I = 3, then the values of magnetic quantum numbers are

Options

A. `+-1, +- 2, +- 3`
B. `0, +-1, +-2, +-3`
C. `-1, -2, -3`
D. `0 +1, +2, +3`

Answer

To find the values of the magnetic quantum number (m) when the azimuthal quantum number (l) is given as 3, we can follow these steps:

### Step-by-Step Solution:

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

2. **Identify the Given Value**:
- Here, we are given that l = 3.

3. **Determine the Range of Magnetic Quantum Number (m)**:
- The values of m can be calculated using the formula:
\[ m = -l, -l + 1, ..., 0, ..., l - 1, l \]
- For l = 3, the possible values of m will be:
\[ m = -3, -2, -1, 0, +1, +2, +3 \]

4. **List the Values**:
- Therefore, the complete set of values for the magnetic quantum number when l = 3 is:
\[ m = -3, -2, -1, 0, +1, +2, +3 \]

5. **Conclusion**:
- The values of the magnetic quantum number (m) for l = 3 are:
\[ -3, -2, -1, 0, +1, +2, +3 \]