The first ionization energy for potassium (K) is 419 kJ/mol, and the second ionization energy for calcium (Ca) is 1145 kJ/mol. Using concepts from this unit, explain why they are different even though they are isoelectric (have the same number of electrons).
K(g)→K+(g)+e − Ca+(g)→Ca2+(g)+e −
The Correct Answer and Explanation is:
The difference in ionization energies for potassium (K) and calcium (Ca) can be attributed to their atomic structure and the effective nuclear charge experienced by their valence electrons. Although both elements are isoelectronic (having the same electron configuration), they differ in their atomic numbers, which significantly impacts their ionization energies.
Potassium, with an atomic number of 19, has a total of 19 protons in its nucleus. When potassium loses one electron to form (K^+), the resulting ion has 18 electrons, corresponding to the electron configuration of argon. The first ionization energy of potassium is relatively low at 419 kJ/mol because its outermost electron is in the fourth energy level (4s), where it experiences more shielding from the inner electrons. The effective nuclear charge (Z_eff) that this outer electron feels is lessened by the repulsion from the core electrons, making it easier to remove.
On the other hand, calcium has an atomic number of 20 and possesses 20 protons. When it loses one electron to form (Ca^+), the ion still has 19 electrons (also isoelectronic with argon), but the (Ca^+) ion has a greater nuclear charge (20 protons) acting on these electrons. This increased nuclear charge leads to a higher effective nuclear charge felt by the remaining electrons, particularly those in the outermost shell. Consequently, when a second electron is removed to form (Ca^{2+}), the energy required (the second ionization energy) is significantly higher at 1145 kJ/mol. The (Ca^{2+}) ion is more stable due to this higher nuclear charge, which tightly binds the remaining electrons, making it more difficult to remove an additional electron.
In summary, the primary reason for the disparity in ionization energies between potassium and calcium, despite their isoelectronic nature, lies in the different nuclear charges. Calcium, having a higher atomic number, experiences a greater effective nuclear charge that leads to a higher ionization energy for removing its second electron compared to potassium’s first electron.