Gold has a close-packed structure which can be viewed as-spheres occupying 0.74 of the total volume. If the density of gold is 19.3 g/cc, calculate the apparent radius of a gold ion in the solid

Explanation

As the packing fraction is 0.74 , packing can be hcp or fcc. Knowing that gold has fcc lattice, Z=4
`rho=(ZxxM)/(a^3xxN_0) " " therefore 19.3=(4xx197)/(a^3xx6.023xx10^23) "or" a=4.07xx10^(-8)` cm
For fcc, `r=a/(2sqrt2)=(4.07xx10^(-8))/(2xx1.414)=1.439xx10^(-8)` cm