Question

question 5 (2 points) which of the following are a possible set of 4 quantum numbers? n = 0, l = 1, m_l = 2, m_s = +1/2 n = 1, l = 1, m_l = 0, m_s = +1/2 n = 1, l = 0, m_l = 0, m_s = +1/2 n = 2, l = 1, m_l = 2, m_s = +1/2

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 $m_l$ can take values $m_l=-l,-l + 1,\cdots,l$. The spin quantum number $m_s=\pm\frac{1}{2}$.

Step2: Analyze option 1

For $n = 0$, this is incorrect because $n$ must be a positive integer starting from 1.

Step3: Analyze option 2

For $n = 1$, $l$ can only be 0 (since $l$ ranges from 0 to $n - 1$ and $n=1$ gives $l = 0$), but here $l = 1$, so this is incorrect.

Step4: Analyze option 3

For $n = 1$, $l = 0$ (since $l$ ranges from 0 to $n - 1$). When $l = 0$, $m_l = 0$ (because when $l = 0$, $m_l$ has only one value which is 0), and $m_s=+\frac{1}{2}$ is a valid spin - quantum number value. This set is valid.

Step5: Analyze option 4

For $n = 2$, $l = 1$, then $m_l$ can take values $-1,0,1$. But here $m_l = 2$, so this is incorrect.

Answer:

$n = 1,l = 0,m_l = 0,m_s=+\frac{1}{2}$