Question

Why is the fifth ionization energy of carbon so much larger than its fourth?

Short answer

The fifth ionization energy of carbon is significantly larger than the fourth because it involves removing an electron from the inner 1s orbital, which is much more strongly bound to the nucleus.

Step-by-step solution

Understanding Electron Configuration

The electron configuration of an atom tells us how electrons are distributed in atomic orbitals. For carbon, the ground state electron configuration is 1s² 2s² 2p². The first four electrons to be ionized (removed) will come from the outermost shells, which are the 2s and 2p orbitals.

Considering the Ionization Energies

Ionization energy increases as each electron is removed because the remaining electrons experience a stronger effective nuclear charge, which holds them more tightly to the nucleus. The first four ionization energies correspond to removing electrons from the 2s and 2p orbitals.

Comparing the Fourth and Fifth Ionization Energies

The fifth ionization energy involves removing an electron from the 1s orbital, after the 2s and 2p orbitals have been emptied. This is a much deeper and closer electron to the nucleus, which is much more strongly bound due to the very high effective nuclear charge it experiences once the other electrons have been removed.

Understanding the Jump in Ionization Energy

The drastic increase in the fifth ionization energy compared to the fourth is because the fourth ionization energy completes the removal of outer electrons, and the fifth ionization energy requires removing an electron from a completely filled, lower energy level, namely the 1s orbital.

Key concepts

Electron Configuration

The electron configuration of an atom is vital in understanding its chemical behavior, including ionization energy patterns. For carbon, with the atomic number 6, the configuration is expressed as 1s² 2s² 2p². In simple terms, this indicates that two electrons occupy the first shell's 's' orbital, and the second shell contains two electrons in the 's' orbital and two in the 'p' orbital.
Electrons fill orbitals in a way that minimizes energy, starting with the lowest energy levels first, following the Aufbau principle. As one moves outward from the nucleus, the energy levels and orbitals become more complex and hold more electrons. These configurations can be determined by following Hund's Rule and the Pauli Exclusion Principle, ensuring each orbital is singly occupied before any is doubly occupied, and that no two electrons can have the same four quantum numbers, respectively.
Understanding electron configuration helps explain why the fifth ionization energy for carbon is significantly higher—it involves disrupting a filled 1s orbital, which is at a much lower energy state and closer to the nucleus compared to the previously removed 2s and 2p electrons.

Effective Nuclear Charge

Effective nuclear charge (ENC) is the net positive charge experienced by an electron in a multi-electron atom. The concept plays a critical role in ionization energy discussions. Each electron in an atom experiences both the positive charge of the protons in the nucleus and the repulsive force from other electrons. The ENC is lower than the actual nuclear charge because of this shielding effect.
As electrons are removed from an atom during ionization, the ENC on the remaining electrons increases. This is because there are fewer electrons to shield the positive charge of the nucleus. Therefore, it becomes more difficult—and requires more energy—to remove another electron due to the stronger attractive force of the nucleus. This increasing ENC contributes to the pattern of increasing ionization energies, culminating in the significantly higher energy required to remove the tightly bound electron closest to the nucleus.

Atomic Orbitals

Atomic orbitals are regions within an atom where there is a high probability of finding electrons. Orbitals are categorized into types—s, p, d, and f—each with a different shape, where the 's' orbital is spherical and the 'p' orbital dumbbell-shaped. The configuration of carbon, discussed earlier, encompasses the 1s and 2p orbitals.
The 1s orbital is the closest to the nucleus and holds up to two electrons. It is these electrons that are bound more tightly to the nucleus due to their lower energy level and greater ENC. Upon reaching the point where an electron must be removed from the 1s orbital—as in the fifth ionization energy of carbon—the required energy jumps dramatically. This is because these inner orbitals are less shielded from the attractive force of the protons in the nucleus compared to those in higher, more diffuse orbitals like 2s and 2p.