Consider the following sets of quantum numbers.
(i) `{:(n,l,m,s,),(3,0,0,+1//2,):}`
(ii) `{:(n,l,m,s,),(2,2,1,+1//2,):}`
(iii) `{:(n,l,m,s,),(4,3,-2,-1//2,):}`
(iv) `{:(n,l,m,s,),(1,0,-1,-1//2,):}`
(v) `{:(n,l,m,s,),(3,2,3,+1//2,):}`
Which of the following sets of quantum number is not possible ?

Options

A. (ii),(iii) and (iv)
B. (i),(ii),(iii) and (iv)
C. (ii),(iv) and (v)
D. (i) and (iii)

Explanation

To determine which set of quantum numbers is not possible, we need to analyze each set based on the rules governing quantum numbers. The four quantum numbers are:

1. Principal quantum number (n): Indicates the energy level and can take positive integer values (n = 1, 2, 3, ...).
2. Azimuthal quantum number (l): Indicates the subshell and can take integer values from 0 to (n-1).
3. Magnetic quantum number (m): Indicates the orientation of the orbital and can take integer values from -l to +l.
4. Spin quantum number (s): Indicates the spin of the electron and can be either +1/2 or -1/2.

Now, let's analyze each set of quantum numbers:

### Set (i): (n=3, l=0, m=0, s=+1/2)
- **n = 3**: Valid (can be 1, 2, 3, ...)
- **l = 0**: Valid (l can be 0 to n-1, so l can be 0, 1, or 2)
- **m = 0**: Valid (m can be from -l to +l, so for l=0, m can only be 0)
- **s = +1/2**: Valid (spin can be +1/2 or -1/2)

**Conclusion**: This set is possible.

### Set (ii): (n=2, l=2, m=1, s=+1/2)
- **n = 2**: Valid
- **l = 2**: Not valid (l can only be 0 or 1 for n=2)
- **m = 1**: Valid (but irrelevant since l is not valid)
- **s = +1/2**: Valid

**Conclusion**: This set is not possible due to l.

### Set (iii): (n=4, l=3, m=-2, s=-1/2)
- **n = 4**: Valid
- **l = 3**: Valid (l can be 0, 1, 2, or 3 for n=4)
- **m = -2**: Valid (m can be from -3 to +3)
- **s = -1/2**: Valid

**Conclusion**: This set is possible.

### Set (iv): (n=1, l=0, m=-1, s=-1/2)
- **n = 1**: Valid
- **l = 0**: Valid
- **m = -1**: Not valid (m can only be 0 for l=0)
- **s = -1/2**: Valid

**Conclusion**: This set is not possible due to m.

### Set (v): (n=3, l=2, m=3, s=+1/2)
- **n = 3**: Valid
- **l = 2**: Valid (l can be 0, 1, or 2 for n=3)
- **m = 3**: Not valid (m can only be from -2 to +2 for l=2)
- **s = +1/2**: Valid

**Conclusion**: This set is not possible due to m.

### Final Conclusion
The sets of quantum numbers that are not possible are:
- Set (ii): (2, 2, 1, +1/2)
- Set (iv): (1, 0, -1, -1/2)
- Set (v): (3, 2, 3, +1/2)

### Summary
The answer to the question is that the sets of quantum numbers that are not possible are (ii), (iv), and (v).

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