Yes, chromium could be one.
Right from the start, you can guess that the unknown element must be a d-block element, or a transition metal.
That must be the case because in order to be able to accomodate six unpaired electrons you need to have access to the five d-orbitals transition metals have access to.
As you know, each orbital can hold a maximum of two electrons of different spin.
When degenerate atomic orbitals are filled, they follow Hund’s Rule, which states that one electron is added to each degenerate orbital in a subshell before two electrons can be added to the same orbital in a subshell.
This implies that you can have a maximum of five unpaired electrons, one in each of the five d-orbitals.
So where will the sixth unpaied electron be placed?
Take a look at the of manganese, ##”Mn”##
##”Mn: ” [“Ar”] 3d^5 4s^2##
Manganese has five unpaired electrons in its five 3d-orbitals and two paired electrons in its 4s-orbital.
This is in fact a clue – you can have six unpaired electrons if you have five unpaired electrons in the 3d-orbitals and one unpaired electron in the 4s-orbital.
The element that matches this electron configuration is chromium, ##”Cr”##
##”Cr: ” [“Ar”] 3d^5 4s^1##
You can rad more about why chromium’s electron configuration looks like that here:
http://socratic.org/questions/why-do-electron-configurations-of-chromium-and-copper-contradict-the-aufbau-prin
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