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A compound consisting of the monovalent ...

A compound consisting of the monovalent ions `A^+ ,B^-` crystallizes in the body-centred cubic lattice. (i)What is the formula of the compound ? (ii)If one of `A^+` ions from the corner is replaced by a monovalent ions `C^+`, what would be the simplest formula of the resulting compound ?

Text Solution

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(i)Contribution of `A^+` ions present at the corners towards unit cell =`8xx1/8=1`
Contribution of `B^-` ion present at the body-centre=1
`therefore` Ratio of `A^+ :B^-` =1:1 .Hence , the formula is AB.
(ii)`A^+` ions at the corners =7. Hence, their contribution towards unit cell=`7/8`
`C^+` ion at one corner contributes =`1/8`
`B^-` ion at the body centre has contribution =1
Hence, ratio of A:B:C=`7/8:1/8:1=7:1:8 therefore ` Formula will be `A_7BC_8`
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