The crystal system of a compound with unit cell dimensions `a=0.387,b=0.387` and `c=0.504` and `alpha=beta=90^(@)` and `gamma=120^(@)`is

Options

A. Cubic
B. Hexagonal
C. Orthorhombic
D. Rhombohedral

Answer

To determine the crystal system of the given compound, we will analyze the provided unit cell dimensions and angles step by step.

### Step 1: Identify the unit cell dimensions and angles
The unit cell dimensions are given as:
- \( a = 0.387 \)
- \( b = 0.387 \)
- \( c = 0.504 \)

The angles are given as:
- \( \alpha = 90^\circ \)
- \( \beta = 90^\circ \)
- \( \gamma = 120^\circ \)

### Step 2: Compare the dimensions
From the dimensions:
- \( a = b \) (both are equal to 0.387)
- \( c \) is different (0.504)

### Step 3: Compare the angles
From the angles:
- \( \alpha = 90^\circ \)
- \( \beta = 90^\circ \)
- \( \gamma = 120^\circ \)

### Step 4: Determine the crystal system
Now, we will compare these characteristics with the known crystal systems:

1. **Cubic**: All sides are equal (\( a = b = c \)) and all angles are \( 90^\circ \). This does not fit our case.

2. **Hexagonal**: Two sides are equal (\( a = b \)), one side different (\( c \)), and angles \( \alpha = \beta = 90^\circ \) and \( \gamma = 120^\circ \). This fits our case.

3. **Orthorhombic**: All sides are different (\( a \neq b \neq c \)) and all angles are \( 90^\circ \). This does not fit our case.

4. **Rhombohedral**: All sides are equal (\( a = b = c \)) but angles are not \( 90^\circ \). This does not fit our case.

### Conclusion
Based on the analysis, the only crystal system that fits the given dimensions and angles is the **Hexagonal** crystal system.

### Final Answer
The crystal system of the compound is **Hexagonal**.

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