The quantum number which determines the number of sub-energy level is in any main energy level is

Options

A. n
B. l
C. m
D. `s`

Explanation

To determine the quantum number that indicates the number of sub-energy levels in any main energy level, we need to understand the relationship between the principal quantum number and the sub-energy levels.

### Step-by-Step Solution:

1. **Understand the Principal Quantum Number (n)**:
- The principal quantum number, denoted as \( n \), indicates the main energy level of an electron in an atom. The value of \( n \) can be any positive integer (1, 2, 3, ...).

2. **Identify the Sub-Energy Levels**:
- Each main energy level can contain one or more sub-energy levels. The number of sub-energy levels corresponds to the value of \( n \).
- For example:
- For \( n = 1 \) (K shell), there is 1 sub-energy level (1s).
- For \( n = 2 \) (L shell), there are 2 sub-energy levels (2s, 2p).
- For \( n = 3 \) (M shell), there are 3 sub-energy levels (3s, 3p, 3d).
- For \( n = 4 \) (N shell), there are 4 sub-energy levels (4s, 4p, 4d, 4f).

3. **Establish the Relationship**:
- From the examples above, we can see a pattern: the number of sub-energy levels in a main energy level is equal to the principal quantum number \( n \).
- Therefore, the relationship can be summarized as:
\[ \text{Number of sub-energy levels} = n \]

4. **Conclusion**:
- The quantum number that determines the number of sub-energy levels in any main energy level is the principal quantum number \( n \).

### Final Answer:
The quantum number which determines the number of sub-energy levels in any main energy level is \( n \).

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