Orthorhombic crystal has the following unit cell parameters:

Options

A. `a= b= c, alpha= beta= gamma=90^(@)`
B. `a= bne c, alpha= beta= gamma=90^(@)`
C. `ane bne c, alpha= beta=gamma=90^(@),`
D. `a=bnec, alpha= beta=90^(@),gamma=120^(@)`

Answer

To determine the correct unit cell parameters for an orthorhombic crystal, we need to understand the characteristics of this crystal system. Here’s a step-by-step solution:

### Step 1: Understand the Orthorhombic Crystal System
- The orthorhombic crystal system is defined by three edge lengths and three interfacial angles.
- The edge lengths are denoted as \( a \), \( b \), and \( c \).
- The interfacial angles are denoted as \( \alpha \), \( \beta \), and \( \gamma \).

### Step 2: Identify the Properties of Edge Lengths
- In an orthorhombic crystal, the edge lengths are not equal to each other. Therefore, we have:
\[ a \neq b \neq c \]

### Step 3: Identify the Properties of Interfacial Angles
- All interfacial angles in an orthorhombic crystal are equal to 90 degrees. Thus, we have:
\[ \alpha = \beta = \gamma = 90^\circ \]

### Step 4: Analyze the Given Options
- **Option A**: \( a = b = c \) - This is incorrect because, in an orthorhombic system, all edge lengths are not equal.
- **Option B**: \( a = b \neq c \) - This is also incorrect because it suggests two edge lengths are equal, which is not true for orthorhombic crystals.
- **Option C**: \( a \neq b \neq c \) - This is correct as it aligns with the properties of the orthorhombic system.
- **Option D**: \( \alpha = \beta \neq \gamma \) - This is incorrect because all angles must be 90 degrees.

### Step 5: Conclusion
- The correct option that describes the unit cell parameters for the orthorhombic crystal system is **Option C**: \( a \neq b \neq c \) and \( \alpha = \beta = \gamma = 90^\circ \).