[Teddy3333]

Take, for example, Chromium. Wikipedia says that Chromium sublevels fill [Ar] 3d⁵ 4s¹. How is this possible? It seems to me that sublevel 3d would simply fill up, instead we have a free floating electron in the next sublevel.
Thanks!

[Wald_ron]

3d5 is more stable than 3d6 or 3d4 4s2
this is due to columbic repulsion (pi_c)
and exchange energy (pi_e)

columb's law says the force is proportional to the product of the charges over the distance squared.

The d have 5 orbitals , each orbital may hold a maximum of two electrons

 the lowest energy that an orbital can have ( and thus most stable ) is when the electrons are far apart       

thus:
2 electrons in same orbital  higher E than 2 electrons in different orbitals

furthermore, electrons may exchange, and move to different orbitals, which means lower energy still.

The net result is having 5e- in 3d is lower in energy than having 2 in 4s.

[Teddy3333]

3d5 is more stable than 3d6 or 3d4 4s2
this is due to columbic repulsion (pi_c)
and exchange energy (pi_e)

columb's law says the force is proportional to the product of the charges over the distance squared.

The d have 5 orbitals , each orbital may hold a maximum of two electrons

 the lowest energy that an orbital can have ( and thus most stable ) is when the electrons are far apart       

thus:
2 electrons in same orbital  higher E than 2 electrons in different orbitals

furthermore, electrons may exchange, and move to different orbitals, which means lower energy still.

The net result is having 5e- in 3d is lower in energy than having 2 in 4s.

Very interesting... So, even though the sublevels don't arrange "right" (some numbers coming in front of other), the orbitals also come into play in determining where the e- will actually end up? Hm. Interesting.

[fledarmus]

Just one of the things that make transition metal chemistry so interesting. The 4s orbital is slightly lower in energy than the 3d orbitals, and electrons would be assigned there first. However, there is more energy required to put a second electron in an orbital than there is to put the first electron in the orbital, due to repulsion of the electrons (this is why you put one electron in each of the . There is also some extra stability gained by having a group of sublevels half full.

So although you would assign two electrons to the 4s orbital before assigning any to the 3d orbitals, the repulsion of the two 4s orbitals and the extra stability gained by having 1 electron in each of the 3d orbitals is just enough to overcome the actual energy difference between a 4s and 3d orbital. Your filling order would be:

4s2 3d1
4s2 3d2
4s2 3d3
4s1 3d5
4s2 3d5