$(12,00$ Puanlar$)$

$4.$ Ceramic compounds $AB$ and $AC$ both have the zinc blende crystal structure and are soluble in one another at all concentrations. Determine the concentration in weight percent of $AC$ that must be added to $AB$ to yield a unit cell edge length of $0\mathrm{.}5304nm.$ The densities of $AB$ and $AC$ are $4\mathrm{.}8\frac{g}{c}{m}^3$ and $4\mathrm{.}2\frac{g}{c}{m}^3,$ respectively. The atomic weights of $A,B,$ and $C$ are $30,80,$ and $60\frac{g}{m}ol,$ respectively.