Practicing Success

Target Exam

CUET

Subject

Chemistry

Chapter

Physical: Solid State

Question:

Match List I with List II.

List I

(Lattice point)

List II

(Contribution)

(A) Corner of cube (I) 1
(B) Edge of cube (II) \(\frac{1}{2}\)
(C) Face of cube (III) \(\frac{1}{4}\)
(D) Body-centre (IV) \(\frac{1}{8}\)

 

Options:

(A)-(I), (B)-(III), (C)-(II), (D)-(IV)

(A)-(IV), (B)-(III), (C)-(II), (D)-(I)

(A)-(III), (B)-(II), (C)-(IV), (D)-(I)

(A)-(II), (B)-(I), (C)-(III), (D)-(IV)

Correct Answer:

(A)-(IV), (B)-(III), (C)-(II), (D)-(I)

Explanation:
The correct answer is option 2. (A)-(IV), (B)-(III), (C)-(II), (D)-(I)
 

List I

(Lattice point)

List II

(Contribution)

(A) Corner of cube (IV) \(\frac{1}{8}\)
(B) Edge of cube (III) \(\frac{1}{4}\)
(C) Face of cube (II) \(\frac{1}{2}\)
(D) Body-centre (I) 1

To match List I (Lattice Point ) with List II (contributions), we need to understand how atoms at different positions within the unit cell contribute to the overall lattice structure.

1. Corner of Cube: An atom at the corner of the cube is shared among 8 unit cells, so its contribution to one unit cell is \(\frac{1}{8}\).

2. Edge of Cube: An atom at the edge of the cube is shared among 4 unit cells, so its contribution to one unit cell is \(\frac{1}{4}\).

3. Face of Cube: An atom on the face of the cube is shared between 2 unit cells, so its contribution to one unit cell is \(\frac{1}{2}\).

4. Body-Centre: An atom at the body center of the cube belongs entirely to that unit cell, so its contribution is 1.

Given these points:

(A) Corner of cube \(\rightarrow\) (IV): A corner atom's contribution of \(\frac{1}{8}\) per unit cell is correct for 8 corners contributing to one atom per unit cell.

(B) Edge of cube \(\rightarrow\) (III): An edge atom's contribution of \(\frac{1}{4}\) per unit cell matches with 12 edges contributing to 3 atoms per unit cell (though typically there are 12 edges, each contributing \(\frac{1}{4}\)).

(C) Face of cube \(\rightarrow\) (II): A face atom's contribution of \(\frac{1}{2}\) per unit cell matches with 6 faces contributing to 3 atoms per unit cell.

(D) Body-centre \(\rightarrow\) (I): A body-centered atom's contribution of 1 is correct as it is wholly within one unit cell.

Thus, the correct answer is: (A)-(IV), (B)-(III), (C)-(II), (D)-(I)