The ratio of number of pentagons in `C_(60)` and trigons (triangles) in white phosphorus,is______.

Options

A. a. 3:1
B. b. 4:3
C. c. 5:1
D. d. 2:1

Explanation

To solve the problem of finding the ratio of the number of pentagons in \( C_{60} \) (Buckminsterfullerene) and the number of triangles in white phosphorus (\( P_4 \)), we can follow these steps:

### Step 1: Determine the number of pentagons in \( C_{60} \)

1. **Understanding the structure of \( C_{60} \)**:
- \( C_{60} \) is known as Buckminsterfullerene, which has a soccer ball-like structure composed of carbon atoms.
- It consists of 12 pentagonal faces and 20 hexagonal faces.

2. **Count the pentagons**:
- From the structure, we can see that there are **12 pentagons** in \( C_{60} \).

### Step 2: Determine the number of triangles in white phosphorus (\( P_4 \))

1. **Understanding the structure of \( P_4 \)**:
- White phosphorus consists of four phosphorus atoms arranged in a tetrahedral shape.
- The tetrahedron has 4 triangular faces.

2. **Count the triangles**:
- Therefore, in white phosphorus, there are **4 triangles**.

### Step 3: Calculate the ratio of pentagons to triangles

1. **Setting up the ratio**:
- Let \( A \) be the number of pentagons in \( C_{60} \) (which is 12).
- Let \( B \) be the number of triangles in \( P_4 \) (which is 4).
- The ratio of pentagons to triangles is given by \( A : B \).

2. **Substituting the values**:
- The ratio is \( 12 : 4 \).

3. **Simplifying the ratio**:
- Dividing both sides by 4 gives \( 3 : 1 \).

### Final Answer

The ratio of the number of pentagons in \( C_{60} \) to the number of triangles in white phosphorus is \( 3 : 1 \).

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