Identify which of the following sets of quantum numbers are not possible and explain why.
$(a) n = 0, l = 0, m_l = 0, m_s = +1/2$
$(b) n = 1, l = 0, m_l = 0, m_s = -1/2$
$(c) n = 1, l = 1, m_l = 0, m_s = +1/2$
$(d) n = 2, l = 1, m_l = 0, m_s = -1/2$
$(e) n = 3, l = 3, m_l = 3, m_s = +1/2$
$(f) n = 3, l = 1, m_l = 0, m_s = +1/2$

(A, C, E) The following sets of quantum numbers are not possible:
$(a) n = 0$ is not possible because the principal quantum number $n$ must be a positive integer $(n = 1, 2, 3, \dots)$.
$(c) n = 1, l = 1$ is not possible because for a given $n$,the azimuthal quantum number $l$ can only range from $0$ to $n-1$. Thus,if $n = 1$,$l$ must be $0$.
$(e) n = 3, l = 3$ is not possible because $l$ must always be less than $n$ $(l < n)$. Therefore,$l$ can only take values $0, 1, 2$ when $n = 3$.