Question

Determine the identity of the element that contains exactly (a) two \(6 p\) electrons in the ground state (b) five \(4 f\) electrons in the ground state (c) one \(4 p\) electrons in the ground state (d) seven \(5 d\) electrons in the ground state

Short answer

The elements are (a) lead (Pb) with atomic number 82, (b) promethium (Pm) with atomic number 61, (c) gallium (Ga) with atomic number 31, and (d) gadolinium (Gd) with atomic number 64.

Step-by-step solution

Determine Element with Two 6p Electrons

The periodic table is organized in such a way that the position of an element indicates its electron configuration. Since the question asks for an element with two 6p electrons in the ground state, we look for the second element in the 6p block. This is lead (Pb) with an atomic number of 82.

Identify Element with Five 4f Electrons

The 4f subshell begins filling after barium (Ba), which is atomic number 56. Counting five elements into the 4f block, we reach the element with atomic number 61, which is promethium (Pm).

Find Element with One 4p Electron

The 4p subshell starts to fill immediately after the 4s subshell is filled, which is after the element calcium (Ca), atomic number 20. The first element of the 4p subshell will be the one with one 4p electron. This is gallium (Ga), with an atomic number of 31.

Discover Element with Seven 5d Electrons

The 5d subshell starts to fill after the 6s subshell. That process starts after barium (Ba), atomic number 56, and the two 6s electrons correspond to cesium (Cs) and barium (Ba). The first element with a 5d electron is lanthanum (La), atomic number 57. Counting seven elements into the 5d block, we reach element number 64, which corresponds to gadolinium (Gd).

Key concepts

The Periodic Table and Electron Configurations

The periodic table is not just a systematic display of chemical elements; it's a map for understanding the electron configurations that define the chemical behavior of atoms. As an educator, I'd like to emphasize that the periodic table is organized into periods (horizontal rows) and groups (vertical columns), each representing key electron configuration milestones.

For example, when looking at the periodic table, you can see that atoms grow larger as you move down a group because they are adding more electron shells. Conversely, as you move from left to right across a period, elements gain more protons and electrons, with the electrons filling the available subshells in a pattern described by quantum mechanics. This filling order can be summarized by the Aufbau principle, Hund's rule, and the Pauli Exclusion Principle, which collectively explain why certain positions in the periodic table correspond to specific electron configurations.

Understanding Ground State Electrons

When we talk about 'ground state electrons', we're referring to the electrons arranged in the lowest energy configuration possible for an atom. It's the atom's most stable, non-excited form. For instance, when the exercise requested the identification of elements based on their ground state electron configurations, it implied that we should consider the electrons in the positions they would naturally occupy without any added energy.

In the ground state, electrons fill up 'subshells' in a specific order known as the 'electron configuration'. Each electron occupies the lowest energy orbital available, building up to define the structure and chemistry of the atom. This is why an element's position on the periodic table is directly related to its ground state electron configuration, giving rise to periodic trends such as electronegativity and atomic radius.

The Role of Subshells in Chemistry

Subshells are regions within atomic shells where electrons are likely to be found. They are designated as s, p, d, and f. The concept of subshells is fundamental to understanding chemical behavior and properties because the distribution of electrons across different subshells leads to the variation in bonding and reactivity among elements.

The exercise solutions make clear references to these subshells. For example, '6p' refers to the 'p' subshell in the 6th energy level, and '4f' to the 'f' subshell in the 4th energy level. It is important to note that each subshell type can hold a different maximum number of electrons: s can hold 2, p can hold 6, d can hold 10, and f can hold 14. The way these subshells are filled is determined by quantum mechanics and is consistent across all atoms, providing a predictable pattern for determining the electron configuration of any element based on its position in the periodic table.