What is the number of half-filled orbitals in an atom of chromium?

Dec 31, 2016

Remember that chromium, like molybdenum (but not tungsten), has a half-filled $3 d$ subshell:

$\left[A r\right] 3 {d}^{5} 4 {s}^{1}$

The short version on why it's not $3 {d}^{4} 4 {s}^{2}$ is that maximizing parallel electron spins minimizes the energy of the electron configuration. More detail on that should be lightly researched by reading this answer here.

All core orbitals are doubly-occupied. Therefore, they are not considered in the list of half-filled orbitals.

Half-filled orbitals contain one electron, but there are five $3 d$ orbitals (recall that $l = 2$, so the number of ${m}_{l}$ is $2 l + 1 = 5$). The above valence electron configuration looks like this:

$\underline{\uparrow \textcolor{w h i t e}{\downarrow}}$
$4 s$

$\underline{\uparrow \textcolor{w h i t e}{\downarrow}} \text{ "ul(uarr color(white)(darr))" "ul(uarr color(white)(darr))" "ul(uarr color(white)(darr))" } \underline{\uparrow \textcolor{w h i t e}{\downarrow}}$
$\underbrace{\text{ "" "" "" "" "" "" "" "" "" "" "" "" "" "" }}$

$\textcolor{w h i t e}{a a a a a a a a a a a a a}$ $3 d$

So, now you should see that there are six unpaired electrons, meaning that you have six half-filled orbitals.