## Why # regions of e density= # atomic orbitals?

$sp, sp^{2}, sp^{3}, dsp^{3}, d^{2}sp^{3}$

Mei Blundell_1J
Posts: 32
Joined: Fri Apr 06, 2018 11:01 am
Been upvoted: 1 time

### Why # regions of e density= # atomic orbitals?

I was interested in this fact from Wednesday's lecture. The number of atomic orbitals in an atom is the same as the number of regions of electron density that appear when the atom participates in bonding. Is this just a really cool coincidence? Why is this?

A key part in my question is about why the number of atomic orbitals is the same as the number of hybrid orbitals. I think I'm pretty clear on the second part, which is why the number of hybrid orbitals is the same as the number of regions of electron density.
Last edited by Mei Blundell_1J on Thu May 31, 2018 5:43 pm, edited 1 time in total.

Beverly Shih 1K
Posts: 34
Joined: Wed Nov 15, 2017 3:01 am
Been upvoted: 1 time

### Re: Why # regions of e density= # atomic orbitals?

I think what you're referring to is the line from the lecture slide that "regions of e- density = number of hybrid orbitals". When hybridization occurs, atomic orbitals are mixed to become hybridized orbitals and electrons are redistributed among the hybridized orbitals. For example, when carbon hybridizes, it ends up with 4 unpaired electrons in the 2p3 shell. The 2p3 shell is a mix of the 2s shell (1 orbital) and 2p shell (3 orbitals) so it has 4 hybrid orbitals. All of these orbitals contain unpaired electrons that want to bind to other molecules, so they become regions of electron density. So when it's bonded in a molecule, carbon has 4 hybrid orbitals and 4 regions of electron density.

Mei Blundell_1J
Posts: 32
Joined: Fri Apr 06, 2018 11:01 am
Been upvoted: 1 time

### Re: Why # regions of e density= # atomic orbitals?

Thanks Beverly! This sentence "The 2p3 shell is a mix of the 2s shell (1 orbital) and 2p shell (3 orbitals) so it has 4 hybrid orbitals." was particularly helpful. More specifically, I'm wondering why there are necessarily 4 ways (hybrid orbitals) to mix 4 atomic orbitals.

Beverly Shih 1K
Posts: 34
Joined: Wed Nov 15, 2017 3:01 am
Been upvoted: 1 time

### Re: Why # regions of e density= # atomic orbitals?

The 4 hybrid orbitals (sp3) is just one example of how orbitals can hybridize. In a molecule like HCONH2, the carbon actually has 3 hybrid orbitals (sp2) because it has a single bond with hydrogen, a single bond with nitrogen, and a double bond with oxygen. In the double bond with oxygen, the sigma bond arises from one of the hybridized sp2 orbitals, and the pi bond arises from the leftover p orbital.
Basically, atoms in molecules can have hybridized orbitals like sp, sp2, sp3, sp3d, sp3d2 and other combinations, so they end up with the right number of bonds. It's not always sp3, we just happen to see that a lot because it hybridizes the s orbital and all of the available p orbitals.