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

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

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Answer 1 · 2016-12-31T08:49:21

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

$[Ar] 3d^5 4s^1$

The short version on why it's not $3d^4 4s^2$ 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 $3d$ orbitals (recall that $l = 2$ , so the number of $m_l$ is $2l + 1 = 5$ ). The above valence electron configuration looks like this:

$ul(uarr color(white)(darr))$
$4s$

$ul(uarr color(white)(darr))" "ul(uarr color(white)(darr))" "ul(uarr color(white)(darr))" "ul(uarr color(white)(darr))" "ul(uarr color(white)(darr))$
$underbrace(" "" "" "" "" "" "" "" "" "" "" "" "" "" "" ")$

$color(white)(aaaaaaaaaaaaa)$ $3d$

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

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

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