for the n = 3 electron shell, which of the following quantum numbers are valid? check all that apply.\n□ l =…

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

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

Answer

Explanation:

Step1: Recall the rules for quantum numbers

For a given principal quantum number $n$, the angular - momentum quantum number $l$ can take values from $0$ to $n - 1$. Here $n = 3$, so $l=0,1,2$.

Step2: Recall the rule for the magnetic quantum number $m$

For a given $l$, the magnetic quantum number $m$ can take values from $-l$ to $+l$.

Step3: Check each option

  • For $l = 3$: Since $n=3$ and $l$ ranges from $0$ to $n - 1=2$, $l = 3$ is not valid.
  • For $m = 3$: When $l$ has a maximum value of $2$ for $n = 3$, $m$ ranges from $- 2$ to $2$, so $m = 3$ is not valid.
  • For $l = 0$: Since $0$ is in the range $0\leq l\leq n - 1$ (where $n = 3$), $l = 0$ is valid.
  • For $m=-2$: When $l\geq2$, $m$ can be $- 2$, so $m=-2$ is valid.
  • For $l=-1$: $l$ cannot be negative, so $l=-1$ is not valid.
  • For $m = 2$: When $l\geq2$, $m$ can be $2$, so $m = 2$ is valid.

Answer:

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