^(23)) xx(1)/( 64 xx 10^(-24))`
`rArr 6.2 gcm^(-3)`