Question

Consider these elements: \(\mathrm{P}, \mathrm{Ca}, \mathrm{Si}, \mathrm{S}, \mathrm{Ga}\) $$ \begin{array}{l}{\text { a. Write the electron configuration for each element. }} \\ {\text { b. Arrange the elements in order of decreasing atomic radius. }} \\ {\text { c. Arrange the elements in order of increasing ionization energy. }} \\ {\text { d. Use the electron configurations in part a to explain the differences }} \\ {\text { between your answers to parts b and c. }}\end{array} $$

Short answer

The electron configurations are: P: [Ne]3s^2 3p^3, Ca: [Ar]4s^2, Si: [Ne]3s^2 3p^2, S: [Ne]3s^2 3p^4, Ga: [Ar]3d^10 4s^2 4p^1. In decreasing atomic radius: Ca > Ga > P > Si > S. Increasing ionization energy: Ca < Ga < P < Si < S. Differences are due to shielding effect and effective nuclear charge.

Step-by-step solution

Write Electron Configurations

Determine the atomic number of each element and use it to write the electron configuration for P, Ca, Si, S, and Ga.

Order by Decreasing Atomic Radius

Atomic radius decreases across a period from left to right and increases down a group. Use periodic table trends to order the elements accordingly.

Order by Increasing Ionization Energy

Ionization energy increases across a period and decreases down a group. Use these trends to organize the elements by increasing ionization energy.

Explain Differences

Use the electron configurations to explain why atomic radius and ionization energy trends are different. Factors include effective nuclear charge and electron shielding.

Key concepts

Atomic Radius

Understanding the concept of atomic radius is central to grasping the structure of atoms in the periodic table. It refers to the distance from the nucleus of an atom to the outer boundary of the electron cloud. Generally, the atomic radius increases as we move down a group in the periodic table because each successive element has an additional electron shell, which outweighs the increase in nuclear charge, providing more distance between the nucleus and the outer electrons.

Conversely, as we move across a period from left to right, the atomic radius decreases. This happens because electrons are added to the same shell, but the nuclear charge also increases, pulling electrons closer to the nucleus. This 'pull' is often described as effective nuclear charge. It's important for students to realize that while the number of protons in a nucleus increases across a period, leading to a stronger attraction between the protons and electrons, there's little added electron shielding, resulting in a smaller atomic radius.

For example, in the exercise provided, we could predict Calcium (Ca) would have a larger atomic radius than Silicon (Si) because it is situated to the left of Silicon on the periodic table. Following this concept will allow students to accurately arrange elements in order of decreasing atomic radius.

Ionization Energy

Ionization energy is the energy required to remove an electron from an atom in the gas phase. The concept is crucial for understanding how atoms interact and form bonds. It is indicative of an element's reactivity; the higher the ionization energy, the less likely the atom is to lose an electron and form a positive ion.

As one proceeds across a period on the periodic table, the ionization energy tends to increase. This is due to the increasing nuclear charge which more effectively holds onto the electrons. However, students should also note exceptions to this rule. They occur due to the stability of filled and half-filled subshells. For instance, Group 18 elements (noble gases) have high ionization energies because their electron configurations are very stable.

Understanding these trends is instrumental when arranging elements by increasing ionization energy. From the given exercise, one could infer that Phosphorus (P) would have higher ionization energy than Gallium (Ga) because P is located to the left of Ga in the periodic table and also has a half-filled subshell which is relatively stable.

Periodic Table Trends

The periodic table is structured in such a way that it reveals several trends in the properties of the elements, including atomic radius and ionization energy, as discussed above. Another important trend to consider is electronegativity, which increases across a period and decreases down a group.

Understanding these trends is pivotal when trying to predict the chemical behavior of elements based on their position in the periodic table. For instance, elements on the right side of the periodic table tend to gain electrons to become anions, while those on the left lose electrons to form cations. These behaviors are linked to the trends in atomic radius and ionization energy.

The exercise improvement advice is to focus on the interplay between electron configuration, effective nuclear charge, and electron shielding since they are the basis for many of these trends. By exploring these relationships, students can develop a deeper understanding of why certain trends exist and how to apply this knowledge to solve exercises involving the arrangement of elements by their physical or chemical properties.