3.2: Question 3.E.09 PASS - ranking atomic radius

Exercise \(\PageIndex{3.E.09}\)

Based on their positions in the periodic table, list the following atoms in order of increasing radius: Ca, Cs, Mg, Rb.

Answer

Mg, Ca, Rb, Cs

See LibreText 3.2 Periodic Variations in Elemental Properties

Strategy Map

Step	Hint
1. Recognize the context of the question and confirm the requested format of the answer.	The question requires understanding of atomic radii Must list in order from smallest to largest atomic radii Recall LibreText 3.2.2 Variation in Covalent Radius
2. Find each element on the periodic table.	Note the periods (row #; top to bottom), groups (column #; left to right) and atomic number (Z)
3. Recall relevant concepts that impact atomic radii and summarize the periodic trends to sort them into descending or ascending sizes.	Consider effective nuclear charge (Zeff) See LibreText 3.2.1 Effective Nuclear Charge: Penetration and Shielding Atomic radii increases as you move down a period, and decreases and you move right across and group the largest element is located at the bottom left of the periodic table the smallest element is located at the top right of the periodic table

Solution

The locations of Ca, Cs, Mg, and Rb on the periodic table:

• Ca, atomic number 20, group 2, period 4
• Cs, atomic number 55, group 1, period 6
• Mg, atomic number 12, group 2, period 3
• Rb, atomic number 37, group 1, period 5

List smallest to largest in atomic radii: Mg < Ca < Rb < Cs

Answer:

In order of increasing radius: Mg, Ca, Rb, Cs

Guided Solution

Guided Solution	Hint
This is a theory problem that requires understanding and application of concepts related to the shape of atomic orbitals, effective nuclear charge, and atomic radii.	See LibreText 2.5 The Shape of Atomic Orbitals Recognize that as principal quantum number (n) increases (i.e., as you move down the periodic table) the size of the orbital increases See LibreText 3.2.1 Effective Nuclear Charge: Penetration and Shielding See LibreText 3.2.2 Variation in Covalent Radius Recognize that as Zeff increases (i.e., as you move left to right across the periodic table) the size of the orbital decreases
Question Based on their positions in the periodic table, list the following atoms in order of increasing radius: Ca, Cs, Mg, Rb.	This question asks us to tank the given elements by their size. See LibreText Supplemental Modules (Physical and Theoretical Chemistry) - Atomic Radii
Consider what characteristics may influence the distance between the nucleus and valence electron(s)	The nucleus is positively charged while electrons are negatively charged. The stronger the attractive force between the nucleus and the electron, the more tightly (i.e., closely) it will be held Principal quantum number (n) Shielding: consider how many complete shells of electrons are between the valence electrons and the nucleus Effective Nuclear Charge (Zeff) Shielding: electrons in the same shell (i.e., across the same row) are not effective at shielding the attractive forces from the nucleus as you move left to right across a row, the number of protons and effective nuclear charge (i.e., positive charge felt by the valence electron) increases the electrons are held more tightly (i.e., closer) to the nucleus and atomic radii decreases (n) influences size more than (Zeff)
Summarize the trend of atomic radii across the periodic table	The atomic radius decreases from left to right, and increases from top to bottom the largest element is located at the bottom left of the periodic table the smallest element is located at the top right of the periodic table
Locate the elements on the Periodic Table Ca (calcium), atomic number 20, group 2, period 4 Cs (cesium), atomic number 55, group 1, period 6 Mg (magnesium), atomic number 12, group 2, period 3 Rb (rubidium), atomic number 37, group 1, period 5
List the elements in order of increasing principal quantum number (n) Mg (period 3) Ca (period 4) Rb (period 5) Cs (period 6)	As (n) increases, the size of the orbital increases Recall: The valence electrons for all of the listed elements are in s-orbitals Mg (3s) Ca (4s) Rb (5s) Cs (6s) Note: Because all the elements are in different periods, we do not need to consider their group location (i.e., relative position from left to right) See Figure 3.2.3 in: LibreText 3.2.2 Variation in Covalent Radius
Answer Mg, Ca, Rb, Cs	Listed from smallest to largest atomic radii: Mg < Ca < Rb < Cs
Does this make chemical sense?	It makes sense that size increases as principal quantum number increases. The periodic table is arranged logically with each row representing an increased (n). As the 'n' value increases, the size of the orbital is increased. This is because there are complete shells (i.e., core electrons) in between the nucleus and the valence electrons. The core electrons effectively shield the positive attractive force that is felt by the valence electrons. Therefore, the more core electrons, the weaker the attractive force; the valence electrons are held more weakly (i.e., at a further distance) from the nucleus resulting in an increased atomic radii.

(question source adapted from 6.5.9 from 6.E: Electronic Structure and Periodic Properties (Exercises): https://chem.libretexts.org/Bookshelves/General_Chemistry/Chemistry_1e_(OpenSTAX)/06%3A_Electronic_Structure_and_Periodic_Properties_of_Elements/6.E%3A_Electronic_Structure_and_Periodic_Properties_(Exercises), shared under a CC BY 4.0 license, authored, remixed, and/or curated by OpenStax, original source question 75 https://openstax.org/books/chemistry-2e/pages/6-exercises, Access for free at https://openstax.org/books/chemistry/pages/1-introduction)