[Cr4zyM4tt]

I read somewhere that Carbon seem to have a valency of 2 as it has 2 unpaired electrons but it has 4 due to hybridisation.

My main question is, do atom tend to achieve stability by pairing their unpaired electrons only and not fill up the shell? Or do they try to achieve a noble gas configuration? If the former is true, can't atoms just arrange electrons in pairs in the first place which is in theory less stable.

Another question, for transition metals, they don't seem to achieve a noble gas configuration right?

[mikasaur]

Carbon is special because the 2s and 2p subshells are so close in energy that one of the electrons from the 2s will "move" to the 2p while bonding, allowing for an sp³ hybridization like you say. When it does this it can easily achieve a noble gas configuration via 4 σ-bonds (single bonds) to other atoms (like hydrogen).

An atom like nitrogen already has a full 2s and 1 electron in each of the three orbitals, each of those three with the same spin due to the Pauli exclusion principle. Nitrogen doesn't behave like Carbon because there's nowhere for that 2s electron to go. Nitrogen happily achieves a noble configuration by forming 3 single bonds.

[Borek]

An atom like nitrogen already has a full 2s and 1 electron in each of the three orbitals, each of those three with the same spin due to the Pauli exclusion principle

Nope. Pauli exclusion principle doesn't say anything about spins of electrons on different orbitals. Hund's rule says that the lowest energy state is the one with the highest mutiplicity and this is why we will typically write nitrogen 2s and 2d as        , but there is nothing wrong with the atom that is        , it just has a bit higher energy.

[mikasaur]

Interesting, Borek. I hadn't thought of that before. Thanks!

[Vidya]

I read somewhere that Carbon seem to have a valency of 2 as it has 2 unpaired electrons but it has 4 due to hybridisation.

My main question is, do atom tend to achieve stability by pairing their unpaired electrons only and not fill up the shell? Or do they try to achieve a noble gas configuration? If the former is true, can't atoms just arrange electrons in pairs in the first place which is in theory less stable.

Another question, for transition metals, they don't seem to achieve a noble gas configuration right?

Carbon is a nonmetal and it can not lose 4 electrons or gain 4 electrons which is energetically not feasible.To complete its octet it needs to share 4 electrons which it can achieve in its excited state of electronic configuration.You can check this video for better understanding.
https://www.youtube.com/watch?v=aAv2J9r_-tg

[Enthalpy]

"Pairing" electrons doesn't by itself bring an energetic advantage. (And just in case of doubt: the magnetic interaction between two electrons is very weak). So since electrons repel another due to their charge, a lone carbon atom (something rare) puts two unpaired electrons on 2p_x and 2p_y because they're farther apart there (an other reason exists, Hundt's rule, yes), and a lone nitrogen atom puts three unpaired electrons on 2p_x, 2p_y and 2p_z.

The whole trick of paired electrons is when this permits to put more (=two each) electrons on an orbital of lower energy. Take H₂ as an example: at small distance, what were two 1s orbital become one bonding and one antibonding orbitals, which would be energy-neutral or even unfavourable, BUT the two possible spins permit both electrons to occupy the bonding orbital, resulting in a net gain.

Sometimes orbitals are favourable enough that two electrons there have a lower energy (2p in a lone carbon atom), sometimes the energies are close enough that repulsion puts the electrons apart (2p_x and 2p_y have the same energy in a lone carbon atom), and sometimes it depends (transition elements).

This holds for molecular orbitals too. O₂ has two lone electrons on two molecular orbitals of identical energy.