Explain,giving reasons,which of the following sets of quantum numbers are not possible.
$(a)$ $n=0, l=0, m_{l}=0, m_{s}=+\frac{1}{2}$
$(b)$ $n=1, l=0, m_{l}=0, m_{s}=-\frac{1}{2}$
$(c)$ $n=1, l=1, m_{l}=0, m_{s}=+\frac{1}{2}$
$(d)$ $n=2, l=1, m_{l}=0, m_{s}=-\frac{1}{2}$
$(e)$ $n=3, l=3, m_{l}=-3, m_{s}=+\frac{1}{2}$
$(f)$ $n=3, l=1, m_{l}=0, m_{s}=+\frac{1}{2}$

(A) Not possible: The principal quantum number $n$ must be a positive integer $(n \geq 1)$.
$(b)$ Possible: $n=1, l=0, m_{l}=0, m_{s}=-\frac{1}{2}$ follows all rules.
$(c)$ Not possible: For a given $n$,$l$ can only range from $0$ to $n-1$. For $n=1$,$l$ must be $0$.
$(d)$ Possible: $n=2, l=1, m_{l}=0, m_{s}=-\frac{1}{2}$ follows all rules.
$(e)$ Not possible: For $n=3$,$l$ can only be $0, 1, 2$. It cannot be $3$.
$(f)$ Possible: $n=3, l=1, m_{l}=0, m_{s}=+\frac{1}{2}$ follows all rules.