Which of the following sets of quantum number is INCORRECT?
(I) `n=3, l = 4, m=0, s=+(1)/(2)`
(II) `n=3, l = 3, m = +3, s=+(1)/(2)`
(III) `n=6, l = 0, m=+1, s=-(1)/(2)`
(IV) `n=4, l = 2, m = +2, s=0`

Options

A. I, II, IV
B. I, II, III,IV
C. I, III, IV
D. I, III

Explanation

To determine which of the given sets of quantum numbers is incorrect, we need to analyze each set based on the rules governing quantum numbers.

### Quantum Numbers Overview:
1. **Principal Quantum Number (n)**: Can take any positive integer value (1, 2, 3,...).
2. **Azimuthal Quantum Number (l)**: Can take values from 0 to (n-1).
3. **Magnetic Quantum Number (m)**: Can take values from -l to +l, including zero.
4. **Spin Quantum Number (s)**: Can take values of +1/2 or -1/2.

### Analyzing Each Set:

**Set I: \( n=3, l=4, m=0, s=+\frac{1}{2} \)**
- Here, \( n = 3 \) is valid.
- However, \( l = 4 \) is invalid because \( l \) must be in the range \( 0 \) to \( n-1 = 2 \).
- Therefore, this set is **incorrect**.

**Set II: \( n=3, l=3, m=+3, s=+\frac{1}{2} \)**
- \( n = 3 \) is valid.
- \( l = 3 \) is invalid for the same reason as above; \( l \) must be less than \( n \) (i.e., \( l \) can only be 0, 1, or 2).
- Therefore, this set is **incorrect**.

**Set III: \( n=6, l=0, m=+1, s=-\frac{1}{2} \)**
- \( n = 6 \) is valid.
- \( l = 0 \) is valid.
- However, \( m = +1 \) is invalid because for \( l = 0 \), the only possible value for \( m \) is 0.
- Therefore, this set is **incorrect**.

**Set IV: \( n=4, l=2, m=+2, s=0 \)**
- \( n = 4 \) is valid.
- \( l = 2 \) is valid.
- However, \( m = +2 \) is invalid because for \( l = 2 \), \( m \) can take values of -2, -1, 0, +1, or +2, but the spin quantum number \( s \) cannot be 0; it must be either +1/2 or -1/2.
- Therefore, this set is **incorrect**.

### Conclusion:
All four sets of quantum numbers are incorrect.

### Final Answer:
**All sets of quantum numbers (I, II, III, IV) are incorrect.**

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