Match List I with List II. List I (Lattice point) List II (Contributi…

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)