chemistry : class12 Nonprimitive Unit Cell : Crystalline solids : Solid State MCQ Questions and Answers
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Nonprimitive Unit Cell
MCQ questions and answers.
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MCQ Questions
1. A unit cell has lattice points at all eight corners and at the centers of all six faces, with no lattice point at its body center. How many lattice points are effectively associated with this unit cell, and what type of unit cell is it?
A.
2; body-centred unit cell
B.
4; face-centred unit cell
C.
6; base-centred unit cell
D.
8; primitive unit cell
Correct Answer:
4; face-centred unit cell
Explanation:
The eight corner points contribute 8 × 1/8 = 1, while the six face-centre points contribute 6 × 1/2 = 3. Therefore, the unit cell contains 4 lattice points and is face-centred, a nonprimitive unit cell.
2. A conventional unit cell contains one lattice point at each corner, one at the body centre, and one at the centre of each pair of opposite faces. How many lattice points belong effectively to this cell?
A.
2
B.
3
C.
4
D.
5
Correct Answer:
3
Explanation:
The corner points contribute 1, the body-centre point contributes 1, and the two face-centre points contribute 2 × 1/2 = 1. Thus, the total is 3 lattice points, characteristic of a base-centred nonprimitive unit cell.
3. Which modification of a primitive cubic unit cell produces a body-centred nonprimitive unit cell without changing the positions of the corner lattice points?
A.
Adding lattice points at the centres of all six faces
B.
Adding one lattice point at the centre of the cube
C.
Adding lattice points at the midpoints of all twelve edges
D.
Removing four of the eight corner lattice points
Correct Answer:
Adding one lattice point at the centre of the cube
Explanation:
A body-centred unit cell retains the eight corner lattice points and includes one additional lattice point at the body centre. Its effective lattice-point count becomes 1 + 1 = 2, so it is nonprimitive.
4. A cubic unit cell has an effective lattice-point count of four. If its only lattice points are located at corners and face centres, which statement is necessarily correct?
A.
It is a primitive cubic unit cell
B.
It is a body-centred cubic unit cell
C.
It is a face-centred cubic unit cell
D.
It is a base-centred cubic unit cell
Correct Answer:
It is a face-centred cubic unit cell
Explanation:
A cubic cell with corner and face-centre lattice points has 1 effective point from corners and 3 from six face centres, giving 4 in total. This is the face-centred cubic nonprimitive unit cell.
5. In a nonprimitive unit cell, a lattice point located at the centre of one face is shared equally by how many adjacent unit cells, and what fraction is assigned to the selected unit cell?
A.
Two unit cells; 1/2
B.
Four unit cells; 1/4
C.
Six unit cells; 1/6
D.
Eight unit cells; 1/8
Correct Answer:
Two unit cells; 1/2
Explanation:
A face-centre lattice point lies on the common boundary of two unit cells. Therefore, each unit cell is assigned one-half of that lattice point.
6. A unit cell contains eight corner lattice points, three lattice points at the centres of mutually perpendicular pairs of opposite faces, and one body-centre lattice point. What is its effective number of lattice points?
A.
3
B.
4
C.
5
D.
6
Correct Answer:
5
Explanation:
The corners contribute 8 × 1/8 = 1, the six face-centre points contribute 6 × 1/2 = 3, and the body-centre point contributes 1. The total effective count is 1 + 3 + 1 = 5.
7. Which set of lattice-point contributions correctly represents a face-centred nonprimitive unit cell?
A.
8 × 1/8 + 1 = 2
B.
8 × 1/8 + 6 × 1/2 = 4
C.
8 × 1/8 + 12 × 1/4 = 4
D.
6 × 1/2 + 1 = 4
Correct Answer:
8 × 1/8 + 6 × 1/2 = 4
Explanation:
A face-centred unit cell has eight corner lattice points and six face-centre lattice points. Their contributions are 1 and 3, respectively, giving four effective lattice points.
8. A nonprimitive cubic unit cell has lattice points at all eight corners and at the midpoints of all twelve edges, but nowhere else. What is its effective lattice-point count?
A.
2
B.
3
C.
4
D.
6
Correct Answer:
4
Explanation:
The eight corners contribute 1. Each edge-centre point is shared by four unit cells, so the twelve edge points contribute 12 × 1/4 = 3. Hence, the total is 4 effective lattice points.
9. A unit cell has an effective lattice-point count of two and contains a lattice point at the centre of the cell. If all eight corners are also occupied, which type of nonprimitive unit cell is represented?
A.
Face-centred
B.
Base-centred
C.
Body-centred
D.
Edge-centred
Correct Answer:
Body-centred
Explanation:
The eight corner points contribute one effective lattice point, and the lattice point at the body centre contributes one more. The total of two identifies a body-centred nonprimitive unit cell.
10. Two adjacent unit cells share a complete face containing a lattice point at its centre. If that face-centre point is counted independently in both cells, what error occurs in the total lattice-point count for the pair?
A.
The shared point is omitted once
B.
The shared point is counted twice instead of once
C.
The shared point is counted four times instead of twice
D.
The shared point contributes one-half to neither cell
Correct Answer:
The shared point is counted twice instead of once
Explanation:
A face-centre lattice point belongs half to each of the two adjacent cells, so the pair should contain one complete lattice point. Counting it fully in both cells counts it twice and produces an overcount of one lattice point.
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