Maximum number of nodes are present in :

Options

A. 5s
B. 5p
C. 5d
D. All have same number of nodes

Answer

To determine the maximum number of nodes present in the given orbitals, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Concept of Nodes**:
- A node is a point or plane where the electron density is zero.
- There are two types of nodes: radial nodes and angular nodes.

2. **Formulas for Nodes**:
- **Radial Nodes**: The number of radial nodes can be calculated using the formula:
\[ \text{Radial Nodes} = n - l - 1 \]
- **Angular Nodes**: The number of angular nodes is given by:
\[ \text{Angular Nodes} = l \]
- **Total Nodes**: The total number of nodes is the sum of radial and angular nodes:
\[ \text{Total Nodes} = \text{Radial Nodes} + \text{Angular Nodes} = (n - l - 1) + l = n - 1 \]

3. **Identify the Principal Quantum Number (n)**:
- For the given orbitals, we need to identify the principal quantum number \( n \):
- For **5s**, \( n = 5 \)
- For **5p**, \( n = 5 \)
- For **5d**, \( n = 5 \)

4. **Calculate the Total Number of Nodes for Each Orbital**:
- For **5s**:
\[ \text{Total Nodes} = n - 1 = 5 - 1 = 4 \]
- For **5p**:
\[ \text{Total Nodes} = n - 1 = 5 - 1 = 4 \]
- For **5d**:
\[ \text{Total Nodes} = n - 1 = 5 - 1 = 4 \]

5. **Conclusion**:
- All three orbitals (5s, 5p, and 5d) have the same number of nodes, which is 4.

### Final Answer:
The maximum number of nodes present in the given orbitals (5s, 5p, and 5d) is **4**.

---