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
p = ` ( Z xx M)/ (a^(3) xx N_(0)) therefore 19.3 = ( 4 xx 197)/ (a^(3) xx 6.023 xx 10^(23)) or a= 4.07 xx 10^(-8) ` cm
For fcc, ` r = a / (2sqrt2) = ( 4.07 xx 10^(-8))/ (2xx 1.414) = 1.439 xx 10^(-8) ` cm