Question

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which of the following sets of quantum numbers are valid (enter v) and which are invalid (enter i) for the known elements?
part 1
$n = 2, l = 3, m_l = 0, m_s=+\frac{1}{2}$
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Explanation:

Step1: Recall quantum - number rules

The principal quantum number $n$ can take positive integer values ($n = 1,2,3,\cdots$). The angular - momentum quantum number $l$ can take values from $0$ to $n - 1$. The magnetic quantum number $m_l$ can take values from $-l$ to $+l$, and the spin quantum number $m_s=\pm\frac{1}{2}$.

Step2: Check the given values

Here, $n = 2$. According to the rule for $l$, $l$ can take values $0$ and $1$ ($l$ ranges from $0$ to $n - 1$, so when $n = 2$, $l=0,1$). But in the given set, $l = 3$ which violates the rule $l\leq n - 1$.

Answer:

I