The orbitals which have same number of nodes are

Options

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

Explanation

To determine which orbitals have the same number of nodes, we need to understand the concept of nodes in quantum mechanics. Nodes are points in an orbital where the probability of finding an electron is zero. The number of nodes in an orbital can be calculated using the formula:

**Number of Nodes = n - 1**

where **n** is the principal quantum number.

### Step-by-Step Solution:

1. **Identify the Principal Quantum Numbers**:
- For the orbitals in question, we need to identify their principal quantum numbers (n).
- For example:
- 2s: n = 2
- 2p: n = 2
- 3s: n = 3
- 3p: n = 3
- 3d: n = 3
- 4s: n = 4
- 4p: n = 4
- 4d: n = 4

2. **Calculate the Number of Nodes**:
- Using the formula, we can calculate the number of nodes for each orbital:
- For 2s: Nodes = 2 - 1 = 1
- For 2p: Nodes = 2 - 1 = 1
- For 3s: Nodes = 3 - 1 = 2
- For 3p: Nodes = 3 - 1 = 2
- For 3d: Nodes = 3 - 1 = 2
- For 4s: Nodes = 4 - 1 = 3
- For 4p: Nodes = 4 - 1 = 3
- For 4d: Nodes = 4 - 1 = 3

3. **Compare the Number of Nodes**:
- Now, we can compare the number of nodes:
- 2s and 2p both have 1 node.
- 3s, 3p, and 3d all have 2 nodes.
- 4s, 4p, and 4d all have 3 nodes.

4. **Conclusion**:
- The orbitals that have the same number of nodes are:
- 2s and 2p (1 node)
- 3s, 3p, and 3d (2 nodes)
- 4s, 4p, and 4d (3 nodes)

### Final Answer:
The orbitals which have the same number of nodes are:
- 2s and 2p (1 node)
- 3s, 3p, and 3d (2 nodes)
- 4s, 4p, and 4d (3 nodes)