If the value of azimuthal quantum number of an electron is 2, then which of the following values of magnetic quantum numbers is not permissible,

Options

A. 3
B. 2
C. 0
D. 1

Explanation

To solve the question, we need to determine the permissible values of the magnetic quantum number (m) when the azimuthal quantum number (l) is given as 2.

### Step-by-Step Solution:

1. **Understand the Quantum Numbers**:
- The azimuthal quantum number (l) determines the shape of the orbital and can take values from 0 to n-1, where n is the principal quantum number.
- The magnetic quantum number (m) describes the orientation of the orbital and can take values from -l to +l.

2. **Identify the Given Value**:
- In this case, the azimuthal quantum number (l) is given as 2.

3. **Determine the Range of m Values**:
- The permissible values of the magnetic quantum number (m) can be calculated using the formula:
\[ m = -l, -l + 1, ..., 0, ..., l - 1, l \]
- For l = 2, the values of m will be:
\[ m = -2, -1, 0, +1, +2 \]

4. **List the Possible m Values**:
- Therefore, the possible values of m when l = 2 are:
\[ m = -2, -1, 0, +1, +2 \]

5. **Identify the Non-Permissible Value**:
- Now, we need to check which of the provided options is not permissible. Since the values of m can only range from -2 to +2, any value outside this range is not permissible.
- For example, if one of the options is 3, then it is not permissible because it exceeds the maximum value of +2.

### Conclusion:
The value of the magnetic quantum number that is not permissible when the azimuthal quantum number is 2 is **3**.