The parameters of the unit cell of a substance are `a = 2.5, b = 2.0 , c = 4.0 , alpha = 90^(@), beta = 120^(@) gamma = 90^(@)`. The crystal system of the substance is :

Options

A. Hexagonal
B. Orthorhombic
C. Monoclinic
D. Triclinic

Answer

To determine the crystal system of the substance based on the given parameters of the unit cell, we can follow these steps:

### Step 1: Identify the Edge Lengths
The parameters given are:
- \( a = 2.5 \)
- \( b = 2.0 \)
- \( c = 4.0 \)

Here, we see that all three edge lengths \( a \), \( b \), and \( c \) are different.

### Step 2: Identify the Angles
The angles provided are:
- \( \alpha = 90^\circ \)
- \( \beta = 120^\circ \)
- \( \gamma = 90^\circ \)

From this, we note that:
- \( \alpha \) and \( \gamma \) are both \( 90^\circ \)
- \( \beta \) is \( 120^\circ \)

### Step 3: Determine the Crystal System
Now, we can classify the crystal system based on the edge lengths and angles:

1. **Cubic**: All edges are equal and all angles are \( 90^\circ \).
2. **Tetragonal**: Two edges are equal, and all angles are \( 90^\circ \).
3. **Orthorhombic**: All edges are different, and all angles are \( 90^\circ \).
4. **Hexagonal**: Two edges are equal, and angles are \( 120^\circ \) and \( 90^\circ \).
5. **Monoclinic**: All edges are different, with two angles at \( 90^\circ \) and one angle not at \( 90^\circ \) (which is \( 120^\circ \) in this case).
6. **Triclinic**: All edges are different and all angles are different.
7. **Trigonal**: This is a subset of hexagonal and has specific symmetry.

Given that:
- All three edge lengths are different (\( a \neq b \neq c \))
- Two angles are \( 90^\circ \) and one angle is \( 120^\circ \)

This matches the criteria for the **Monoclinic** crystal system.

### Conclusion
The crystal system of the substance is **Monoclinic**.

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