Question

If the core electrons were \(100 \%\) effective at shielding the valence electrons from the nuclear charge and the valence electrons provided no shielding for each other, what would be the effective nuclear charge felt by a valence electron in (a) \(\mathrm{Na}\) (b) \(S,(\mathbf{c}) \mathrm{Cl} ?\)

Short answer

The effective nuclear charge (Z_eff) felt by a valence electron is (a) 1 for Na, (b) 6 for S, and (c) 7 for Cl, assuming core electrons completely shield the valence electrons.

Step-by-step solution

Understanding Effective Nuclear Charge

The effective nuclear charge (Z_eff) is the net positive charge experienced by an electron in a multi-electron atom. The actual nuclear charge (Z) is diminished by the shielding effect of the inner electrons. If core electrons completely shield the valence electrons, Z_eff for a valence electron is calculated by subtracting the number of core electrons from the atomic number.

Calculate Z_eff for Sodium (Na)

For sodium (Na), which has an atomic number of 11, there is 1 valence electron in the 3s orbital, and 10 core electrons (2 from the 1s orbital and 8 from the 2s and 2p orbitals). Thus, Z_eff = Z - number of core electrons = 11 - 10 = 1.

Calculate Z_eff for Sulfur (S)

For sulfur (S), the atomic number is 16, meaning there are 16 protons in the nucleus. Sulfur has 6 valence electrons in the 3p orbital, and 10 core electrons (2 in 1s, 2 in 2s, and 6 in 2p orbitals). Hence, Z_eff = 16 - 10 = 6.

Calculate Z_eff for Chlorine (Cl)

Chlorine (Cl) has an atomic number of 17, so it has 17 protons. With 7 valence electrons in the 3p orbital and 10 core electrons (2 in 1s, 2 in 2s, and 6 in 2p orbitals), the effective nuclear charge for a valence electron in Cl is Z_eff = 17 - 10 = 7.

Key concepts

Electron Shielding

When exploring the intricacies of atomic behavior, electron shielding emerges as a vital concept to comprehend. In essence, it refers to the phenomenon where the core electrons—that is, the electrons located in the inner orbitals—partially block the outermost electrons (valence electrons) from the full attractive force of the protons in the nucleus.

This partial blockage is because core electrons serve as a 'shield', reducing the effective nuclear charge felt by the valence electrons. As such, although the overall charge of the nucleus (the atomic number) stays constant, the experience of that charge for each electron varies depending on its position within the atom's electron cloud.

From a practical perspective, envisioning this concept is akin to the sun being obscured by clouds; while its energy is still present, it doesn't reach the ground with the same intensity. Similarly, in an atom, the attractive pull from the nucleus is mitigated by the intervening electron layers. This understanding is crucial when considering properties such as ionization energy and atomic size, which are influenced by how strongly valence electrons are bound to the nucleus.

Valence Electrons

At the heart of an atom's chemical interactions lie its valence electrons. Circumnavigating the outermost orbitals, these electrons hold the pivotal role of engaging in bond formation with other atoms. It's their involvement that dictates the atom's capacity to participate in chemical reactions and gives rise to the formation of molecules.

Valence electrons are the electrons that determine an element's placement in the periodic table and thereby play a primary part in understanding the table's structure and the element's chemical properties. For example, elements in the same group (vertical column) typically have the same number of valence electrons, which accounts for their shared chemical behaviors.

Furthermore, the concept discussed in the original exercise focuses on a hypothetical scenario where valence electrons are not affected at all by the presence of other valence electrons. This simplification leads to a direct calculation of the effective nuclear charge, reinforcing the concept's importance within the atomic structure and illustrating its impact in a practical context.

Atomic Structure

Delving into atomic structure unveils a miniature world of protons, neutrons, and electrons arranged in a highly ordered manner. Protons and neutrons form the atomic nucleus, serving as the dense core of the atom, while electrons swarm in orbitals around this nucleus, creating a 'cloud' of negative charge that balances the positive charge of the protons.

The structure introduces several key layers, or shells, that electrons occupy, with increasing distance from the nucleus accommodating electrons with higher energy levels. These shells are further divided into subshells and orbitals, where a specific number of electrons can reside. Understanding these layers is pivotal because it not only influences how we perceive electron shielding but also informs us about chemical reactivity and bonding potential of an element.

A deeper comprehension of atomic structure allows us to explain why certain elements exhibit particular properties and how they will react with others. In the context of the textbook exercise, recognizing the atomic structure is essential to calculate the effective nuclear charge and appreciate how each electron shell contributes to the overall behavior of an atom.