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X-ray diffraction studies show that edge...

X-ray diffraction studies show that edge length of a unit cell of NaCl is 0.56 nm. Density of NaCl was found to be `2.16g//"cc".` What type of defect is found in the solid? Calculate the percentage of `Na^(+)` and `Cl^(-)` ions that are missing.

Text Solution

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Density `(rho)=(z xxM)/(N_(o)xx a^(3))`
`= (4xx58.5)/(6.023xx10^(23)xx(0.5627xx10^(-7))^(3))`
`= 2.1805 g//cm^(3)`
Observed density `= 2.164 g//cm^(3)` which is less than calculated density because some ions are missing.
Actual constant units per unit cell can be calculated as :
`z = (rho xx N_(o)xx a^(3))/(M)`
`= (2.164xx6.023xx10^(23)xx(0.5627xx10^(-7))^(3))/(58.5)`
= 3.969
Missing units `= 4-3.969 = 0.031`
`therefore` % missing of `Na^(+)` and `Cl^(-)=(0.031)/(4)xx100 = 0.775 %`
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