A cubic crystal possesses in all ........... planes of symmetry:

Options

A. 9
B. 13
C. 1
D. 23

Answer

To determine the total number of planes of symmetry in a cubic crystal, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Concept of Plane of Symmetry**:
- A plane of symmetry is an imaginary plane that divides a crystal into two equal halves, where one half is the mirror image of the other.

2. **Identify the Structure of a Cube**:
- Visualize the cubic crystal structure. A cube has three axes: the x-axis, y-axis, and z-axis.

3. **Determine Rectangular Planes of Symmetry**:
- A cube has three rectangular planes of symmetry, which are aligned with the axes:
- One plane parallel to the yz-plane (dividing the cube into left and right halves).
- One plane parallel to the xz-plane (dividing the cube into front and back halves).
- One plane parallel to the xy-plane (dividing the cube into top and bottom halves).

4. **Determine Diagonal Planes of Symmetry**:
- A cube also has six diagonal planes of symmetry. These planes cut through the cube diagonally:
- Each diagonal plane connects opposite edges of the cube.
- There are two diagonal planes for each pair of opposite faces (front-back, left-right, top-bottom).

5. **Calculate Total Planes of Symmetry**:
- Add the number of rectangular planes (3) and diagonal planes (6):
- Total planes of symmetry = 3 (rectangular) + 6 (diagonal) = 9.

6. **Conclusion**:
- Therefore, a cubic crystal possesses a total of **9 planes of symmetry**.

### Final Answer:
A cubic crystal possesses in all **9 planes of symmetry**.

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