Gold (r = 0.144nm) crystallises in a face-centred unit cell. What is the length of a side of the cell?

Explanation

In a face-centred cubic unit cell, relation between radius ( r) of atoms and edge-length (a) of unit cell : r = `a/(2sqrt2)`
Given: r = 0.144 nm
`therefore" "a=0.144xx2sqrt2nm=0.407nm`
`therefore" "` The edge length of the unit cell = 0.407 nm