For a gaseous carbon atom undergoing successive ionizations, which of the following ionization steps requires the greatest amount of ionization energy?

Introduction / Context:
Ionization energy is the energy required to remove an electron from a gaseous atom or ion. For a given element, successive ionization energies increase as more electrons are removed, because the remaining electrons experience a stronger effective nuclear attraction. This question focuses on a carbon atom and asks which successive ionization step requires the most energy, that is, which step has the highest ionization energy among the options listed.

Given Data / Assumptions:

• We consider carbon in the gaseous state undergoing successive ionizations.
• The steps are: C (g) -> C+ (g) + e-, C+ (g) -> C2+ (g) + e-, C2+ (g) -> C3+ (g) + e-, and C3+ (g) -> C4+ (g) + e-.
• Each step removes one more electron from an increasingly positively charged ion.
• We assume no major electronic shell changes occur that would reduce ionization energy as we proceed.

Concept / Approach:
For any element, the first ionization energy (removal of the first electron from a neutral atom) is lower than subsequent ionization energies, because after one electron is removed, the resulting cation holds the remaining electrons more tightly. As the charge on the ion increases (C+, C2+, C3+), the electrostatic attraction between the positively charged nucleus and the remaining electrons grows stronger, making it progressively more difficult to remove another electron. Therefore, the fourth ionization (removing an electron from C3+ to form C4+) requires the greatest amount of energy among the given steps, because it is removing an electron from the most positively charged ion listed.

Step-by-Step Solution:
Step 1: Identify that C (g) -> C+ (g) + e- is the first ionization, removing an electron from a neutral atom. Step 2: Recognise that C+ (g) -> C2+ (g) + e- is the second ionization, starting from a positively charged ion, which is already more difficult than the first. Step 3: Note that C2+ (g) -> C3+ (g) + e- is the third ionization, requiring even more energy due to the higher positive charge on the starting ion. Step 4: Observe that C3+ (g) -> C4+ (g) + e- is the fourth ionization, involving removal of an electron from a triply charged cation, where electrons are most strongly attracted to the nucleus. Step 5: Conclude that the fourth ionization step, C3+ (g) -> C4+ (g) + e-, has the highest ionization energy among the options and select it as the correct answer.

Verification / Alternative check:
Successive ionization energy data for atoms with a few electrons show a clear pattern: each additional electron removed requires more energy than the previous one, with occasional large jumps when a new electron shell is emptied. For carbon, as electrons are removed, the effective nuclear charge experienced by the remaining electrons increases, reducing shielding and making further removal more difficult. While the exact numerical values are not needed here, the trend of increasing ionization energy with increasing positive charge on the ion supports the conclusion that the fourth ionization is the largest among the four listed steps.

Why Other Options Are Wrong:
The first ionization step, C (g) -> C+ (g) + e-, starts from a neutral atom and, by definition, has the lowest ionization energy of the series. The second ionization, C+ (g) -> C2+ (g) + e-, has a higher energy requirement than the first but less than the third and fourth. The third ionization, C2+ (g) -> C3+ (g) + e-, is higher still but still does not exceed the difficulty of removing an electron from C3+, which is more strongly bound. Thus, each step requires more energy than the previous, and none of the earlier steps can surpass the fourth ionization in energy requirement.

Common Pitfalls:
Some students may mistakenly think that the first ionization energy is always the largest because it starts from the neutral atom or may confuse the trend with electron affinity trends. Another pitfall is not recognising that as positive charge builds up on the ion, the electrostatic attraction to the remaining electrons becomes stronger, so it becomes progressively harder, not easier, to remove electrons. To avoid these errors, remember that successive ionization energies generally increase with each electron removed, so the later ionization steps typically require more energy than earlier ones, unless a new shell is being accessed in a special way.

Final Answer:
The ionization process that requires the greatest amount of energy is C3+ (g) -> C4+ (g) + e-, the fourth ionization step of carbon.