Calculate the fraction of lattice sites that are Schottky defects for cesium chloride at its melting temperature (645C). Assume an energy for defect formation of 1.86eV.
Number of lattice sites per cubic meter (N)
N=(NA[tex]\rho[/tex])/(ACS + ACL)
Where NA = Avogadros number, [tex]\rho[/tex] = density, ACS = 132.91 g/mol and ACL = 35.45 g/mol
Equilibrium number (NS)
NS = N * e^(-QS/2kT)
Where QS = Schottky defect, k = Boltzmanns Constant, and T = temp in Kelvin
The Attempt at a Solution
I found the density of Cesium Chloride to be 3.99 g/cm^3
N = (6.02.10^23 atoms/mol)(3.99 g/cm^3)(10^6 cm^3/m^3)/(132.91 g/mol + 35.45 g/mol)
From this is I got 1.43 x 10^28 lattice sites/m^3
When I plug this into the NS equation I get 1.16 x 10^24, and I know this is wrong. I am supposed to solve for a NS/N ratio, and the correct answer is 7.87 x 10^-6.
I am not sure what to do here, any help would be appreciated. Thanks