Explain why the first ionization energy of potassium is much larger than the first ionization energy of calcium.

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The first ionization energy of potassium is 419 kJ/mol while calcium's is 376 kJ/mol.  Note that the first ionization energy is the amount of energy needed to remove an outer electron from the atom.  For calcium, we have a much larger atom because we have more electrons and the electrons are at energy levels farther from the nucleus.  As a result the effective nuclear charge felt by those outer electrons is less than the charge felt by an inner electron.  Since the potassium is a smaller atom, its outer electrons have a greater effective nuclear charge so it's harder to remove them from the atom.

Think of it like a magnet on the refrigerator.  If you put a magnet directly on the refrigerator, it requires a certain amount of force to remove it.  If you start putting papers between the magnet and the refrigerator, the force needed to remove the magent is less because the attractive force between the refrigerator and the magnet is diminished (i.e. shielded) by the presence of the paper.  The more papers, the weaker the attractive force between the two, the easier it is to remove the magnet.



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