If m has seven values, the value of azimuthal quantum number should be

Options

A. 1
B. 2
C. 3
D. 4

Answer

To determine the value of the azimuthal quantum number (l) when the magnetic quantum number (m) has seven possible values, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding 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) can take values from -l to +l, including zero. Therefore, the total number of values for m is given by the formula:
\[ \text{Number of m values} = 2l + 1 \]

2. **Setting Up the Equation**:
- We need to find the value of l such that the number of m values equals 7. Thus, we can set up the equation:
\[ 2l + 1 = 7 \]

3. **Solving for l**:
- Rearranging the equation gives:
\[ 2l = 7 - 1 \]
\[ 2l = 6 \]
\[ l = \frac{6}{2} = 3 \]

4. **Conclusion**:
- The azimuthal quantum number (l) that corresponds to 7 values of the magnetic quantum number (m) is 3.

### Final Answer:
The value of the azimuthal quantum number (l) should be **3**.

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