The energy needed to remove one electron from a gaseous potassium atom is only about two-thirds as much as that needed to remove one electron from a gaseous calcium atom, yet nearly three times as much energy as that needed to remove one electron from K1 as from Ca1. What expla- nation can you give for this contrast ?

Ionization of K+ will affect the inert gas core of the atom while ionization of Ca+ will not.

Explanation:

Potassium loses one electron in its outermost shell to become K+ it now has an inert or noble gas electron configuration; it is not quite energetically costly to ionize potassium.

Removing an electron from K+ removes an electron from a closed shell (inert gas configuration) since its outermost shell now contains exactly eight electrons. However, losing an electron from Ca+ gives Ca2+, which now has a closed shell or inert gas configuration

beta decay is the answer