Which of the following sub - shells is not permitted ?

Options

A. (a)4f
B. (b)4d
C. (c)3s
D. (d)4g

Answer

To determine which of the following sub-shells is not permitted, we need to understand the relationship between the principal quantum number (n) and the azimuthal quantum number (l).

### Step-by-Step Solution:

1. **Understanding Quantum Numbers**:
- The principal quantum number (n) indicates the energy level or shell.
- The azimuthal quantum number (l) indicates the shape of the orbital and can take values from 0 to (n-1).

2. **Identifying Allowed Values of l**:
- For a given value of n, the possible values of l are:
- l = 0 (s subshell)
- l = 1 (p subshell)
- l = 2 (d subshell)
- l = 3 (f subshell)
- l = 4 (g subshell)
- Therefore, for n = 4, the allowed values of l are 0, 1, 2, and 3.

3. **Evaluating the Options**:
- **Option A: 4f**
- Here, n = 4 and l = 3 (f subshell). This is permitted.
- **Option B: 4d**
- Here, n = 4 and l = 2 (d subshell). This is permitted.
- **Option C: 3s**
- Here, n = 3 and l = 0 (s subshell). This is permitted.
- **Option D: 4g**
- Here, n = 4 and l = 4 (g subshell). This is not permitted because l cannot be equal to n.

4. **Conclusion**:
- The sub-shell that is not permitted is **4g**.

### Final Answer:
The sub-shell that is not permitted is **4g**.