How many quantum number are needed in designate an orbital ? Name them

Explanation

To determine how many quantum numbers are needed to designate an orbital and to name them, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Orbitals**: An orbital is defined as a region around the nucleus of an atom where there is a high probability of finding an electron.

2. **Identifying Quantum Numbers**: To specify an orbital, three quantum numbers are required:
- **Principal Quantum Number (n)**: This number indicates the main energy level or shell in which the electron resides. It can take positive integer values (n = 1, 2, 3, ...).
- **Azimuthal Quantum Number (l)**: This number determines the shape of the orbital and indicates the subshell (s, p, d, f). The value of l can range from 0 to (n-1). For example, if n = 2, l can be 0 (s subshell) or 1 (p subshell).
- **Magnetic Quantum Number (m)**: This number specifies the orientation of the orbital within a given subshell. It can take integer values from -l to +l, including zero. For example, for a p subshell (l = 1), m can be -1, 0, or +1.

3. **Example of Designating an Orbital**: To illustrate, let’s designate the 3p orbital:
- The principal quantum number (n) is 3.
- The azimuthal quantum number (l) for p is 1.
- The magnetic quantum number (m) for the px orbital is -1.

4. **Conclusion**: Therefore, to designate an orbital, three quantum numbers are required: the principal quantum number (n), the azimuthal quantum number (l), and the magnetic quantum number (m).

### Summary of Quantum Numbers:
- **Principal Quantum Number (n)**: Indicates the shell.
- **Azimuthal Quantum Number (l)**: Indicates the subshell.
- **Magnetic Quantum Number (m)**: Indicates the orientation of the orbital.

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