1. Tardigrade
  2. Question
  3. Chemistry
  4. In crystalline solids atoms or molecules are arranged in a regular and long range order fashion in a three dimensional pattern. These have sharp melting point, flat faces, sharp edges, bounded by well defined planes. A large number of unit cells, each of which possess a definite geometry bounded by plane faces give rise to the formation of a crystal. A point at the corner of unit cell contributes for 1 / 8 of each such point to unit cell. A point along an edge contributes for 1 / 4 of each such point to unit cell. A body centred point contributes for 1 each such points to unit cell. Coordination number is the number of nearest neighbours that each is surrounded by an oppositely charged ions. Radius of unit cell in sc, fcc and bcc is (a/2), (a/2 √2) and (√3 a/4) where a is edge length of cell. A mineral having the formula A B2 crystallises in the cubic closed packed lattice, with A2+ atoms occupying the lattice points and B-tetrahedral voids. The co-ordination number of A, B and fraction of the tetrahedral sites occupied by B atom respectively are:

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Q. In crystalline solids atoms or molecules are arranged in a regular and long range order fashion in a three dimensional pattern. These have sharp melting point, flat faces, sharp edges, bounded by well defined planes. A large number of unit cells, each of which possess a definite geometry bounded by plane faces give rise to the formation of a crystal. A point at the corner of unit cell contributes for $1 / 8$ of each such point to unit cell. A point along an edge contributes for $1 / 4$ of each such point to unit cell. A body centred point contributes for 1 each such points to unit cell. Coordination number is the number of nearest neighbours that each is surrounded by an oppositely charged ions. Radius of unit cell in sc, fcc and bcc is $\frac{a}{2}, \frac{a}{2 \sqrt{2}}$ and $\frac{\sqrt{3} a}{4}$ where $a$ is edge length of cell.
A mineral having the formula $A B_2$ crystallises in the cubic closed packed lattice, with $A^{2+}$ atoms occupying the lattice points and $B^{-}$tetrahedral voids. The co-ordination number of $A, B$ and fraction of the tetrahedral sites occupied by $B$ atom respectively are:

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Solution:

$A B_2$ has bcc structure, $A^{2+}$ possess face centred cubic lattice. $B^{-}$ions occupy all the ( $\left.100 \%\right)$ tetrahedral voids. Thus each $A^{2+}$ is in contact with $B^{-}$and each $B^{-}$with $4 A^{2+}$ ions.