Final answer:
Calcium (Ca) has a higher first ionization energy than potassium (K) due to having more protons in its nucleus, which results in a stronger attraction to electrons. Potassium (K) has a much higher second ionization energy compared to Ca because the second electron is removed from a shell closer to the nucleus after the first valence electron has been removed. Therefore, correct option is c.
Step-by-step explanation:
The concept you're asking about involves ionization energy, which is the energy required to remove an electron from an atom or ion. For the elements calcium (Ca) and potassium (K), we notice different ionization energies due to their atomic structures and the number of protons in their nuclei.
Let's first look at calcium (Ca). Ca has a first ionization energy of 590 kJ/mol which is higher than K's first ionization energy of 419 kJ/mol. This is because Ca has more protons in its nucleus (20 compared to K's 19), resulting in a stronger attraction for electrons and a higher first ionization energy.
Concerning the second ionization energy, it is significantly higher for both elements than their first ionization energies because they are removing an electron from a positively charged ion, which requires more energy.
K has a much larger increase to 3050 kJ/mol for its second ionization energy because the second electron is being removed from an energy level closer to the nucleus after the removal of the first valence electron.
For Ca, the second electron removed is also a valence electron, making the second ionization energy 1145 kJ/mol, which is higher than the first but significantly lower than K's second ionization energy.