Tiêu đề 4.SOLID STATE - ISM SIR.pdf ✅

SOLID STATE 128 NISHITH Multimedia India (Pvt.) Ltd., JEE ADVANCED - VOL - VI NISHITH Multimedia India (Pvt.) Ltd., FCC Unit Cell : In a FCC unit cell, each corner atom is shared by 8 unit cells and each face centered atom is shared by 2 unit cells, so the number of effective atoms in a FCC unit cell would be 1 1 8 6 4 8 2                 . Thus the rank of a FCC unit cell is 4, This is shown in Figure. HCP Unit Cell : Hexagonal Close Packing: Each corner atom would be common to 6 other unit cells, therefore their contribution to one unit cell would be 1/6. Total number of atom in 1 hcp unit cell = 12 6 (from 12 corners) + 2 2 (from 2 face centred) + 3 1 (from body centre) = 6. (a) (b) Hexagonal closest packing of spheres: (a) normal and (b)diagramatic view Illustration 1: What is the simplest formula of a solid whose unit cell has the atom A at each corner, the atom B at each face centre and a atom C at the body centre. (A) A2 BC (B) AB2 C (C) AB3 C (D) ABC2 Solution: An atom at the corner of a cube is shared among 8 unit cells. As there are 8 corners in a cube, number of corner atom (A) per unit cell 1 8 1 8         A face-centred atom in a cube is shared by two unit cells. As ther are 6 faces in a cube, number of face-centred atoms (B) per unit cell = 6  1 2 = 3. An atom in the body of the cube is not shared by other cells.  Number of atoms (C) at the body centre per unit cell = 1. Hence (C), the formula of the solid is AB3 C. Illustration 2: Potassium crystallizes in a body centred cubic lattice. What is the approximate number of unit cells in 4.0g of potassium? Atomic mass of potassium = 39 (A) 3.09 × 1022 (B) 2.09 × 1021 (C) 4.10 × 1021 (D) 3.09 × 1020 Solution: There will be eight atoms at corners of the cube and one atom at the body centre.  Number of atoms per unit cell = 1 8 8        + 1 = 2  Number of unit cells in 4.0 g of potassium = 23 4 6.023 10 39 2   = 3.09 × 1022 Hence ‘A’ is the correct Choice. In CCP unit cell there are 8 tetrahedral voids and 4 octahedral voids. No. of tetrahedral voids in an unit cell = No. of octahedral voids ́ 2 * The HCP and CCP arrangements can also be shown as below :
NISHITH Multimedia India (Pvt.) Ltd., 129 JEE MAINS - CW - VOL - I JEE ADVANCED - VOL - VI SOLID STATE NISHITH Multimedia India (Pvt.) Ltd., a b b (a) (b) (a) (b) Hexagonal closest packing of spheres: (a) normal and (b) exploded view Fig : Cubic closest packing of spheres : (a) generation of unit from closest packed layers and (b) rotation to show cubic symmetry. VOIDS IN FCC UNIT CELL Tetrahedral voids : Fig. (a) Eight tetrahedral voids per unit cell of ccp strcutre (b) One tetrahedral voids showing the geometry. (a) (b) Octahedral voids : Octahedral Void Octahedron Fig. Location of octahedral voids per unit cell of ccp or fcc lattice. At the body centre of the cube and at the centre of each edge. Illustration 3: Ferric oxide crystallizes in a hexagonal close packed array of oxide ions with two out of Every three. Octahedral holes occupied by ferric ions. The formula of the ferric oxide is (A) FeO (B) Fe3O4 (C) Fe2O3 (D) None of these Solution : Suppose the number of oxide ions (O2–) in the packing = N. No. of octahedral voids = N