Calculate energy for vacancy formation in silver given that

Calculate energy for vacancy formation in silver given that the equilibrium number 800 C (1073 K, is 3.6 x 10^22/m^2. The atomic weigh, and density (at 800 C) for silver are. 107.9 g/mol and 9.5 g/cm^2. The following table shows the atomic radius, crystal structure, electronegativity and common valence for several elements; for those that are nonmetals, only atomic radii Which of these elements would you expect to form the following with copper: A substitution solid solution of incomplete solubility? An interstitial solid solution?

Solution

Nv = N e^ (-E/kt)   ...............................................1

Where Nv = 3.6 * 10^23

k = 1.38 * 10^-23

T = 1073 K

and E is the energy

N = Avogadro number * density / atomic weight = (6.023 * 10^23 * 9500)/(107.9) = 5.303 * 10^25

Taking log on both sides on equation 1, we get

ln (Nv) = ln N - (E/kT)

ln N/Nv = E/kT

E = 7.392 * 10^-20 J