For tetragonal crystal, which statement is incorrect ?

Options

A. All the axial length are not equal
B. Two axial angle are equal
C. Two axial length are equal
D. None of these

Answer

To determine which statement about tetragonal crystals is incorrect, we need to analyze the properties of tetragonal crystal systems based on their unit cell parameters.

### Step-by-Step Solution:

1. **Understanding the Tetragonal Crystal System**:
- The tetragonal crystal system is one of the seven crystal systems in crystallography.
- It is characterized by having two equal axial lengths and one different axial length.

2. **Defining Axial Lengths**:
- In a tetragonal crystal, the axial lengths are defined as follows:
- Let \( a \) and \( b \) be the lengths of the two equal axes.
- Let \( c \) be the length of the third axis, which is different from \( a \) and \( b \).
- Therefore, the relationship can be expressed as:
\[ a = b \neq c \]

3. **Defining Axial Angles**:
- The axial angles in a tetragonal crystal system are defined as:
- \( \alpha = \beta = \gamma = 90^\circ \)
- This means all the angles between the axes are right angles.

4. **Analyzing Statements**:
- Now, we need to evaluate the statements provided regarding the tetragonal crystal system:
- Statement 1: "All axial lengths are equal." (Incorrect)
- Statement 2: "Two axial angles are equal." (Correct)
- Statement 3: "Two axial lengths are equal." (Correct)
- Statement 4: "All axial angles are 90 degrees." (Correct)

5. **Identifying the Incorrect Statement**:
- Based on the definitions and properties, the statement that "All axial lengths are equal" is incorrect because, in a tetragonal crystal, only two lengths are equal while the third is different.

### Conclusion:
The incorrect statement regarding tetragonal crystals is that "All axial lengths are equal."