If the value of principal quantum number is 3, the total possible values for magnetic quantum number will be

Options

A. 1
B. 4
C. 9
D. 12

Explanation

To solve the question regarding the total possible values for the magnetic quantum number when the principal quantum number \( n \) is 3, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Principal Quantum Number (n)**:
The principal quantum number \( n \) indicates the energy level of an electron in an atom. In this case, \( n = 3 \).

2. **Determine the Possible Values for the Azimuthal Quantum Number (l)**:
The azimuthal quantum number \( l \) can take values from 0 to \( n-1 \). For \( n = 3 \), the possible values of \( l \) are:
- \( l = 0 \) (s orbital)
- \( l = 1 \) (p orbital)
- \( l = 2 \) (d orbital)

3. **Calculate the Magnetic Quantum Number (m_l) Values**:
The magnetic quantum number \( m_l \) can take values from \( -l \) to \( +l \), including zero. Therefore, for each value of \( l \):
- For \( l = 0 \): \( m_l = 0 \) (1 value)
- For \( l = 1 \): \( m_l = -1, 0, +1 \) (3 values)
- For \( l = 2 \): \( m_l = -2, -1, 0, +1, +2 \) (5 values)

4. **Total Possible Values of Magnetic Quantum Number**:
Now, we sum the possible values of \( m_l \) for each \( l \):
- From \( l = 0 \): 1 value
- From \( l = 1 \): 3 values
- From \( l = 2 \): 5 values

Total = \( 1 + 3 + 5 = 9 \)

5. **Conclusion**:
Thus, the total possible values for the magnetic quantum number when the principal quantum number is 3 is **9**.

### Final Answer:
The total possible values for the magnetic quantum number when \( n = 3 \) is **9**.

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