The unit cell with crystallographic dimensions , `a= b nec " and " alpha = beta=gamma = 90^0`

Options

A. Cubic
B. Tetragonal
C. Monoclinic
D. Hexagonal

Answer

To solve the problem regarding the unit cell with the given crystallographic dimensions, we can follow these steps:

### Step 1: Understand the given dimensions
We have:
- \( a = b \)
- \( c \neq a \) (or \( c \neq b \))
- \( \alpha = \beta = \gamma = 90^\circ \)

### Step 2: Identify the type of crystal system
From the given conditions:
- Since \( a = b \) and \( c \neq a \), this indicates that the lengths of the edges are not all equal.
- The angles \( \alpha, \beta, \gamma \) being \( 90^\circ \) indicates that the unit cell is orthogonal.

### Step 3: Compare with known crystal systems
1. **Cubic**: All edges are equal (\( a = b = c \)) and all angles are \( 90^\circ \). This does not fit our case.
2. **Monoclinic**: All edges are different (\( a \neq b \neq c \)) with two angles at \( 90^\circ \) and one angle not \( 90^\circ \). This does not fit our case.
3. **Tetragonal**: Two edges are equal (\( a = b \)) and the third edge is different (\( c \neq a \)). All angles are \( 90^\circ \). This fits our case.
4. **Hexagonal**: Two edges are equal (\( a = b \)), but the angles are \( 120^\circ \) for two angles and \( 90^\circ \) for the third angle. This does not fit our case.

### Step 4: Conclusion
Based on the analysis, the unit cell described is a **Tetragonal** unit cell.

### Final Answer
The correct answer is **Tetragonal**.

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