The orbitals having the same number of spherical nodes are :

Options

A. 4p, 3d
B. 3p , 4d
C. 4s, 5p
D. 2s, 3d

Explanation

To solve the question regarding orbitals having the same number of spherical nodes, we will use the formula for calculating the number of spherical nodes in an orbital, which is given by:

**Formula for Spherical Nodes:**
\[ \text{Number of Spherical Nodes} = n - l - 1 \]
where:
- \( n \) is the principal quantum number,
- \( l \) is the azimuthal quantum number.

### Step-by-Step Solution:

1. **Identify the Orbitals:**
We are given several orbitals to analyze: 4p, 3d, 4d, 4s, and 5p.

2. **Calculate Spherical Nodes for Each Orbital:**
- **For 4p:**
- \( n = 4 \) (principal quantum number)
- \( l = 1 \) (for p orbitals)
- Spherical Nodes = \( 4 - 1 - 1 = 2 \)

- **For 3d:**
- \( n = 3 \) (principal quantum number)
- \( l = 2 \) (for d orbitals)
- Spherical Nodes = \( 3 - 2 - 1 = 0 \)

- **For 4d:**
- \( n = 4 \) (principal quantum number)
- \( l = 2 \) (for d orbitals)
- Spherical Nodes = \( 4 - 2 - 1 = 1 \)

- **For 4s:**
- \( n = 4 \) (principal quantum number)
- \( l = 0 \) (for s orbitals)
- Spherical Nodes = \( 4 - 0 - 1 = 3 \)

- **For 5p:**
- \( n = 5 \) (principal quantum number)
- \( l = 1 \) (for p orbitals)
- Spherical Nodes = \( 5 - 1 - 1 = 3 \)

3. **Compare the Results:**
- 4p has 2 spherical nodes.
- 3d has 0 spherical nodes.
- 4d has 1 spherical node.
- 4s has 3 spherical nodes.
- 5p has 3 spherical nodes.

4. **Identify Orbitals with the Same Number of Spherical Nodes:**
- 4s and 5p both have 3 spherical nodes.

### Final Answer:
The orbitals having the same number of spherical nodes are **4s and 5p**.