If the azimuthal quantum number has a value of `2` what are the permitted values of the magnetic quantum number m ?

Explanation

To determine the permitted values of the magnetic quantum number \( m \) when the azimuthal quantum number \( l \) has a value of 2, we can follow these steps:

### Step 1: Understand the Quantum Numbers
The four quantum numbers are:
- Principal quantum number (\( n \)): Indicates the energy level.
- Azimuthal quantum number (\( l \)): Indicates the subshell (shape of the orbital).
- Magnetic quantum number (\( m \)): Indicates the orientation of the orbital.
- Spin quantum number (\( s \)): Indicates the spin of the electron.

### Step 2: Identify the Relationship Between Quantum Numbers
The azimuthal quantum number \( l \) can take values from 0 to \( n-1 \). For each value of \( l \), the magnetic quantum number \( m \) can take values from \( -l \) to \( +l \).

### Step 3: Given Value of Azimuthal Quantum Number
In this case, the azimuthal quantum number \( l \) is given as 2. This corresponds to the d-orbital.

### Step 4: Determine the Permitted Values of \( m \)
Since \( l = 2 \):
- The magnetic quantum number \( m \) can take values from \( -l \) to \( +l \).
- Therefore, the values of \( m \) will be:
\[ m = -2, -1, 0, +1, +2 \]

### Final Answer
The permitted values of the magnetic quantum number \( m \) when the azimuthal quantum number \( l \) is 2 are:
\[ m = -2, -1, 0, +1, +2 \]

---