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Even though electron affinity and ionization energy are opposites of each other (the former is energy required to add an e-, while the latter is energy required to remove an e-), they have the same trend on the periodic table. why is this this the case?
Electron affinity is how likely an element is to gain an electron while electron ionization is the energy required to lose an electron. If we look at Fluorine we can see why these two concepts have the same trend. Fluorine has a high electron affinity because it wants to gain an electron to have an octet. Conversely, Fluorine does not want to lose its electrons and would require a lot of energy to lose an electron. Therefore, it also has a high ionization energy.
noble gases are exception for electron affinity because since their outermost energy levels are completely filled with electrons, therefore, another electron cannot enter that level. This means that noble gases have basically zero electron affinity and highest ionization energies.
I think the reason you are confused is because you have an incorrect definition of electron affinity. Since electron affinity is how much an element "wants" an electron, it only makes sense that the more an element wants an electron, the harder (greater energy) it will take to take an electron away from that element. So as EA increases, so does IE, and vice versa.
Electron affinity is the how likely an atom is to gain an electron, and ionization energy is the energy required to remove an electron. Electron affinity therefore increases as you go across the periodic table because the effective nuclear charge is increasing. Effective nuclear charge is dependent on the number of protons in the atom. Because effective nuclear charge is increasing, the nucleus is more likely to hold on to its electrons. Therefore, the energy required to remove an electron increases.
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