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If energy is required to add the electron to gaseous atom (electron affinity - in case of noble gases) then why is further energy (ionization energy) required to remove it?

The reason for ionization energy to be positive is that it is energy required from electron at some distance $r$, to take it to infinity (with random E=0).

How is electron affinity explained in similar way?

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  • $\begingroup$ What about e.g. the Wikipedia article is unclear to you? $\endgroup$
    – ACuriousMind
    Jul 16 '15 at 23:47
  • $\begingroup$ my doubt is Not about individual Concept.... Infact about its relation to each Other. Isnt the above statement Contradict the Law of conservation of energy $\endgroup$
    – AMS
    Jul 16 '15 at 23:48
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Start with some neutral atom $X$:

  1. The electron affinity is the energy change when an electron travels from infinity to the atom to create the negatively charged ion $X^-$.

  2. The ionisation energy is the energy change when one of the electrons in the neutral atom $X$ is removed to infinity to create the positive ion $X^+$.

If I interpret your question correctly you are suggesting that the energies required for the two processes (1) and (2) should be equal and opposite. However the two processes are completely different, with different numbers of electrons and different end products, and their energies are not related.

If you take the energy add an electron to $X$ to produce $X^-$, and the energy to remove an electron from $X^-$ to produce $X$, the the two energies will be equal and opposite.

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