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It's harder to remove a second electron from an atom because removing the first one gives the atom an overall net positive charge. Therefore, the attraction that's exerted on each electron gets larger, making it harder to remove. And yes, there are multiple ionization energies for an element
It is always more difficult to remove the second electron because the net positive charge exerted by the nucleus affects it greater than the electrons in the outer shells. As you remove more electrons, the more energy it takes to remove each one.
It is harder to remove a second electron because removing the first electron gave the atom (now ion) a positive charge. This indicates that the pull of the nucleus is strong because less electrons means less electron-electron repulsion, resulting in the radii slightly decreasing, and therefore causing the outermost electrons to be even closer to the nucleus.
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