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Br^- ions form a close packed structure....

`Br^-` ions form a close packed structure. If the radius of `Br^–` ions is 195 pm, calculate the radius of the cation that just fits into the tetrahedral hole. Can a cation `A^+` having a radius of 82 pm be shipped into be octahedral hole of the crystal `A^+ Br^–` ?

Text Solution

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Radius of cation just fitting into tetrahedral hole = Radius of tetrahedral hole
`= 0.225xx r_(Br^(-))`
`= 0.225xx195=43.875` pm
Radius ratio `((r^(+))/(r^(-)))=(82)/(195)=0.4205`
This radius ratio lies in the range 0.414 - 0.732 hence, cation can slip into octahedral hole.
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