Question

which of the following sets of quantum numbers could describe an electron in the orbital shown below? a $n = 3$, $l = 2$, $m_{l}=-2$ b $n = 2$, $l = 1$, $m_{l}=-1$ c $n = 3$, $l = 1$, $m_{l}=0$ d $n = 3$, $l = 0$, $m_{l}=0$ e $n = 4$, $l = 1$, $m_{l}=1$

Explanation:

• The orbital shown is a spherical - shaped \(s\) orbital. For an \(s\) orbital, the angular momentum quantum number \(\ell = 0\).
• The principal quantum number \(n\) can be any positive integer (\(n = 1,2,3,\cdots\)). For a given \(\ell = 0\), the magnetic quantum number \(m_{\ell}=0\) (since \(m_{\ell}\) ranges from \(-\ell\) to \(+\ell\) and when \(\ell = 0\), \(m_{\ell}=0\)).

Answer:

D. \(n = 3\), \(\ell=0\), \(m_{\ell}=0\)