Question

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 = +1/2 part 2 n = 5, l = 3, m_l = 5, m_s = +1/2

Explanation:

Step1: Recall quantum - number rules

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

Step2: Analyze Part 1

Given $n = 2$, the possible values of $l$ are $0$ and $1$ ($l$ ranges from $0$ to $n - 1$). Since $l = 3$ here, this set of quantum numbers is invalid.

Step3: Analyze Part 2

Given $n = 5$, $l$ can range from $0$ to $4$. Here $l = 3$ is valid. For $l = 3$, $m_l$ can range from $- 3$ to $3$. Since $m_l=5$ which is outside this range, this set of quantum numbers is invalid.

Answer:

Part 1: I
Part 2: I