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Which of the following sets of quantum n...

Which of the following sets of quantum numbers represent an impossible arrangement :-
`{:(,n,l,m,m_(s),),((A),3,2,-2,(1)/(2),),((B),4,0,0,(1)/(2),),((C),3,2,-3,(1)/(2),),((D),5,3,0,(1)/(2),):}`

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To determine which set of quantum numbers represents an impossible arrangement, we need to analyze each set based on the rules governing quantum numbers. The four quantum numbers are: 1. **Principal Quantum Number (n)**: This can take positive integer values (1, 2, 3,...). 2. **Azimuthal Quantum Number (l)**: This can take integer values from 0 to (n-1). 3. **Magnetic Quantum Number (m)**: This can take integer values from -l to +l, including zero. 4. **Spin Quantum Number (s)**: This can take values of +1/2 or -1/2. Now, let's evaluate each option: ### Option A: (n=3, l=2, m=-2, s=1/2) - **n = 3**: Valid. - **l = 2**: Valid since l can be from 0 to n-1 (0, 1, 2). - **m = -2**: Valid since m can range from -l to +l (-2, -1, 0, 1, 2). - **s = 1/2**: Valid. **Conclusion**: This set is valid. ### Option B: (n=4, l=0, m=0, s=1/2) - **n = 4**: Valid. - **l = 0**: Valid since l can be from 0 to n-1 (0, 1, 2, 3). - **m = 0**: Valid since m can only be 0 when l = 0. - **s = 1/2**: Valid. **Conclusion**: This set is valid. ### Option C: (n=3, l=2, m=-3, s=1/2) - **n = 3**: Valid. - **l = 2**: Valid since l can be from 0 to n-1 (0, 1, 2). - **m = -3**: Invalid. Since l = 2, m can only range from -2 to +2. - **s = 1/2**: Valid. **Conclusion**: This set is invalid due to m = -3. ### Option D: (n=5, l=3, m=0, s=1/2) - **n = 5**: Valid. - **l = 3**: Valid since l can be from 0 to n-1 (0, 1, 2, 3, 4). - **m = 0**: Valid since m can range from -l to +l (-3, -2, -1, 0, 1, 2, 3). - **s = 1/2**: Valid. **Conclusion**: This set is valid. ### Final Answer: The impossible arrangement is **Option C**: (n=3, l=2, m=-3, s=1/2). ---
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