Question

if $\ell = 0$, which of the following may be true?
answer:
a $n = 6$
b $m_\ell = - 1$
c $m_\ell = 1$
d $m_s = 1$
e $m_s = 0$

Explanation:

Step1: Recall quantum number rules

For a given principal quantum number \(n\), the magnetic quantum number \(m_{\ell}\) ranges from \(-\ell\) to \(\ell\). When \(\ell = 0\), \(m_{\ell}=0\). The spin quantum number \(m_s=\pm\frac{1}{2}\). Also, \(n\geq\ell + 1\). If \(\ell = 0\), \(n\) can be \(n = 1,2,3,\cdots\) (but \(n = 6\) is not restricted by \(\ell=0\) in terms of the relationship \(n\geq\ell + 1\) as \(6\geq0 + 1\)).

Step2: Analyze each option

• Option A: Since \(n\geq\ell+1\) and \(\ell = 0\), \(n\) can be \(n = 6\) (because \(6\geq0 + 1\)).
• Option B: When \(\ell=0\), \(m_{\ell}=0

eq - 1\).

• Option C: When \(\ell = 0\), \(m_{\ell}=0

eq1\).

• Option D: \(m_s=\pm\frac{1}{2}

eq1\).

• Option E: \(m_s=\pm\frac{1}{2}

eq0\).

Answer:

A. \(n = 6\)