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Electronegativity is a chemical property that says how well an atom can attract electrons towards itself.

The electron affinity of an atom or molecule is defined as the amount of energy released when an electron is added to a neutral atom or molecule in the gaseous state to form a negative ion.

However,fluorine is taken as the most electronegative element but chlorine is accepted as the element with most electron affinity.

But shouldn't the atom which attracts the electron the strongest also release the most energy?

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I wouldn't shoot this down so quickly - consider, e.g. Mulliken electronegativity, defined as the average of the electron affinity and ionisation energy. If you think about it, electronegativity depends not only on how strongly an atom pulls other electrons to itself, but also how willing it is to give up its own electrons. The former can be somewhat represented by the EA, the latter by the IE.

One point that hasn't been mentioned is that electronegativity is not a physical parameter which can be measured. It is a human construct, which is often helpful in explaining chemical reactivity, but at the end of the day it is not something which can be derived from physics. Therefore, there is no real reason to expect that there should be any one-to-one correlation between the EN and the EA (unless the EN scale is explicitly defined to follow the EA). For example, if you use the more common Pauling scale (defined by bond dissociation energies), there's no real reason why the trend in EN should match the trend in EA exactly.

Broadly speaking, the trends match (because of what you've said) - e.g. both EN and EA generally increase going across a period. However, the small details like chlorine vs. fluorine won't necessarily match.

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You should keep in mind that electron affinity is a property of atoms, while electronegativity is a property of atoms when they form bonds with other atoms.

Fluorine is indeed the most electronegative element, which means that if there is a bond between an atom of fluorine and an atom of another element, then the fluorine atom will attract the electrons of the bond towards itself. When it comes to electron affinity, chlorine has a lower value than fluorine because fluorine is small, so when you add an electron to it, the increase in attraction of the electrons to the nucleus leads to more energy being released when an electron is added. Chlorine, on the other hand, has an increased atomic radius so the distance from the electron to protons increases and the electrons have less of an attraction to the nucleus meaning that when an electron is added lesser energy will be released due to the lesser attractions.

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this question is good even I had the same question and I searched web and found that it already has an answer here although the answer is bit long but it's coomprehensive. The answer has mainly to do with sum of electron affinity and ionization energy of the atom being considered.

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