A compound AB has rock salt type structure. The formula weight of AB is 6.023 Y amu, and the closest

Question

A compound AB has rock salt type structure. The formula weight of AB is 6.023 Y amu, and the closest A-B distance is $Y^{1/3}$ nm, where Y is an arbitrary number. Find the calculated density of lattice in $kg~m^{-3}$. If the observed density of lattice is found to be $20~kg~m^{-3}$, predict the type of defect present.

Professor PC Thomas Classes · Answer

Closest A-B distance = $a/2 = Y^{1/3}~nm \Rightarrow a = 2Y^{1/3} 	imes 10^{-9}~m$. For rock salt (fcc), $Z = 4$. Molar mass = $6.023Y~g/mol = 6.023Y 	imes 10^{-3}~kg/mol$. Density $= \frac{Z 	imes M}{N_A 	imes a^3} = \frac{4 	imes 6.023Y 	imes 10^{-3}}{6.023 	imes 10^{23} 	imes 8Y 	imes 10^{-27}} = 5~kg~m^{-3}$. Since observed density ($20~kg~m^{-3}$) > calculated density, interstitial atoms must be present, indicating a metal excess defect.