Solid State Test - 19

(d) CsCI has bcc structure.
Closest dista nce between Cs⁺ and Cl^- is the sum of radii of Cs⁺ and CI^- = 169 + 181 = 350 pm

Cubic diagonal = √3 a

Closest distance is one-half of the cubic diagonal

(d) AB₂ crystallises as cubic close packed (ccp).

Thus, A²⁺ is surrounded by eight B^- and B^- is surrounded by four A²⁺ .

Thus, coordinatio n number of A²⁺ = B

coordination number of B^- = 4

Number of atoms in tetrahedral in small cube of unit cell of atom B = 4

Thus, fraction occupied = 4/4 = 1 (100%)

(c)

AB = a, AC = a

BC² = AB² + AC² =2a²

Radius =r

then BC = CD + DE + EB = r + 2r + r = 4r 

∴ 16r² = 2a²

(c)

Tetrahedral holes = 8, Octahedral holes = 4 Cobalt atoms = 8/8 =1

Oxide ions = 4/2 =2

Thus, formula is CoO₂

(b) Unit cell of fee is divided into eight small cubes. Each cube has four atoms at alternate positions. When joined to each other, they make a regular tetrahedron.
Thus, number of tetrahedral void in small cube = 1 and in eight cubes, voids = 8.

Note  If number of atoms in a cube = N, then, number of octahedral voids = N and number of tetrahedral voids = 2N

(a) Edge length = a, Volume of one face = a³ Volume of six faces of a cube = 6a³ = V Radius = r

fee can be hexagonal closest packed (hep)

or cubic closest packed (ccp)

z = number of atoms in unit cell.

(c) Close packing in two-dimensions can be Type I A A A ...... ty p e The second row may be ^ placed in contact with the first one such that the spheres of A the second row are exactly . above those of the first row.
The spheres of the two rows A are aligned horizontally as well as vertically. In this arrangement, each sphere is in contact with four of its neighbours.
Thus, its coordination number = 4 and is called square close packing in two-dimensions.
Atom A (•) is in contact with four others.

Type II ABAB... type The second row may be placed above the first in a staggered manner such that its spheres fit in the depressions of the first row.
First row arrangement: A type Second row arrangement: 8 type Third row arrangement: A type and so on There is less free space and packing is more efficient than the square close packing. Each sphere is in contact with six of its neighbours and coordination number = 6 in two-dimensions. It is called two dimensional hexagonal close-packing. Voids formed in this case are triangular in shape. If the apex of the triangles downward in the first row, it is upward in the second row.

 (a)

In a bcc structure, the atoms tou ch each other along the body diagonal.

Radius of the atom = r

AB² = 8C² + AC² 
BC² = BD² + CD² = a² + a² = 2a² 

Volume of one atom = 

Volume of N₀ atoms in one mole of the metal

= 6.02 x 10²³ x 1.48 x 10^-23 cm³ = 8.93 cm³

(b)

Structure is cubic close packing.
Number of atoms of M = (from edge centre) +1 (from body centre) =2

Number of atoms of X =   (from corners of the cube) +  (from face centre)  =4

Thus, M : X = 2 : 4 = 1 : 2 Hence, the empirical formula of the compound is MX₂.

(a) Ratio of r+ /r_ will decid e the type of unit cell 

For AX    hence, AX has bcc structure.

Thus, octahedral or square planar structure.

(i)

Body-centred cubic Every cation (Cs⁺) is coordinated to eight anions (Br^- ) and every anion (Br^- ) is coordinated to eight cations (Cs⁺).
Thus, (i) -> (s)

(ii) Face-centred cubic Every cation (Na⁺) is coordinated to six anions (Cl^- ) and every anion (Cl^- ) is coordinated to six cations (Na⁺).
Thus, (ii) -> (q)

(iii) Face-centred cubic (tetrahedral void) Every cation (Zn²⁺) is coordinated to four anions (S^2-) and vice-versa.
Thus, (iii) —> (p)

(iv) Face-centred cubic (antifluorite) EveryCa²⁺ is coordinated to eight fluoride and every F^- is coordinated to fourCa2+ (to balance charge).

4Ca²⁺ + 8F^-
Thus, (iv) —> (r)