The second ionization energy of potassium is much higher than the first ionization energy because…

The options are:

a) The atom has a larger radius after the removal of the first electron
b) The effective nuclear charge for valence electrons decreases
c) The second electron is removed from a stable noble gas core
d) The second electron is a valence electron
e) Answers a & b are correct

e) Answers a & b are correct

The correct answer is c) The second electron is removed from a stable noble gas core.

The second ionization energy of potassium is higher than the first ionization energy because after the first electron is removed, the remaining atom now has a stable noble gas electron configuration. This means that the second electron is being removed from a more stable state, which requires more energy to overcome the increased attraction between the electron and the remaining positively charged nucleus. Therefore, the second ionization energy is higher than the first ionization energy.

To determine why the second ionization energy of potassium is much higher than the first ionization energy, let's go through each of the provided options:

a) The atom has a larger radius after the removal of the first electron: This option is not correct. After the removal of the first electron, the remaining electron(s) are attracted more strongly to the positively charged nucleus, which actually results in a smaller atomic radius.

b) The effective nuclear charge for valence electrons decreases: This option is also not correct. The effective nuclear charge experienced by valence electrons remains the same after the first electron is removed, as there is no change in the number of protons in the nucleus.

c) The second electron is removed from a stable noble gas core: This option is correct. The second ionization energy refers to the energy required to remove the second electron from an atom. In the case of potassium, after the first electron is removed, the remaining electron configuration is similar to that of a noble gas, argon. This stable noble gas core provides increased stability, making it more difficult to remove a second electron.

d) The second electron is a valence electron: This option is also correct. Valence electrons are the outermost electrons of an atom. In the case of potassium, the first electron being removed is a valence electron. The second ionization energy refers to the energy required to remove the second electron, which is indeed a valence electron.

e) Answers a & b are correct: This option is incorrect because option a is incorrect. Therefore, only option e (answers a & b are correct) is not correct.

Taking into consideration the explanations above, the correct answer to the question is:

c) The second electron is removed from a stable noble gas core
d) The second electron is a valence electron