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Why is the electronegativity of oxygen greater than of carbon?

Answer
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Hint :An atom is more stable when the electrons in its outermost orbitals are either all paired or are all unpaired, rest of the configurations are less stable.

Complete Step By Step Answer:
Electronegativity is the tendency of an atom in a molecule to attract the shared pair of electrons towards itself. Electronegativity increases as you go across a period from left to right as the nuclear charge increases and atomic size decreases. As we go down the group, the nuclear charge increases but is compensated by the fact that orbitals also increase, therefore, the electronegativity decreases.
Therefore, we can say that carbon has a bigger orbital than that of oxygen.
Now we will write the electronic configuration of oxygen and carbon, so as to at least see their electronic configuration.
$
  O = 1{s^2}2{s^2}2{p^4} \\
  C = 1{s^2}2{s^1}2{p^3} \\
 $
As we can see in the electronic configuration of oxygen it has two unpaired electrons in its second orbital, therefore it must be too eager to pair with electrons in its affinity and therefore making it electronegative.
The electronic configuration of carbon states that there are four electrons in the outermost orbital.
These four electrons are all unpaired as the most stable state is which while all have paired or unpaired, nothing in between, rest all are less stable. So, if carbon is in such a stable state then its tendency to attract electrons is very low making it very less electronegative than any non-metal as itself.
The electronegativity of oxygen is greater than carbon due to attraction from its paired and unpaired electrons while carbon has a stable state and it is difficult for it to gain 4 electrons, too much energy would be needed.

Note :
Carbon and its group elements all have four electrons in the outermost orbit making them the best element for covalent bonds. Carbon and its derivatives are used very vividly in our world now.