Which of following unit cell does not exist in cubic system?

Options

A. primitive
B. body centered
C. face centered
D. end centered

Explanation

To determine which of the following unit cells does not exist in the cubic system, we need to analyze each option provided:

1. **Primitive Cubic (P)**: In a primitive cubic unit cell, there is one atom at each of the eight corners of the cube. This structure does exist in the cubic system.

2. **Body-Centered Cubic (BCC)**: In a body-centered cubic unit cell, there are atoms at each of the eight corners and one atom at the center of the cube. This structure also exists in the cubic system.

3. **Face-Centered Cubic (FCC)**: In a face-centered cubic unit cell, there are atoms at each of the eight corners and one atom at the center of each of the six faces of the cube. This structure exists in the cubic system as well.

4. **N-Centered**: An n-centered unit cell would require that the unit cell has vectors a ≠ b ≠ c, which is not possible in a cubic system where all sides are equal (a = b = c) and all angles are 90 degrees. Therefore, an n-centered unit cell does not exist in the cubic system.

Based on this analysis, the answer is that the **N-Centered unit cell does not exist in the cubic system**.

### Step-by-Step Solution:
1. **Identify the unit cells**: List the types of unit cells provided in the question.
2. **Analyze each unit cell**:
- Primitive Cubic: Exists in cubic system.
- Body-Centered Cubic: Exists in cubic system.
- Face-Centered Cubic: Exists in cubic system.
- N-Centered: Does not exist in cubic system.
3. **Conclusion**: The N-Centered unit cell is the only one that does not exist in the cubic system.