The quantum number l and the number of electrons (n) in the sub level are related by

Options

A. `n = 2l +1`
B. `l = 2n +1`
C. `n = 4l +2`
D. `n = 2l^(2)`

Explanation

To solve the question regarding the relationship between the quantum number \( l \) and the number of electrons \( n \) in a sublevel, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Quantum Number \( l \)**:
- The quantum number \( l \) (azimuthal quantum number) defines the shape of the orbital and can take values from \( 0 \) to \( n-1 \), where \( n \) is the principal quantum number.

2. **Determining the Number of Orbitals**:
- For a given value of \( l \), the number of orbitals (\( m \)) is given by the formula:
\[ m = 2l + 1 \]
- This formula accounts for the different orientations of the orbitals.

3. **Maximum Number of Electrons per Orbital**:
- According to the Pauli Exclusion Principle, each orbital can hold a maximum of 2 electrons.

4. **Calculating Total Number of Electrons**:
- To find the total number of electrons (\( n \)) in a sublevel, we can use the relationship:
\[ n = 2 \times m \]
- Substituting the expression for \( m \):
\[ n = 2 \times (2l + 1) \]
- Simplifying this gives:
\[ n = 4l + 2 \]

5. **Conclusion**:
- Thus, the relationship between the quantum number \( l \) and the number of electrons \( n \) in the sublevel is:
\[ n = 4l + 2 \]

### Final Answer:
The relationship is \( n = 4l + 2 \).

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