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State which of the following sets of qua...

State which of the following sets of quantum number would be possible and which would not be permisible for an electron in an atom.
(i) `n=3,I=3,m_(l)=+3, m_(s)=+(1)/(2)`
(ii) `n=3,I=3,m_(l)=+1, m_(s)=-(1)/(2)`
(iii) `n=5,I=4,m_(l)=+3, m_(s)=(1)`
(iv) `n=0,I=0,m_(l)=0, m_(s)=+(1)/(2)`
(v) `n=4,I=3,m_(l)=-2, m_(s)=-(1)/(2)`

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To determine which sets of quantum numbers are permissible for an electron in an atom, we need to apply the rules governing quantum numbers. The quantum numbers are: 1. **Principal Quantum Number (n)**: It can take positive integer values (n = 1, 2, 3, ...). 2. **Azimuthal Quantum Number (l)**: It can take integer values from 0 to (n - 1). 3. **Magnetic Quantum Number (m_l)**: It can take integer values from -l to +l. 4. **Spin Quantum Number (m_s)**: It can take values of +1/2 or -1/2. Let's analyze each set of quantum numbers step by step: ### (i) n = 3, l = 3, m_l = +3, m_s = +1/2 - **n = 3**: Valid (n must be a positive integer). - **l = 3**: Not valid. For n = 3, l can be 0, 1, or 2 (l must be in the range 0 to n - 1). - **m_l = +3**: Not valid. Since l = 3 is invalid, m_l cannot be +3. - **m_s = +1/2**: Valid (m_s can be +1/2 or -1/2). **Conclusion**: This set is **not permissible**. ### (ii) n = 3, l = 3, m_l = +1, m_s = -1/2 - **n = 3**: Valid. - **l = 3**: Not valid. Same reason as above. - **m_l = +1**: Not valid because l = 3 is invalid. - **m_s = -1/2**: Valid. **Conclusion**: This set is **not permissible**. ### (iii) n = 5, l = 4, m_l = +3, m_s = 1 - **n = 5**: Valid. - **l = 4**: Valid. For n = 5, l can be 0, 1, 2, 3, or 4. - **m_l = +3**: Valid. For l = 4, m_l can range from -4 to +4. - **m_s = 1**: Not valid. m_s can only be +1/2 or -1/2. **Conclusion**: This set is **not permissible**. ### (iv) n = 0, l = 0, m_l = 0, m_s = +1/2 - **n = 0**: Not valid. n must be a positive integer (n = 1, 2, 3, ...). - **l = 0**: Valid only if n is valid. - **m_l = 0**: Valid only if l is valid. - **m_s = +1/2**: Valid. **Conclusion**: This set is **not permissible**. ### (v) n = 4, l = 3, m_l = -2, m_s = -1/2 - **n = 4**: Valid. - **l = 3**: Valid. For n = 4, l can be 0, 1, 2, or 3. - **m_l = -2**: Valid. For l = 3, m_l can range from -3 to +3. - **m_s = -1/2**: Valid. **Conclusion**: This set is **permissible**. ### Summary of Results: 1. (i) Not permissible 2. (ii) Not permissible 3. (iii) Not permissible 4. (iv) Not permissible 5. (v) Permissible
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