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A compount AB has a rock type structure ...

A compount `AB` has a rock type structure with `A:B=1:1`. The formula weight of `AB` is `6.023 Y am u` and the closed `A-B` distance is `Y^(1//3) nm.`
`(i)` Find the density of lattice.
`(ii)` If the density of lattice is found to be `20 kg m^(-3)`, then predict the type of defect.

Text Solution

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Calculations of the density of unit cell.
Density `(rho)=(ZxxM)/(N_(0)xx(a)^(3))`
For Rock salt structure (Z) = 4 , M = 6.022 Y amu = 6.022 g `mol^(-1)`
`N_(0)=6.022xx10^(23)"mol"^(-1),a=2Y^(1//3)nm=(2xxY^(1//3)xx10^(-9)m)`
`therefore" Density"(rho)=(4xx(6.022"Y g mol"^(-1)))/((6.022xx10^(23)"mol"^(-1))xx(2xxY^(1//3)xx10^(-9)"mol")^(3))`
`=5xx10^(3)"g mol"^(-1)="5 kg mol"^(-1)`
(b) Type of the point defect.
The measured density of unit cell = `"20 kg m"^(-3)`
Since the measured density of unit cell is very high as compared to calculate density, the crystal suffers from metal excess defect.
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