Which of the following orbitals does not exist ?

Options

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

Explanation

To determine which of the following orbitals does not exist, we need to analyze the quantum numbers associated with each orbital. The two important quantum numbers to consider are:

1. **Principal Quantum Number (n)**: This indicates the energy level of the electron and can take positive integer values (1, 2, 3, ...).

2. **Azimuthal Quantum Number (l)**: This indicates the shape of the orbital and can take values from 0 to (n-1). The values of l correspond to different types of orbitals:
- l = 0 corresponds to s orbitals
- l = 1 corresponds to p orbitals
- l = 2 corresponds to d orbitals
- l = 3 corresponds to f orbitals

### Step-by-Step Solution:

1. **Identify the Orbitals Given**:
Let's consider the orbitals mentioned: 6s, 3p, 2d, and 4f.

2. **Check Each Orbital**:
- **6s**:
- Here, n = 6 and l = 0 (for s orbitals).
- Since l (0) is less than n (6), this orbital exists.

- **3p**:
- Here, n = 3 and l = 1 (for p orbitals).
- Since l (1) is less than n (3), this orbital exists.

- **2d**:
- Here, n = 2 and l = 2 (for d orbitals).
- Since l (2) is equal to n (2), this is not possible. Therefore, the 2d orbital does not exist.

- **4f**:
- Here, n = 4 and l = 3 (for f orbitals).
- Since l (3) is equal to n-1 (3), this orbital exists.

3. **Conclusion**:
Based on the analysis, the orbital that does not exist is **2d**.

### Final Answer:
The orbital that does not exist is **2d**.

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