Explain giving reasons, which of the following sets of quantum numbers are not possible?
(a) n=0, l=0, `m_(l)=0, m_(s)=+1/2`
(b) `n=1, l=0, m_(l)=0, m_(s)=-1/2`
(c) `n=1, l=1, m_(l)=0, m_(s)=+1/2`
(d) `n=2, l=1, m_(l)=0, m_(s)=-1/2`
(e) `n=3, l=3, m_(l)=-3, m_(s)=+1/2`
(f) `n=3, l=1, m_(l)=0, m_(s)=+1/2`

Explanation

To determine which sets of quantum numbers are not possible, we need to understand the rules governing quantum numbers:

1. **Principal Quantum Number (n)**: This number can take positive integer values (n = 1, 2, 3,...). It represents the main energy level or shell.
2. **Azimuthal Quantum Number (l)**: This number can take integer values from 0 to (n-1). It represents the subshell (s, p, d, f).
3. **Magnetic Quantum Number (m_l)**: This number can take integer values from -l to +l, including zero. It represents the orientation of the orbital.
4. **Spin Quantum Number (m_s)**: This number can take values of +1/2 or -1/2, representing the spin of the electron.

Now, let's analyze each option:
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