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A cubic unit cell contains manganese ion...

A cubic unit cell contains manganese ions at the corners and fluoride ions at the centre of each face.
(a) What is the empirical formula ? (b) What is the C.N. of `Mn^(2+)` ion ?
(c) Calculate the edge length of the unit cell if the radius of `Mn^(2+)` ion is `0.65Å` and that of `F^(-)` ion is `1.36Å`.

Text Solution

Verified by Experts

The correct Answer is:
(a) `MnF^(3)` (b) C.N=6 (c) `4.02Å`
Number of `Mn^(2+)` ions at the corners `=8xx1//8=1`
Numbe of `F^(-)` ions at the centre of the faces `=6xx1//2=3`
Emprirical formula `MnF_(3)`.
(b) C.N. of `Mn^(2+)` ions = 6 (structure being face centred)
(c) `a=2(r^(+)-r^(-))=2(0.65+1.36)=4.02Å`.
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