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A crystalline ionic compound consisting ...

A crystalline ionic compound consisting of `M^(+)andX^(-)` ions crystallises in cubic structure. The unit cell of the compound has `M^(+)` ions at its corners and an `X^(-)` ion at its body centre. Determine the simplest formula of the compound.

Text Solution

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`M^(+)` ions are at the corners of the cubic unit cell, each of which is shared equally by eight adjoining cubes. There are eight corners per cube. Therefore, number of `M^(+)` ions per unit cell `=8xx1/8=1`.
One `X^(-)` ion is at the body centre of the cubic unit cell. It is wholly within the unit cell, and hence its contribution to the unit cell is 1. Thus the unit cell contains one `X^(-)` ion.
Therefore, the ratio of `M^(+)` to `X^(-)` ions in the unit cell is `1:1`. Hence the simplest formula of the compound would be MX.
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