The splitting of spectral lines under the influence of magnetic field is called and can be explained with the help of ...............quantum number.

Answer

### Step-by-Step Solution:

1. **Identify the Phenomenon**: The question asks about the splitting of spectral lines when subjected to a magnetic field. This phenomenon is known as the **Zeeman effect**.

2. **Understanding the Zeeman Effect**: The Zeeman effect occurs when the energy levels of electrons in an atom are split into multiple levels due to the presence of a magnetic field. This results in the splitting of spectral lines observed in atomic spectra.

3. **Quantum Numbers**: To explain the Zeeman effect, we need to consider the relevant quantum numbers. There are four types of quantum numbers:
- Principal quantum number (n)
- Azimuthal quantum number (l)
- Magnetic quantum number (m)
- Spin quantum number (s)

4. **Focus on the Magnetic Quantum Number**: The splitting of spectral lines can be explained with the help of the **magnetic quantum number (m)**. This quantum number determines the orientation of the orbitals in a magnetic field.

5. **Conclusion**: Therefore, the splitting of spectral lines under the influence of a magnetic field is called the **Zeeman effect**, and it can be explained with the help of the **magnetic quantum number**.

### Final Answer:
The splitting of spectral lines under the influence of magnetic field is called the **Zeeman effect** and can be explained with the help of the **magnetic quantum number**.

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