Class 12 Chemistry The Solid State Placing third layer over the second layer , Covering Octahed

Placing third layer over the second layer : Covering Octahedral Voids

  • The third layer may be placed above the second layer in a manner such that its spheres cover the octahedral voids.
  • When placed in this manner, the spheres of the third layer are not aligned with
    those of either the first or the second layer. This arrangement is called “C’
  • Only when fourth layer is placed, its spheres are aligned with those of the first layer.
  • This pattern of layers is often written as ABCABC........... This structure is called cubic close packed (ccp) or face-centered cubic (fcc) structure.

  • Metals such as copper and silver crystallize in this structure. Both these types of close packing are highly efficient and 74% space in the crystal is filled. In either of them, each sphere is in contact with twelve spheres. Thus, the coordination number is 12 in either of these two structures.

Question: A compound is formed by two elements M and N. The element N
forms ccp and atoms of M occupy 1/3rd of tetrahedral voids. What
is the formula of the compound?

Answer: The ccp lattice is made by the atoms of the element N.

Here, the Number of tetrahedral voids = 2 X number of particles of the elements N.

According to the question, the atoms of element M occupy = 1/3rd of the tetrahedral voids.

Therefore, the number of atoms of M is equal to

 2 x 1/3 = 2/3rd of the number of atoms of N.

Therefore, the ratio M:N = 2/3 :1   = 2:3

Hence formula of the compound is M2N3.

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