Question

question 15 (0.25 points) listen which of the following set of quantum numbers cannot exist? a) $n = 5, l = 4, m_l = 3, m_s = +1/2$ b) $n = 5, l = 3, m_l = +1, m_s = +1/2$ c) $n = 4, l = 3, m_l = 3, m_s = +1/2$ d) $n = 5, l = 2, m_l = +2, m_s = +1/2$ e) $n = 4, l = 2, m_l = +1, m_s = +1$

Explanation:

Step1: Recall quantum number rules

The valid ranges are:

• $n \geq 1$ (integer)
• $0 \leq l \leq n-1$ (integer)
• $-l \leq m_l \leq +l$ (integer)
• $m_s = +\frac{1}{2}$ or $-\frac{1}{2}$

Step2: Check option a

$n=5$, $l=4$ (valid, $4 \leq 5-1=4$); $m_l=3$ (valid, $-4 \leq 3 \leq 4$); $m_s=+\frac{1}{2}$ (valid).

Step3: Check option b

$n=5$, $l=3$ (valid, $3 \leq 5-1=4$); $m_l=+1$ (valid, $-3 \leq 1 \leq 3$); $m_s=+\frac{1}{2}$ (valid).

Step4: Check option c

$n=4$, $l=3$ (valid, $3 \leq 4-1=3$); $m_l=3$ (valid, $-3 \leq 3 \leq 3$); $m_s=+\frac{1}{2}$ (valid).

Step5: Check option d

$n=5$, $l=2$ (valid, $2 \leq 5-1=4$); $m_l=+2$ (valid, $-2 \leq 2 \leq 2$); $m_s=+\frac{1}{2}$ (valid).

Step6: Check option e

$n=4$, $l=2$ (valid, $2 \leq 4-1=3$); $m_l=+1$ (valid, $-2 \leq 1 \leq 2$); $m_s=+1$ (invalid, only $\pm\frac{1}{2}$ allowed).

Answer:

e) $n = 4, l = 2, m_l = +1, m_s = +1$