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 $l=0,1,2$. The magnetic quantum number $m$ can take values from $-l$ to $+l$.

Step2: Check the validity of $l$ values

  • For $l = 3$, since $n=3$ and $l$ should satisfy $l\leq n - 1=2$, $l = 3$ is not valid.
  • For $l = 0$, since $0\leq2$, $l = 0$ is valid.
  • For $l=-1$, $l$ cannot be negative, so $l=-1$ is not valid.

Step3: Check the validity of $m$ values

  • When $l$ can be at most $2$, for $m = 3$, since $m$ values range from $-l$ to $+l$ and the maximum $l$ is $2$, $m = 3$ is not valid.
  • For $m=-2$, when $l\geq2$, $m=-2$ is a valid value as it is in the range $[-l, +l]$.
  • For $m = 2$, when $l\geq2$, $m = 2$ is a valid value as it is in the range $[-l, +l]$.

Answer:

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