From the following sets quantum number state which are possible. Explain why the other are not permitted ?
a. `n = 0, l = 0, m= 0, s = + 1//2`
b. `n = 1, l = 0, m= 0, s = - 1//2`
c. `n = 1, l = 1, m= 0, s = + 1//2`
d. `n = 1, l = 0, m= +1, s = + 1//2`
e. `n = 0, l = 1, m= -1, s = - 1//2`
f. `n = 2, l = 2, m= 0, s = - 1//2`
g. `n = 2, l = 1, m= 0, s = - 1//2`

Explanation

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

1. **Principal Quantum Number (n)**: It must be a positive integer (n = 1, 2, 3,...). It cannot be zero or negative.
2. **Azimuthal Quantum Number (l)**: It can take values from 0 to (n-1). Therefore, for a given n, l must be less than n.
3. **Magnetic Quantum Number (m)**: It can take values from -l to +l, including zero.
4. **Spin Quantum Number (s)**: It can be +1/2 or -1/2.

Now, let's evaluate each set of quantum numbers provided in the question:
...