Which statement is correct for n=5, m=3

Options

A. l=4
B. l=0, l,3, s=`+1/2`
C. l=3
D. All are correct

Answer

To determine the correct statements for the quantum numbers n=5 and m=3, we need to understand the relationships between the principal quantum number (n), the azimuthal quantum number (l), and the magnetic quantum number (m).

### Step-by-Step Solution:

1. **Identify the Principal Quantum Number (n)**:
- Given: n = 5.
- The principal quantum number (n) indicates the energy level of an electron in an atom.

2. **Determine Possible Values for the Azimuthal Quantum Number (l)**:
- The azimuthal quantum number (l) can take values from 0 to (n-1).
- For n = 5, the possible values of l are:
- l = 0, 1, 2, 3, 4.

3. **Understand the Magnetic Quantum Number (m)**:
- The magnetic quantum number (m) can take values from -l to +l.
- Therefore, for each value of l, the possible values of m are:
- If l = 0, then m = 0.
- If l = 1, then m = -1, 0, +1.
- If l = 2, then m = -2, -1, 0, +1, +2.
- If l = 3, then m = -3, -2, -1, 0, +1, +2, +3.
- If l = 4, then m = -4, -3, -2, -1, 0, +1, +2, +3, +4.

4. **Check the Given Value of m**:
- Given: m = 3.
- For m = 3 to be valid, l must be at least 3 (since m can go from -l to +l).
- Therefore, if l = 3, m = 3 is valid.
- If l = 4, m = 3 is also valid.

5. **Conclusion**:
- The correct statements for n = 5 and m = 3 are:
- l can be 3 or 4.
- m = 3 is valid when l = 3 or l = 4.

### Summary of Correct Statements:
- If l = 3, then m can be -3, -2, -1, 0, +1, +2, +3 (which includes m = 3).
- If l = 4, then m can be -4, -3, -2, -1, 0, +1, +2, +3, +4 (which also includes m = 3).