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What is the formula of AB solid in which A atoms are face-centred and B atoms are available on eight edges of side:A.$A{B_2}$B.${A_2}{B_{}}$C.${A_4}{B_3}$D.${A_3}{B_2}$

Last updated date: 15th Sep 2024
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Hint: To answer this question you should recall the concept of close packing in a solid crystal. Voids refer to the gaps between the constituent particles. These voids in solid crystals mean the vacant space between the constituent particles

Complete Step by step solution:
As (A) Atoms are present on the face centre. Thus effective atoms are:
A $= \dfrac{1}{2} \times 6 = 3$

As (B) atoms are present on eight edges. Thus effective atoms are:
B = $\dfrac{1}{4} \times 8 = 2$
Hence, the $AB$ solid contains 3 atoms of A and 2 atoms of B.
Hence, the formula becomes ${A_3}{B_2}$

Thus, the correct option is option D.

Note: Crystalline solids show regular and repeating pattern arrangement of constituent particles resulting in two types of interstitial voids in a 3D structure:
1.Tetrahedral voids: In case of a cubic close-packed structure, the second layer of spheres is present over the triangular voids of the first layer. This results in each sphere touching the three spheres of the first layer. When we join the centre of these four spheres, we get a tetrahedron and the space left over by joining the centre of these spheres forms a tetrahedral void.
2.Octahedral voids: Adjacent to tetrahedral voids you can find octahedral voids. When the triangular voids of the first layer coincide with the triangular voids of the layer above or below it, we get a void that is formed by enclosing six spheres. This vacant space which is formed by the combination of the initial formed triangular voids of the first layer and that of the second layer is known as Octahedral Voids.