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

Gold has a close-packed structure with a packing fraction value of 0.74. This shows that it has a face-centred cubic cell. The number of ions in a face-centred unit cell is 4.
Now, density `=("mass of unit cell")/("volume of unit cell")`
or `19.3 = (4 xx (197) xx 1.66 xx 10^(-24))/a^(3) , a = 4.07 xx 10^(-8)` cm.
In a face-centred cubic cell,
radius `=(sqrt(2)a)/4 = (sqrt(2) xx 4.07 xx 10^(-8))/4 = 1.439 xx 10^(-8) cm`