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The answer for question 4.57 says that a higher electronegativity for an atom makes its orbitals have lower energy. Why is that?
Electronegativity is directly proportional to effective nuclear charge, so when electronegativity is high, the nuclear charge is high as well. The high nuclear charge strongly attracts the electrons and pulls them in, decreasing the energy of the orbitals.
Can you apply the same logic to a relationship between electronegativity and atomic size? As in would more electronegative atoms be smaller in size?
I think that the more electronegative an atom is, the more easy it is to attract electrons. This goes up in a diagonal trend, so increase as group goes to the right and as period goes up, disregarding noble gases. The atomic radius will increase as group goes to the left and period goes down. There is not necessarily a correlation however because there may be exceptions.
As an example, consider the most electronegative element F. When it comes to effective nuclear charge, smaller atoms tend to have higher effective nuclear charge because the nucleus is less shielded therefore its nucleus pulls electrons toward it more easily than say, Cl, which is also quite electronegative, but less so than F, O, and N. I do not know that having a higher effective nuclear charge makes the orbitals have lower energy, but rather, but rather these especially electronegative atoms at the top of the p-block with high effective nuclear charge simply--intrinsically have lower energy orbitals.
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