An electron has magnetic quantum number as '-3'. Its principal quantum number is

Options

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

Answer

To determine the principal quantum number (n) when the magnetic quantum number (m_l) is given as -3, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Magnetic Quantum Number (m_l)**:
- The magnetic quantum number (m_l) can take on integer values ranging from -l to +l, where l is the azimuthal (or angular momentum) quantum number.

2. **Identifying Possible Values of m_l**:
- For a given value of l, the possible values of m_l are: -l, -(l-1), ..., 0, ..., (l-1), l.
- If m_l = -3, it implies that l must be at least 3 because m_l can take values from -l to +l.

3. **Determining the Azimuthal Quantum Number (l)**:
- Since m_l = -3, we can conclude that l = 3 (because -3 is the lowest value of m_l for l = 3).

4. **Relating l to the Principal Quantum Number (n)**:
- The relationship between the principal quantum number (n) and the azimuthal quantum number (l) is given by the formula:
\[ l = n - 1 \]
- Rearranging this formula gives:
\[ n = l + 1 \]

5. **Calculating n**:
- Substituting the value of l we found:
\[ n = 3 + 1 = 4 \]

6. **Conclusion**:
- Therefore, the principal quantum number (n) when the magnetic quantum number (m_l) is -3 is **4**.

### Final Answer:
The principal quantum number (n) is **4**.