Question

Figure 8.16 shows that in the \(Z=3\) to 10 filling of the \(n=2\) shell (lithium to neon), there is an upward trend in elements' first ionization energies. Why is there a drop as \(Z\) goes from 4 to \(5,\) from ber yllium to boron?

Short answer

The first ionization energy drops from Beryllium to Boron because Beryllium, with its fully filled 2s shell, is more stable, thereby requiring a higher ionization energy to remove an electron. In contrast, Boron begins a new shell (2p), which is less stable and therefore requires less energy to remove an electron.

Step-by-step solution

Understand Ionization Energy and Electron Shells

The first ionization energy is the energy required to remove one electron from a neutral atom. The electron configuration of an atom, i.e., how the electrons are distributed among various atomic orbitals, plays a significant role in determining the ionization energy. Due to the Pauli Exclusion Principle, no two electrons can have the same quantum number, necessitating the filling of electrons in the orbitals in a specified way known as the Aufbau principle. In this case, atomic number \(Z=4\) corresponds to Beryllium (Be) and \(Z=5\) corresponds to Boron (B). Be is the end of an electron shell (2s), while B is starting a new shell (2p).

Explain Ionization Energy of Beryllium

Let's consider the case of Beryllium first. Beryllium has an electron configuration of \(1s^2 2s^2\). All the electrons are paired and the outer shell (2s) is fully filled, thus making Beryllium stable. When an atom is stable, it is difficult to remove an electron from it, thus requiring a higher ionization energy.

Explain Ionization Energy of Boron

Now let's consider Boron. Its electron configuration is \(1s^2 2s^2 2p^1\). Boron starts a new shell (2p) after filling the 2s shell. The \(2p\) shell has a higher energy level than the \(2s\) shell, and not every electron in this shell is paired, which makes Boron less stable compared to Beryllium. So, it is slightly easier to remove an electron from Boron, requiring less ionization energy.

Comparing Ionization Energies

Comparing the ionization energies of Beryllium and Boron, Beryllium, which is more stable due to the fully filled 2s shell, requires more energy (higher ionization energy) to remove an electron than it's needed for Boron. Therefore, a drop in ionization energy is seen as \(Z\) goes from 4 to 5, from Beryllium to Boron.

Key concepts

Electron Configuration

Electron configuration describes how electrons are distributed in an atom's atomic orbitals. Each electron in an atom is arranged into energy levels, or shells, starting from the closest to the nucleus. Each shell can hold a specific maximum number of electrons, determined by the formula \(2n^2\).
For example, the first shell can hold up to 2 electrons, and the second shell can hold up to 8. Electrons occupy orbitals in a way that minimizes the overall energy of the atom.

• The innermost shells are filled first before progressing to outer shells.
• For Beryllium, the electron configuration is \(1s^2 \,2s^2\), indicating all electrons are in the lower energy states.
• For Boron, the electron configuration is \(1s^2 \,2s^2 \,2p^1\), adding an electron in the higher energy \(2p\) orbital, leading to less stability.

Pauli Exclusion Principle

The Pauli Exclusion Principle is a fundamental tenet in quantum mechanics, stating that no two electrons in the same atom can have the same set of four quantum numbers. This principle essentially ensures that each electron has a unique address within the atom, dictating how electrons fill available orbitals.
Due to this, even if two electrons share the same energy level and subshell, they must differ in one quantum property, usually their spins. This requirement results in pairing electrons in orbitals:

• Each orbital can hold a maximum of two electrons with opposite spins.
• This principle explains the stability of fully filled and half-filled orbitals.
• It is also why Beryllium's fully filled \(2s^2\) orbital contributes to its higher stability and ionization energy.

Aufbau Principle

The word 'Aufbau' means "building up" in German, and the Aufbau Principle follows this concept in explaining electron filling order in atoms. According to this principle, electrons will fill the lowest energy orbitals first before filling higher ones, functioning as a method to achieve the atom's most stable electron configuration.
When examining each orbital:

• Electrons first fill the \(1s\) orbital, then \(2s\), and so on, based on increasing energy.
• This priority sequence is crucial in understanding the electron configuration differences between Beryllium (\(1s^2 \,2s^2\)) and Boron (\(1s^2 \,2s^2 \,2p^1\)).
• Beryllium's electron shell is fully filled in the \(2s\) state, whereas Boron starts filling the higher energy \(2p\) state.

Atomic Orbitals

Atomic orbitals are regions in an atom where there is a high probability of finding an electron. Each electron is found in these unique spaces, which are defined by complex shapes and energies, and help describe the structure of atoms.
There are several types of orbitals:

• The \(s\) orbital is spherical, with one type per energy level.
• The \(p\) orbitals are dumbbell-shaped and have three variations (\(p_x, \,p_y, \,p_z\)) per energy level starting from the second energy level.
• Atomic orbitals follow specific rules for filling electrons, dictated by their energy levels and the associated quantum numbers of the electrons within them.

When comparing elements like Beryllium and Boron, the distribution of electrons into these orbitals directly impacts their ionization energy, as the differing occupation of these orbitals correlates with stability and reactivity.