The quantum number which determines the shape of the orbital is

Options

A. principal
B. azimuthal
C. magnetic
D. spin

Answer

To determine the quantum number that defines the shape of the orbital, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Quantum Numbers**: Quantum numbers are values that describe the unique quantum state of an electron in an atom. There are four types of quantum numbers: principal (n), azimuthal (l), magnetic (m_l), and spin (m_s).

2. **Identifying the Quantum Numbers**:
- **Principal Quantum Number (n)**: This number indicates the energy level of the electron and is always a positive integer (1, 2, 3,...).
- **Azimuthal Quantum Number (l)**: This number determines the shape of the orbital. It can take values from 0 to (n-1).
- **Magnetic Quantum Number (m_l)**: This number indicates the orientation of the orbital in space and can take values from -l to +l.
- **Spin Quantum Number (m_s)**: This number describes the spin of the electron and can be either +1/2 or -1/2.

3. **Focusing on the Azimuthal Quantum Number (l)**: The azimuthal quantum number (l) is crucial for determining the shape of the orbital:
- If l = 0, the shape is spherical (s orbital).
- If l = 1, the shape is dumbbell (p orbital).
- If l = 2, the shape is more complex (d orbital).
- If l = 3, the shape is even more complex (f orbital).

4. **Conclusion**: Based on the definitions and roles of the quantum numbers, the azimuthal quantum number (l) is the one that determines the shape of the orbital.

### Final Answer:
The quantum number which determines the shape of the orbital is the **azimuthal quantum number (l)**.

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