In a monoclinic unit cell the relation of sides and angles are respectively

Options

A. `a = b != c and alpha = beta = gamma = 90^(º )`
B. `a != b != c and alpha = beta = gamma = 90^(º )`
C. `a != b != c and alpha = gamma = 90^(º ) != beta`
D. `a != b != c and alpha != beta != gamma != 90^(º )`

Answer

To determine the relationship of sides and angles in a monoclinic unit cell, we can follow these steps:

### Step 1: Understand the Definition of a Monoclinic Unit Cell
A monoclinic unit cell is one of the seven crystal systems in crystallography. It is characterized by having three unequal axes and one angle that is not 90 degrees.

### Step 2: Identify the Sides of the Monoclinic Unit Cell
In a monoclinic unit cell, the sides are represented as A, B, and C. The relationship between these sides is that:
- A ≠ B ≠ C
This means that all three sides are of different lengths.

### Step 3: Identify the Angles of the Monoclinic Unit Cell
The angles in a monoclinic unit cell are represented as α (alpha), β (beta), and γ (gamma). The relationships between these angles are:
- α = 90° (angle between sides B and C)
- γ = 90° (angle between sides A and B)
- β ≠ 90° (angle between sides A and C)

### Step 4: Summarize the Relationships
To summarize:
- Sides: A ≠ B ≠ C
- Angles: α = 90°, γ = 90°, β ≠ 90°

### Final Answer
In a monoclinic unit cell, the relationship of sides and angles is:
- Sides: A ≠ B ≠ C
- Angles: α = 90°, γ = 90°, β ≠ 90°

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