Question

(a) The average distance from the nucleus of a \(3 s\) electron in a chlorine atom is smaller than that for a \(3 p\) electron. In light of this fact, which orbital is higher in energy? (b) Would you expect it to require more or less energy to remove a \(3 s\) electron from the chlorine atom, as compared with a \(2 p\) electron?

Short answer

(a) The \(3p\) orbital has higher energy than the \(3s\) orbital in a chlorine atom. (b) It requires more energy to remove a \(2p\) electron from the chlorine atom compared to a \(3s\) electron.

Step-by-step solution

(a) Determine the higher energy orbital: \(3s\) or \(3p\)?

In general, the energy of an orbital in multi-electron atoms increases as the average distance from the nucleus increases. Since the \(3s\) electron in a chlorine atom has a smaller average distance from the nucleus compared to a \(3p\) electron, it has a lower energy. Thus, the \(3p\) orbital has higher energy.

(b) Compare the ionization energy: \(3s\) electron vs. \(2p\) electron in a chlorine atom.

To determine whether it requires more or less energy to remove a \(3s\) electron compared to a \(2p\) electron, we must compare the energy levels of these orbitals. The principal quantum number (\(n\)) of the \(3s\) orbital is greater than that of the \(2p\) orbital; therefore, the energy of the \(3s\) orbital is higher than that of the \(2p\) orbital. Ionization energy is the energy required to remove an electron from an atom, and it generally increases as the energy level of the electron decreases (closer to the nucleus). Since the \(2p\) electron is in a lower energy level, it will require more energy to remove it from the chlorine atom compared to a \(3s\) electron.

Key concepts

Electron Configuration

Understanding electron configuration helps determine how electrons are distributed around the nucleus of an atom. Electrons occupy orbitals that are grouped in shells and subshells, arranged in increasing energy levels. These orbitals include types like s, p, d, and f.

• Order of Filling: Electrons fill orbitals based on the energy levels, starting from the lowest. The order is often remembered using the Aufbau principle, which follows the sequence: 1s, 2s, 2p, 3s, 3p, and so on.
• Relationship to Atomic Number: The atomic number indicates the number of electrons in a neutral atom, guiding the configuration setup. For chlorine, with an atomic number of 17, the electron configuration ends in 3p⁵, following 1s² 2s² 2p⁶ 3s² 3p⁵.
• Pauli Exclusion Principle and Hund's Rule: These rules further refine electron distribution. Maximize unpaired electrons in degenerate orbitals (those of equal energy), and no two electrons can have identical quantum numbers (spin included).

Electron configurations provide the foundation for understanding atomic behavior during chemical reactions and bonding.

Ionization Energy

Ionization energy is critical when considering the reactivity and stability of atoms. It refers to the energy needed to remove an electron from a gaseous atom or ion.

• Energy Levels: Electrons in lower energy levels have higher ionization energy as they are closer to the nucleus, facing a stronger electrostatic attraction. For chlorine, this means the 2p electron, being closer to the nucleus than the 3s or 3p electron, requires more energy to be removed.
• Trends in the Periodic Table: As you move across a period, ionization energy generally increases because the atomic radius decreases, meaning electrons are held more tightly. However, as you move down a group, it decreases due to the increased distance between the outer electrons and the nucleus.
• Successive Ionization Energies: Removing additional electrons requires progressively more energy, especially when breaking into a new electron shell, as seen with elements like chlorine.

Grasping ionization energy aids in predicting how atoms might form ions, particularly in ionic compounds.

Nuclear Distance

The term 'nuclear distance' typically refers to the average distance between the nucleus and an electron in a given orbital. This distance influences several characteristics of atomic behavior, including energy levels and reactivity.

• Impact on Orbital Energy: Electrons closer to the nucleus (lower average nuclear distance) generally reside in lower energy orbitals. For example, the 3s orbital's electrons in chlorine are closer to the nucleus than 3p, indicating lower energy.
• Shielding and Penetration: S orbitals, like 3s, penetrate the inner electron levels, feeling a stronger attraction to the nucleus. This results in a lesser shielding effect from the inner electrons, making s electrons have a shorter nuclear distance compared to p electrons in the same shell.
• Influence on Chemical Properties: The nuclear distance aids in determining atomic size and bonding characteristics. Shorter nuclear distances can lead to higher bonding energies and affect bond lengths and angles in molecules.

Understanding nuclear distance clarifies why certain orbitals have different energy levels and the implications for chemical bonding and atomic interactions.