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

$l = 3$
$m = 3$
$l = 0$
$m = -2$
$l = -1$
$m = 2$

Question

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

$l = 3$
  $m = 3$
  $l = 0$
  $m = -2$
  $l = -1$
  $m = 2$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Quantum Numbers", "Azimuthal Quantum Number" ], "new_concepts": [], "current_concepts": [ "Quantum Numbers", "Azimuthal Quantum Number", "Magnetic Quantum Number" ] } ## Determine allowed values of $l$ $$ \begin{aligned} &n = 3 \ &l \in \{0, 1, \dots, n-1\} = \{0, 1, 2\} \end{aligned} $$ ## Determine allowed values of $m$ $$ \begin{aligned} &m \in \{-l, \dots, +l\} \ &\text{For } l = 2: m \in \{-2, -1, 0, 1, 2\} \ &\text{For } l = 1: m \in \{-1, 0, 1\} \ &\text{For } l = 0: m \in \{0\} \end{aligned} $$ ## Evaluate given options $$ \begin{aligned} &l = 3 \quad \text{(Invalid, since } l \le 2\text{)} \ &m = 3 \quad \text{(Invalid, since } |m| \le l \le 2\text{)} \ &l = 0 \quad \text{(Valid)} \ &m = -2 \quad \text{(Valid, when } l = 2\text{)} \ &l = -1 \quad \text{(Invalid, since } l \ge 0\text{)} \ &m = 2 \quad \text{(Valid, when } l = 2\text{)} \end{aligned} $$

$l = 3$

$m = 3$

$l = 0$

$m = -2$

$l = -1$

$m = 2$

{ "subject": "Natural Science", "question_type": "Multiple Choice", "knowledge_point": [ "Natural Science", "Chemistry", "Quantum Numbers" ] }

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Determine allowed values of \(l\)

Determine allowed values of \(m\)

Evaluate given options

Answer: