If magnetic quantum number of a given electron is represented -3, then what will be its principal number ?

Options

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

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. **Understand the Quantum Numbers**:
- The magnetic quantum number (m_l) can take values from -l to +l, where l is the azimuthal quantum number (also known as the angular momentum quantum number).
- The azimuthal quantum number (l) can take integer values from 0 to (n-1), where n is the principal quantum number.

2. **Identify the Value of l**:
- Given m_l = -3, we can deduce that the maximum value of m_l is equal to +l. Therefore, for m_l to be -3, l must be at least 3.
- The possible values of m_l are: -l, -(l-1), ..., 0, ..., (l-1), +l. Thus, if m_l = -3, then l must be 3.

3. **Relate l to n**:
- The relationship between l and n is given by the equation:
\[ l = n - 1 \]
- Since we have found that l = 3, we can substitute this into the equation:
\[ 3 = n - 1 \]

4. **Solve for n**:
- Rearranging the equation gives:
\[ n = 3 + 1 = 4 \]

5. **Conclusion**:
- Therefore, the principal quantum number (n) corresponding to a magnetic quantum number (m_l) of -3 is **4**.

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