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The amount of energy required to remove an electron increases from left to right. This means that the atoms are able to hold on to their valence electrons more and more tightly. Thus, it gets harder to remove an electron as the atomic number increases.

Going down a group, the element doesn't change much. However, the size of the atom increases greatly, and because of this, so does the distance between the nucleus and the valence electrons. That decreases the magnitude of the force of attraction between the nucleus and the outermost electrons. Thus, IE decreases going down a group from top to bottom.

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