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