How do you calculate calcium and potassium ionization energy?
In general chemistry, you are never asked to calculate them from first principles, but to use them. Their first ionization energies are:
#"K":# #DeltaH_(IE_1) = "4.341 eV"#
#"Ca":# #DeltaH_(IE_1) = "6.113 eV"#
ESTIMATION USING KNOWN ORBITAL POTENTIAL ENERGIES
If you did want to try, you would need the orbital potential energies of the valence orbitals.
Then, by Koopman's approximation theorem, the energy needed to cancel out the valence orbital potential energy of a singly-occupied orbital gives the first ionization energy.
Indeed, the orbital potential energies shown here (Appendix B.9) are
#V_(4s,K) = -"4.34 eV"#
#V_(4s,Ca) = -"6.11 eV"#
So indeed, the energy put into the atom to ionize it (i.e. the ionization energy) is the magnitude of these given orbital potential energies.