Question

which of the following is not a valid set of quantum numbers? n = 3, l = 3, m = 3 n = 1, l = 0, m = 0 n = 2, l = 1, m = 0

Explanation:

Step1: Recall quantum - number rules

The principal quantum number $n$ can take values $n = 1,2,3,\cdots$. The angular - momentum quantum number $l$ can take values $l=0,1,\cdots,n - 1$. The magnetic quantum number $m$ can take values $m=-l,-l + 1,\cdots,0,\cdots,l - 1,l$.

Step2: Analyze the first option

For $n = 3$, the possible values of $l$ are $l = 0,1,2$. Since $l = 3$ is not allowed when $n=3$ (because $l$ must satisfy $l\lt n$), the set $n = 3,l = 3,m = 3$ is not valid.

Step3: Analyze the second option

For $n = 1$, $l$ can only be $l = 0$, and when $l = 0$, $m = 0$ is a valid value. So $n = 1,l = 0,m = 0$ is a valid set.

Step4: Analyze the third option

For $n = 2$, the possible values of $l$ are $l=0,1$. When $l = 1$, the possible values of $m$ are $m=-1,0,1$. So $n = 2,l = 1,m = 0$ is a valid set.

Answer:

$n = 3,l = 3,m = 3$