`A` electron can exist in bound system as well as an independent particle. Which quantum number is always associated with an electron ?

Options

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

Answer

To determine which quantum number is always associated with an electron, we need to analyze the properties of electrons in both bound systems (like atoms) and as independent particles.

### Step-by-Step Solution:

1. **Understanding Quantum Numbers**:
- Electrons are described by four quantum numbers: principal quantum number (n), azimuthal quantum number (l), magnetic quantum number (m_l), and spin quantum number (m_s).
- Each of these quantum numbers provides specific information about the electron's state.

2. **Bound System vs. Independent Particle**:
- In a bound system (like an atom), electrons occupy specific energy levels and orbitals, which are defined by their quantum numbers.
- An independent electron, such as one in free space, can also be described by quantum numbers, but the context changes.

3. **Identifying the Relevant Quantum Number**:
- The azimuthal quantum number (l) defines the shape of the orbital and is related to the angular momentum of the electron.
- For an electron in a bound state, the lowest energy state corresponds to l = 0, which is characteristic of an s orbital.

4. **Conclusion**:
- The azimuthal quantum number (l) is always associated with an electron, regardless of whether it is in a bound system or as an independent particle.
- In the case of an independent electron, it can be considered to have l = 0, indicating it behaves like an s orbital electron.

### Final Answer:
The quantum number that is always associated with an electron is the **azimuthal quantum number (l)**.

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