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 problem of determining 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 main energy level or shell of an electron in an atom. In this case, n = 3.

2. **Determine the Possible Values of the Angular Momentum Quantum Number (l)**:
- For a given principal quantum number n, the angular momentum quantum number (l) can take values from 0 to (n-1).
- Therefore, for n = 3, the possible values of l are:
- l = 0 (s orbital)
- l = 1 (p orbital)
- l = 2 (d orbital)

3. **Calculate the Possible Values of the Magnetic Quantum Number (m)**:
- The magnetic quantum number (m) can take values ranging from -l to +l, including zero.
- For each value of l:
- If l = 0, then m can only be 0 (1 value).
- If l = 1, then m can be -1, 0, +1 (3 values).
- If l = 2, then m can be -2, -1, 0, +1, +2 (5 values).

4. **Count the Total Possible Values of m**:
- Now, we add the possible values of m for each l:
- For l = 0: 1 value
- For l = 1: 3 values
- For l = 2: 5 values
- Total possible values of m = 1 + 3 + 5 = 9.

5. **Final Answer**:
- Therefore, the total possible values for the magnetic quantum number when n = 3 is **9**.

### Conclusion:
The correct option is **C9**.