Question

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

Answer 1

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.