Question

Arrange the following sets of elements in order of increasing atomic size. a. \(\mathrm{Sn}, \mathrm{Xe}, \mathrm{Rb}, \mathrm{Sr}\) b. \(\mathrm{Rn}, \mathrm{He}, \mathrm{Xe}, \mathrm{Kr}\) c. \(\mathrm{Pb}, \mathrm{Ba}, \mathrm{Cs}, \mathrm{At}\)

Short answer

The ordered sets of elements in increasing atomic size are: a. \(\mathrm{Rb}, \mathrm{Sr}, \mathrm{Sn}, \mathrm{Xe}\) b. \(\mathrm{He}, \mathrm{Kr}, \mathrm{Xe}, \mathrm{Rn}\) c. \(\mathrm{At}, \mathrm{Pb}, \mathrm{Ba}, \mathrm{Cs}\)

Step-by-step solution

Identify the Elements in Each Set

For each set of elements, we need to identify their positions in the periodic table. Let's do this for each set: a. Sn (Tin), Xe (Xenon), Rb (Rubidium), Sr (Strontium) b. Rn (Radon), He (Helium), Xe (Xenon) and Kr (Krypton) c. Pb (Lead), Ba (Barium), Cs (Cesium), At (Astatine) ##Step 2: Determine the periodic trends for each set of elements##

Apply the Periodic Trends

Using the periodic trends, we can arrange the elements in each set in order of increasing atomic size. Remember that size increases down a group and decreases across a period. a. Sn is in Group 14, Period 5; Xe is in Group 18, Period 5; Rb is in Group 1, Period 5; Sr is in Group 2, Period 5 b. Rn is in Group 18, Period 6; He is in Group 18, Period 1; Xe is in Group 18, Period 5; Kr is in Group 18, Period 4 c. Pb is in Group 14, Period 6; Ba is in Group 2, Period 6; Cs is in Group 1, Period 6; At is in Group 17, Period 6 ##Step 3: Arrange the elements in the order of increasing atomic size##

Arrange the Elements

Based on the periodic trends and the positions of the elements in the periodic table, we can now arrange the elements in each set in order of increasing atomic size. a. Rb, Sr, Sn, Xe b. He, Kr, Xe, Rn c. At, Pb, Ba, Cs So the final ordered sets are: a. \(\mathrm{Rb}, \mathrm{Sr}, \mathrm{Sn}, \mathrm{Xe}\) b. \(\mathrm{He}, \mathrm{Kr}, \mathrm{Xe}, \mathrm{Rn}\) c. \(\mathrm{At}, \mathrm{Pb}, \mathrm{Ba}, \mathrm{Cs}\)

Key concepts

Atomic Size

Atomic size, also known as atomic radius, is a fundamental property of atoms that varies in a predictable way across the periodic table. The atomic size of an element is primarily determined by two key factors:

• The number of electron shells, or energy levels, which increases as you move down a group in the periodic table.
• The effective nuclear charge, which is the net positive charge experienced by valence electrons, decreases across a period as more protons are added to the nucleus.

Moving down a group, the atomic size increases because each subsequent element in a group has an additional energy level. These extra layers of electrons are further from the nucleus and lessen the overall pull of the nucleus on the outer electrons, resulting in a larger size.
Conversely, as you move from left to right across a period, the effective nuclear charge increases, pulling electrons closer to the nucleus and thus decreasing the size of the atom.
Understanding these trends helps predict how atomic size will change both down a group and across a period.

Periodic Table

The periodic table is a systematic arrangement of the chemical elements, ordered by their atomic numbers, electron configurations, and recurring chemical properties. It provides a valuable framework that illustrates periodic trends of the elements, including atomic size, as well as electronegativity and ionization energy. The table is structured into:

• Periods: Horizontal rows that signify elements with the same number of electron shells.
• Groups: Vertical columns where elements share similar chemical behaviors due to having the same number of electrons in their outermost shell.

The position of an element in the table reveals a wealth of information about its electronic configuration and the general trends it will exhibit. For example, elements on the left side of the periodic table typically have larger atomic sizes because they have fewer protons in their nuclei compared to those on the right, leading to a weaker attraction to the electrons.

Element Groups

Element groups are columns in the periodic table where elements have similar valence electron configurations and exhibit similar chemical properties. For instance, Group 1 contains alkali metals like lithium and sodium, while Group 18 consists of noble gases such as helium and neon. Each group has characteristics that define it:

• Group 1 (Alkali Metals): Highly reactive with one valence electron. They tend to lose this electron easily, leading to a larger atomic size.
• Group 2 (Alkaline Earth Metals): Slightly less reactive than Group 1 and possess two valence electrons.
• Group 17 (Halogens): Reactive non-metals found in compounds rather than free elements.
• Group 18 (Noble Gases): Known for their inertness due to having full valence electron shells, making them non-reactive.

By understanding which group an element belongs to, it's easier to predict its reactivity and the size of its atoms. For instance, elements in Group 1 not only react vigorously due to their large atomic size, but they also increase in size further down the group.