Question

Which pair of elements would you expect to have the most similar atomic radii, and why? $$ \text {a. Si and Ga} \quad \text {b. Si and Ge} \quad \text {c. Si and As} $$

Short answer

Silicon (Si) and Germanium (Ge) are expected to have the most similar atomic radii because they are in the same group on the periodic table.

Step-by-step solution

Understanding the Concept of Atomic Radii

Atomic radius is the distance from the center of an atom's nucleus to its outermost electron shell. In the periodic table, elements in the same group typically have similar atomic radii because they have the same number of electron shells. Moving down a group, the atomic radius increases due to the addition of a new electron shell.

Analyzing Periodic Trends

To compare atomic radii, we should look for elements that are in the same group because they have the most similar electron configurations. Among the given pairs, we should look for elements that belong to the same group in the periodic table.

Identifying Elements in the Same Group

Si (Silicon) is in group 14 of the periodic table. Ga (Gallium) is in group 13, Ge (Germanium) is also in group 14, and As (Arsenic) is in group 15. Since Ge is in the same group as Si, Si and Ge are the pair most likely to have the most similar atomic radii.

Key concepts

Understanding Periodic Trends

To decipher the patterns underlying atomic radii, one must understand the concept of periodic trends. These trends are a result of the periodic table's organizational structure, which reflects the periodicity of elemental properties. Atomic radius – fundamentally the distance from an atom's nucleus to the outer edge of its electron cloud – varies predictably across the periodic table.

As you follow the table from left to right, atomic radii generally decrease. The cause? A rise in nuclear charge without a corresponding increase in electron shell level. This increased nuclear attraction pulls electrons closer, shrinking the atom. Conversely, a downward trek in any group reveals an increase in radii due to additional electron shells being populated, further distancing the outer electrons from the nucleus.

Tip: Remember that cations (positively charged ions) are smaller than their parent atoms due to lost electron shells, whereas anions (negatively charged ions) are larger because of increased electron-electron repulsion within a constant number of shells.

Electron Configurations' Role

In considering atomic radii similarity, electron configurations play a pivotal role. They dictate an atom's chemical behavior and shape the aforementioned trends. Every atom desires the most stable electronic arrangement – often akin to the nearest noble gas's configuration. This means filling or emptying subshells to achieve that stable octet (or duet for hydrogen and helium).

Valence Electrons and Periodicity

Elements within the same group boast identical valence electron configurations, which results in similar chemical and physical properties, including atomic size. As seen in the exercise, Silicon (Si) and Germanium (Ge) share a group, suggesting that their outer electrons are at comparable distances from the nucleus, hence the likeness in radii.

Takeaway: To make precise predictions about atomic size, one should scrutinize an element's position on the periodic table, its electron configuration (particularly of the valence electrons), and its neighbors' configurations.

Periodic Table Groups and Atomic Radii

Exploring the periodic table groups can further clarify questions about atomic size. Each column in the table constitutes a group or family, characterized by elements possessing the same number of electrons in the outermost shell. These electrons are fundamentally responsible for an element's reactivity and, by extension, similarities in behavior across a group.

For instance, Silicon (Si) and Germanium (Ge), as group 14 members, have four electrons in their outermost shell. This likeness points to a parallel in atomic radii. On the other hand, Gallium (Ga) and Arsenic (As) fall into groups 13 and 15, respectively. The differing number of valence electrons implies a distinction in the size of their atomic radii when compared to Silicon (Si).

Fact: Knowing an element's group can almost immediately give you an insight into its properties, such as atomic size, and predict with whom it will share the most resemblance. This is why, in the given exercise, between Si and Ge there's a greater similarity in atomic radii – they're in the same periodic table group, sharing structural and electronic attributes.