The type of crystal system when axial distances $a
e b
e c$ and axial angles $\alpha=\gamma=90^{\circ}$ and $\beta
e90^{\circ}$ is:

Question

Accepted Answer

The correct answer to the question is Option 4: Monoclinic. Here is a detailed explanation justifying why this is the correct choice, along with reasons why the other options are incorrect:

1. **Monoclinic Crystal System (Option 4):**
   - In the monoclinic crystal system, the unit cell is characterized by three unequal axial distances, i.e., $a \ne b \ne c$. This matches the condition given in the question.
   - The angles in the monoclinic system are $\alpha = \gamma = 90^\circ$ and $\beta \ne 90^\circ$. This is exactly the condition specified in the question, confirming that the crystal system described is indeed monoclinic.

2. **Why the Other Options are Incorrect:**

- **Tetragonal (Option 1):**
     - In the tetragonal crystal system, two of the three axial distances are equal, i.e., $a = b \ne c$. This does not match the condition $a \ne b \ne c$ given in the question.
     - Additionally, all angles in the tetragonal system are $90^\circ$, which contradicts the condition $\beta \ne 90^\circ$.

- **Triclinic (Option 2):**
     - The triclinic crystal system has all unequal axial distances, $a \ne b \ne c$, which matches part of the condition. However, in the triclinic system, none of the angles are $90^\circ$, i.e., $\alpha \ne \beta \ne \gamma \ne 90^\circ$. This does not satisfy the condition $\alpha = \gamma = 90^\circ$.

- **Trigonal (Option 3):**
     - In the trigonal crystal system, the axial distances can be equal or unequal, but the angles are typically equal and not necessarily $90^\circ$. The condition $\alpha = \gamma = 90^\circ$ and $\beta \ne 90^\circ$ does not fit the trigonal system's characteristics.

In conclusion, the monoclinic crystal system is the only one that satisfies all the conditions given in the question, making Option 4 the correct answer.