Which of the following are invalid sets of quantum numbers?

Question

$3, 4, 0, 1/2$
$2, 1, 3, 1/2$
$-2, 1, 0, -1/2$
$3, 2, 2, -1/2$
$3, 2, 0, -1/2$

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Answer 1 · 2016-11-09T17:14:32

Several rules apply here:

For the format $(n,l,m_l,m_s)$ :

$(3, 4, 0, 1/2)$ is invalid because $l > n$ .
$(2, 1, 3, 1/2)$ is invalid because $m_l$ is outside the range of $l$ .
$(-2, 1, 0, -1/2)$ is invalid because $n < 1$ .
$(3, 2, 2, -1/2)$ is valid because $n > 1$ , $l < n$ , $m_l$ is within the range of $l$ , and $m_s$ is correctly either $+"1/2"$ or $-"1/2"$ .
$(3, 2, 0, -1/2)$ is valid for the same reason as the fourth choice.