Test: Number of Atoms in a Unit Cell & Closed-Packed Structures (Old NCERT) - NEET MCQ

Octahedral voids occupy the position of edge centre and body centre.

Octahedral sites are created by overlapping two equilateral triangles with apices in opposite directions.

Number of tetrhedral voids per atom in a unit cell is 2.
Hence the total numberof tetrahedral voids =2n.

(2R)² = (R + r)² + (R + r)²
√2 R = R + r
(√2 - 1)R = r
0.414R = r

ABAB packing is hexagonal closepacking in which all atoms occupy 74% of the total space. Hence, 26% of voids are left in the lattice.

In ccp pattern, fourth layer is identical to first layer.

The coordination number is 12

If the radius ratio is between 0.225 and 0.414, it will have a tetrahedral void. The derivation of this actually takes place in reverse where we assume a tetrahedral void and arrive at the value, but the converse also holds true. A tetrahedral void naturally means there are 4 surrounding atoms. So, coordination number will be 4.

Coordination number of crystal lattices which fall in the range of 0.414 - 0.732 is 6.

Limited Ratio 

⟹r_B− = 290 pm

No. of X atom (at the corners) = 1/8 x 8 = 1
No. of Y atoms (fcc) = 6 × 1/2 = 3
hence, the formula is XY₃ 

No. of X atoms = 1/8 x 8 = 1
No. of Y atoms = 1
No. of Z atoms = 12 x 1/4 = 3
Formula of the compound = XYZ₃

Suppose no. of atoms of Z = a

No. of tetrahedral voids = 2a

No. of atoms of Y = 1/3 × 2a = 2a/3

Ratio of atoms of y and Z= 2a/3 : a = 2:3

Hence, the formula of the compound = Y₂Z₃

No. of atoms of P = 8 x 1/8 = 1
No. of atoms of Q = 1 x 1 = 1
The formula of the compound is PQ. Coordination no. of P and Q = 8:8

Each Na⁺ ion is surrounded by 6 Cl^-ions and each Cl^- ion is surrounded by 6 Na⁺ ions in NaCl crystal.

Octahedral sites are occupied by Na⁺ ions in NaCl structure.

Increase of pressure increases coordination number. Hence, by applying high pressure, NaCl type crystal can be changed into CsCl type crystal

CsCl has a bcc structure. Each Cs ion is surrounded by 8 Cl⁻ ions and each Cl⁻ ion is surrounded by 8 Cs⁺ ions. CsCl has a bcc type structure. Thus, the structure has 8 : 8 coordination number.

ZnS has a ccp structure. S²⁻ ions are present at the corners of the cube and centre of each face. Zn²⁺ ions occupy half of the tetrahedral sites. Each Zn²⁺ ion is surrounded by four S²⁻ ions and each S²⁻ ion is surrounded by four Zn²⁺ ions.

ZnS has a ccp structure. S^2- ions at the corners of the cube and centre of each face. Zn²⁺ ions occupy half of the tetrahedral sites. Each Zn²⁺ ion is surrounded by four S^2- ions and each S^2- ion is  surrounded by four Zn²⁺ ions.

Coordination no. of Y (Zn²⁺) is 4.

Each X ion is surrounded by 4Y ions.

Ca²⁺ ions form ccp structure while F^- ions in all tetrahedral holes and coordination numbers are 8 and 4.

In fluorite structure, cations form ccp structure and anions are present in all tetrahedral holes. Hence, no. of Ba2+ ions =8 and no. of Cl− ions = 4

In NaCl type, Cl⁻ ions form ccp structures while Na⁺ ions are present in all octahedral voids.