Question

for the n = 3 electron shell, which of the following quantum numbers are valid? check all that apply.
□ l = 3
□ m = 3
□ l = 0
□ m = -2
□ l = -1
□ m = 2
done

Explanation:

Step1: Recall quantum - number rules

For a given principal quantum number $n$, the angular - momentum quantum number $l$ can take values from $0$ to $n - 1$. The magnetic quantum number $m$ can take values from $-l$ to $l$. Here $n = 3$. So $l$ can be $0,1,2$ and for each $l$, $m$ values range from $-l$ to $l$.

Step2: Analyze $l$ values

Since $n=3$, $l$ cannot be $3$ (because $l$ ranges from $0$ to $n - 1=2$) and $l$ cannot be $- 1$ (as $l\geq0$). So $l = 0$ is valid.

Step3: Analyze $m$ values

When $l = 0$, $m = 0$. When $l=1$, $m=-1,0,1$. When $l = 2$, $m=-2,-1,0,1,2$. So $m = 3$ is not valid, while $m=-2$ and $m = 2$ are valid.

Answer:

$l = 0$, $m=-2$, $m = 2$