which of the following orbitals has three angular nodes?

Options

A. 2s
B. 4s
C. 3d
D. 6f

Answer

To determine which of the given orbitals has three angular nodes, we need to understand the relationship between the azimuthal quantum number (L) and the number of angular nodes in atomic orbitals. Here’s a step-by-step solution:

### Step 1: Understand the concept of angular nodes
Angular nodes are regions in an atom where the probability of finding an electron is zero. The number of angular nodes in an orbital is determined by the azimuthal quantum number (L).

### Step 2: Identify the value of L for each orbital
- For **s orbitals** (e.g., 2s, 4s), L = 0.
- For **p orbitals** (not listed here), L = 1.
- For **d orbitals** (e.g., 3d), L = 2.
- For **f orbitals** (e.g., 6f), L = 3.

### Step 3: List the orbitals and their corresponding L values
1. **2s**: L = 0 (0 angular nodes)
2. **4s**: L = 0 (0 angular nodes)
3. **3d**: L = 2 (2 angular nodes)
4. **6f**: L = 3 (3 angular nodes)

### Step 4: Determine the number of angular nodes for each orbital
- **2s**: 0 angular nodes
- **4s**: 0 angular nodes
- **3d**: 2 angular nodes
- **6f**: 3 angular nodes

### Step 5: Identify the orbital with three angular nodes
From the analysis, we see that the **6f orbital** has three angular nodes.

### Conclusion
The orbital that has three angular nodes is **6f**.

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