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Electronegativity is how well an atom can attract electrons to itself while electron affinity is the amount of energy release when an electron is added. Electron affinity increases from left to right because the electrons that are added to the energy levels becomes closer to the nucleus which creates a stronger attraction.
Electronegativity refers to how well an atom can attract an electron to itself when that atom is within a molecule while electron affinity, as mentioned above, refers to how much energy is released when an atom takes in an electron (the more simple and easier to understand definition would be the atom's attraction for electrons. This contrasts from electronegativity since electronegativity is a property of an atom when it's already paired to create a molecule or compound while electron affinity is a property of an atom by itself). Electron affinity increases because as you go up and right on the periodic table, the atomic radius decreases. As the atomic radius decreases, the effective nuclear charge of the atom becomes stronger, holding on to electrons more tightly.
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