Which of the following set of quantum numbers is an impossible arrangement ?

Options

A. (1) `n = 3,m = -2,s = +1//2`
B. (2) `n = 4,m = 3,s = +1//2`
C. (3) `n = 5,m = 2,s = -1//2`
D. (4) `n = 3,m = -3,s = -1//2`

Explanation

To determine which set of quantum numbers is impossible, we need to analyze each option based on the rules governing quantum numbers. Quantum numbers consist of four values: the principal quantum number (n), the azimuthal quantum number (l), the magnetic quantum number (m), and the spin quantum number (s).

### Step-by-Step Solution:

1. **Understanding Quantum Numbers**:
- **Principal Quantum Number (n)**: Indicates the shell or energy level. It can take positive integer values (1, 2, 3...).
- **Azimuthal Quantum Number (l)**: Indicates the subshell (s, p, d, f). It can take values from 0 to (n-1).
- **Magnetic Quantum Number (m)**: Indicates the orientation of the orbital. It can take values from -l to +l.
- **Spin Quantum Number (s)**: Indicates the spin of the electron, which can be +1/2 or -1/2.

2. **Analyzing Each Option**:
- **Option 1**: n = 3, m = -2, s = +1/2
- For n = 3, possible values of l are 0 (s), 1 (p), 2 (d).
- The maximum value of m for l = 2 (d) is -2, -1, 0, +1, +2.
- Thus, this arrangement is possible.

- **Option 2**: n = 4, m = 3, s = +1/2
- For n = 4, possible values of l are 0 (s), 1 (p), 2 (d), 3 (f).
- The maximum value of m for l = 3 (f) is -3, -2, -1, 0, +1, +2, +3.
- Thus, this arrangement is possible.

- **Option 3**: n = 5, m = 2, s = -1/2
- For n = 5, possible values of l are 0 (s), 1 (p), 2 (d), 3 (f), 4 (g).
- The maximum value of m for l = 2 (d) is -2, -1, 0, +1, +2.
- Thus, this arrangement is possible.

- **Option 4**: n = 3, m = -3, s = -1/2
- For n = 3, possible values of l are 0 (s), 1 (p), 2 (d).
- The maximum value of m for l = 2 (d) is -2, -1, 0, +1, +2.
- Since m = -3 is not a valid value for n = 3, this arrangement is impossible.

3. **Conclusion**:
- The impossible arrangement is found in **Option 4**: n = 3, m = -3, s = -1/2.

### Final Answer:
**The impossible arrangement of quantum numbers is Option 4: n = 3, m = -3, s = -1/2.**