Metallic gold crystallizes in the fcc lattice.
The length of the cubic unit cell is `a = 4.242 A`.
a. What is the closest distance between gold atoms?
b. How many "nearest neighbours" does each gold atom have at the distance calculated in `(a)`?
(c) What is the density of gold? (Aw of Au `= 197.0 g mol^(-1)`)
d. Prove that the packing factor for gold is `0.74`.

Explanation

a = 4.07 Å
(a) `4r=asqrt(2)`
`r=(asqrt(2))/(4)=(4.07xx1.414)/(4)=1.44 Å`
Closest distance between An atoms = 2.88Å
(b)C.N=12
( c) `d=(ZM)/(a^(3)N_(A))=(4xx196)/((4.07xx10^(-8))xx6.023xx10^(23))`
=19.4 `gm//cc`