Problem 25 - Chemistry Central Science

Question

Using only the periodic table, arrange each set of atoms in order of increasing radius: (a) \(\mathrm{Ca}, \mathrm{Mg}\), Be; (b) \(\mathrm{Ga}, \mathrm{Br}\), \(\mathrm{Ge} ;\) (c) \(\mathrm{Al}, \mathrm{T}\), \(\mathrm{Si}\).

Step-by-Step Solution

Answer

The order of atoms in increasing radius are: (a) Be, Mg, Ca; (b) Br, Ge, Ga; (c) Si, Al, T. These orders are determined by their positions in the periodic table, considering that atomic radii increase from top to bottom and decrease from left to right.

Step 1: Introduction to Atomic Radii Tendencies

When we analyze the periodic table, a general tendency can be observed: atomic radii increase from top to bottom and decrease from left to right. This is because as we go down a group, electrons are added to higher energy levels further from the nucleus, which increases the radius. On the other hand, as we go from left to right across a period, electrons are added to the same energy level but the increase in positive charge in the nucleus increases the attraction between the electrons and the nucleus, which pulls the electron cloud closer, and as a result, the atomic radius decreases. So, to arrange these sets of atoms in increasing order of radius, students will need to identify where each element is in the periodic table and use the aforementioned trends to make comparisons.

Step 2: (a) Ca, Mg, Be

To arrange Ca, Mg, and Be in order of increasing radius, first, be aware of their positions on the periodic table: Ca, Mg, and Be are all located in group 2 (the alkaline earth metals), with Be being the highest in the group, Mg below Be, and Ca below Mg. Since atomic radii increase from top to bottom, the radius increases as follows: \( Be < Mg < Ca \) So, the order of increasing radius is: Be, Mg, Ca.

Step 3: (b) Ga, Br, Ge

To arrange Ga, Br, and Ge in order of increasing radius, first, identify their positions on the periodic table. Ga is in group 13, Ge is in group 14, and Br is in group 17. Ga and Ge are in the same period (4), while Br is one row higher in period 3. Since atomic radii decrease from left to right across a period, the order within the same period is: \( Ga > Ge \) Since atomic radii increase from top to bottom and Ga is below Br, the order in terms of periods is: \(Br < Ga\) Therefore, combining the trends, the order of increasing radius is: Br, Ge, Ga.

Step 4: (c) Al, T, Si

To arrange Al, T (technetium), and Si in order of increasing radius, first, locate their positions on the periodic table. Al is in group 13, Si is in group 14, and T is in group 7. Al and Si are in the same period (3), while T is one row further down in period 4. Since atomic radii decrease from left to right across a period, the order within the same period would be: \( Al > Si \) Since atomic radii increase from top to bottom and T is below Al and Si, the order in terms of periods is: \(Al, Si < T\) Therefore, considering both trends, the order of increasing radius is: Si, Al, T.

Key Concepts

Atomic Radius

The atomic radius is the distance from the nucleus of an atom to the outermost shell of electrons. It is a critical measurement in chemistry, as it influences how atoms interact and bond with each other.
Atomic radii are not fixed, but they generally indicate the size of an atom in different contexts. A common way to measure the atomic radius is to use the half-distance between the nuclei of two atoms bonded together in a molecule.
As electrons are more diffuse further out from the nucleus, this measurement adds certainty in characterizing atom sizes.

• Atomic radius tends to be larger for elements that are lower on the periodic table.
• Atoms with more energy levels (shells) usually have larger radii.
• As new electrons fill energy levels farther from the nucleus, the radius grows.

Understanding the atomic radius helps in predicting and explaining molecular geometries and chemical reactivities.

Periodic Trends

Periodic trends are predictable patterns or recurring behaviors observable in the elements of the periodic table. These trends help understand the properties and behaviors of the elements based on their positions on the periodic table.
Such predictable patterns in element properties, like atomic radius, ionization energy, and electronegativity, exist due to the electron configuration and nuclear charge of the elements.
The trends for atomic radius specifically are vivid:

• Atomic radius decreases moving from left to right across a period.
• Innovative repulsion and increased nuclear attraction lead to thinner electron clouds.
• Going from top to bottom within a group, atomic radius increases due to additional energy levels.

These patterns are helpful in justifying and visualizing reactions between different elements.

Alkaline Earth Metals

Alkaline earth metals are a group of metals in group 2 of the periodic table and include elements such as Be, Mg, and Ca. These metals are characterized by their shiny appearance and somewhat reactive nature, especially with water.
Their atomic structures have two electrons in their outermost shell, making them likely to lose two electrons and form +2 ions in chemical reactions.
Key Features of Alkaline Earth Metals include:

• They have larger atomic radii compared to the elements placed in the same period due to fewer protons counteracting increased electron shells.
• Atomic radius increases down the group as more electron shells are added.
• This group includes the likes of Beryllium (Be), Magnesium (Mg), and Calcium (Ca), and going down the group, they become more reactive.

Understanding these metals' radius helps in predicting their reactivity and behavior in chemical reactions.

Group and Period Trends

The periodic table is organized by groups (vertical columns) and periods (horizontal rows), where similar properties appear at regular intervals, known as periodicity. Both trends play a crucial role in understanding chemical properties.
When discussing atomic radii and other properties, recognizing these trends is crucial:

• In a group, elements exhibit heavier and larger atomic structures downward due to added energy levels, increasing the atomic radii.
• Across periods, the radius contracts due to increased nuclear charge attracting electrons more strongly without significantly increasing electron repulsion.
• These trends facilitate comparing the size and reactivity of elements within a group versus across a period.

Comprehending group and period trends is essential for predicting how elements will behave in a chemical context.