A crystal may have one or more planes and one or more axes of symmetry but it has:

Options

A. Two centres of symmetry
B. Only one centre of symmetry
C. No centre of symmetry
D. Three centres of symmetry

Answer

To solve the question, we need to understand the concepts of symmetry in crystal structures. Let's break it down step by step:

### Step 1: Understanding Crystal Symmetry
A crystal can exhibit various types of symmetry, including planes of symmetry and axes of symmetry.

**Hint:** Remember that symmetry in crystals relates to how the structure can be divided or rotated to yield identical halves or parts.

### Step 2: Identifying Planes of Symmetry
A plane of symmetry is an imaginary plane that divides the crystal into two mirror-image halves. A crystal can have multiple planes of symmetry.

**Hint:** Think of a mirror; if you can draw a line through the crystal where both sides look identical, that's a plane of symmetry.

### Step 3: Identifying Axes of Symmetry
An axis of symmetry is an imaginary line around which the crystal can be rotated, and the structure appears unchanged. A crystal can also have multiple axes of symmetry.

**Hint:** Visualize spinning a toy around a stick; if it looks the same after a certain degree of rotation, that stick represents an axis of symmetry.

### Step 4: Understanding Center of Symmetry
The center of symmetry (or inversion center) is a specific point in a crystal structure where for every point in the crystal, there is an identical point at an equal distance on the opposite side of this center.

**Hint:** Imagine a point in the middle of a crystal; if you can find a corresponding point directly opposite it at the same distance, that point is the center of symmetry.

### Step 5: Conclusion on Center of Symmetry
Unlike planes and axes of symmetry, a crystal can only have one center of symmetry. This is because the center is defined as a unique point that reflects all other points in the structure.

**Hint:** Recall that having multiple centers would contradict the definition, as each center would need to be equidistant from all corresponding points.

### Final Answer
A crystal may have one or more planes and one or more axes of symmetry, but it has **only one center of symmetry**.