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Ionization energy is the energy it takes to remove an electron from an atom. The periodic table trends are that ionization energy decreases going down a group because the electrons are farther away from the nucleus so there's less charge pulling them in and the other electrons create a shielding effect. Ionization energy increases going across a period because as more electrons are added, the atomic radius decreases meaning the electrons are held closer and tighter together near the nucleus, which means there's a higher charge keeping them in.
When looking at the trend of ionization energy it can be helpful to look at the trend of atomic radii alongside it. Because the ionization energy is the energy required to remove an electron from an atom, the atomic radius, half the distance between the centers of neighboring atoms, can help to determine how far and electron is from the nucleus of an atom. Thus, as you move down a period, the atomic radius increases which means that electrons are moving further away from the nucleus, so the ionization energy will decrease. In contrast, as you move across a group from left to right, the atomic radius decreases which means that electrons are moving closer to the nucleus, so the ionization energy will increase.
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