Which of the following sate of quantum numbers is not permissible for an electron in an atom?
(i) `n = 1,l = 1, m_(l) 0, m_(s) =+ 1//2`
(ii) `n = 3, l = 1, m_(1) =- 2, m_(s) =- 1//2`
(iii) `n =1, l = 1, m_(l) = 0, m_(s) =+ 1//2`
(iv) `n = 2, l = 0, m_(l) = 0, m_(s) = 1`

Options

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

Explanation

To determine which of the given sets of quantum numbers is not permissible for an electron in an atom, we need to analyze each set according to the rules governing quantum numbers:

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.

Now, let's analyze each option step by step:

### Option (i): `n = 1, l = 1, m_l = 0, m_s = +1/2`
- **n = 1**: Valid.
- **l = 1**: Invalid because l must be in the range of 0 to (n-1) = 0. Thus, l cannot equal 1 when n is 1.
- **Conclusion**: This set is not permissible.

### Option (ii): `n = 3, l = 1, m_l = -2, m_s = -1/2`
- **n = 3**: Valid.
- **l = 1**: Valid (l can be 0, 1, or 2 for n = 3).
- **m_l = -2**: Invalid because m_l must be in the range of -l to +l, which for l = 1 is -1 to +1.
- **Conclusion**: This set is not permissible.

### Option (iii): `n = 1, l = 1, m_l = 0, m_s = +1/2`
- **n = 1**: Valid.
- **l = 1**: Invalid because l must be in the range of 0 to (n-1) = 0.
- **Conclusion**: This set is not permissible.

### Option (iv): `n = 2, l = 0, m_l = 0, m_s = 1`
- **n = 2**: Valid.
- **l = 0**: Valid (l can be 0 or 1 for n = 2).
- **m_l = 0**: Valid (m_l can be 0 when l = 0).
- **m_s = 1**: Invalid because m_s can only be +1/2 or -1/2.
- **Conclusion**: This set is not permissible.

### Summary of Results:
- **Option (i)**: Not permissible (l cannot equal n).
- **Option (ii)**: Not permissible (m_l is out of range).
- **Option (iii)**: Not permissible (l cannot equal n).
- **Option (iv)**: Not permissible (m_s is out of range).

### Final Answer:
All options (i), (ii), (iii), and (iv) are not permissible. However, if the question asks for the most clearly incorrect set, options (i) and (ii) are the most straightforward violations of quantum number rules.