The ratio of number of rectangular plane and diagonal plane in a cubic unit cell

Options

A. `1:2`
B. `3:1`
C. `2:3`
D. `3:4`

Answer

To solve the question regarding the ratio of the number of rectangular planes to diagonal planes in a cubic unit cell, we can follow these steps:

### Step 1: Understand the Types of Planes
- **Rectangular Planes**: These are the planes that are parallel to the sides of the cube. In a cubic unit cell, these planes are formed by cutting the cube along its faces.
- **Diagonal Planes**: These are the planes that cut through the cube diagonally, meaning they intersect the cube from one corner to another.

**Hint**: Remember that rectangular planes align with the edges of the cube, while diagonal planes cut across the cube from vertex to vertex.

### Step 2: Identify the Number of Rectangular Planes
- In a cubic unit cell, there are **3 rectangular planes**. These planes correspond to the three pairs of opposite faces of the cube.

**Hint**: Count the faces of the cube that can be cut parallel to the edges.

### Step 3: Identify the Number of Diagonal Planes
- In a cubic unit cell, there are **6 diagonal planes**. These planes can be visualized as those that cut through the cube diagonally, connecting opposite corners.

**Hint**: Think about how many ways you can slice through the cube diagonally from one vertex to the opposite vertex.

### Step 4: Calculate the Ratio
- Now that we have identified the number of rectangular planes (3) and diagonal planes (6), we can find the ratio of rectangular planes to diagonal planes.

\[ \text{Ratio} = \frac{\text{Number of Rectangular Planes}}{\text{Number of Diagonal Planes}} = \frac{3}{6} = \frac{1}{2} \]

**Hint**: Simplify the fraction to find the simplest form of the ratio.

### Step 5: Conclusion
- The ratio of the number of rectangular planes to diagonal planes in a cubic unit cell is **1:2**.

**Final Answer**: The correct option is **1 ratio 2**.