Question

Identify the correct order in which the covalent radius of the following elements increases 1\. \(\mathrm{Ti}\) 2\. \(\mathrm{Ca}\) 3\. \(\mathrm{Sc}\) (a) \(3,2,1\) (b) \(2,1,3\) (c) \(1,3,2\) (d) \(1,2,3\)

Short answer

Option (c) 1,3,2 is correct.

Step-by-step solution

Understanding the Covalent Radius

The covalent radius of an element is influenced by its position in the periodic table. Generally, the covalent radius increases as you move down a group because additional electron shells are added, increasing the distance of the outer electrons from the nucleus. However, within a period, the covalent radius typically decreases from left to right due to increased effective nuclear charge, which pulls the electron cloud closer to the nucleus.

Identify Element Positions

Identify the period and group positions of Titanium (Ti), Calcium (Ca), and Scandium (Sc) in the periodic table. Ti, Ca, and Sc are all in the fourth period, with Ca (group 2), Sc (group 3), and Ti (group 4). As we move across the period from Ca to Ti, the covalent radius usually decreases.

Comparing Covalent Radii Across Period

Among the elements, Ca is on the far left and typically has the largest covalent radius, followed by Sc, and lastly Ti having the smallest radius. This occurs because as we move from left to right, electrons are added to the same shell while the nucleus becomes more positively charged, attracting the electron cloud closer.

Arrange In Increasing Order

Given that the covalent radius decreases from Ca to Sc to Ti, we recommend arranging them in the order from the smallest to the largest covalent radius, which is Ti, Sc, Ca.

Selection of Correct Answer

The correct order of increasing covalent radius is Ti (1), Sc (3), Ca (2). The corresponding answer choice is (b) 2,1,3, but this does not align with our established order. Instead, use order 1, 3, 2, which aligns with choice (c).

Key concepts

Periodic Table Trends

The periodic table is not just a tabular array of elements; it represents fundamental patterns in chemical behaviors and properties. One of the most significant trends is how atomic size, particularly covalent radius, changes. As you move from left to right across a period, atomic size decreases. This happens because elements on the right side have more protons in their nucleus, which attract electrons more strongly, pulling them closer. Additionally, when you go down a group, atomic size increases since each row adds an electron shell. This added shell increases the distance between the valence electrons and the nucleus, despite the increase in positive charge.

Effective Nuclear Charge

Effective nuclear charge (ENC) is a concept used to describe the net positive charge experienced by an electron in a multi-electron atom. It's an important factor that influences atomic size and covalent radius. The ENC increases across a period from left to right. This happens because there is a greater number of protons in the nucleus, which exerts a stronger pull on the electron cloud. Even though new electrons are added, they don't add significantly to shielding since they are in the same shell. Thus, the outermost electrons are pulled in closer, reducing the atomic size.

• This stronger pull results in a smaller covalent radius.
• The ENC does not change significantly when moving down a group.

The added layers of electron shells in the same group outweigh the increase in nuclear charge, thus increasing atomic size.

Electron Shells

Electron shells describe the arrangement of electrons around an atom's nucleus. These shells are key to understanding periodic trends and the covalent radius of an element. Each element in the periodic table corresponds to a certain number of electron shells. Moving from one period to the next, an additional electron shell is added. This concept explains why atomic size increases down a group. Electron shells also influence shielding, which is the extent to which inner electron shells block the outer electrons from the attractive force of the nucleus.

• As more shells are added, the nucleus's pull on outer electrons weakens.
• This increase in electron shells contributes to a larger covalent radius.

Despite these added shells, elements in the same period have their outermost electrons in the same shell, hence trends such as decreasing atomic size across a period remain consistent.

Atomic Size

Atomic size, measured in terms of covalent radius, is a critical characteristic of atoms that predicts an element's chemical behavior and bonding tendencies. Covalent radius is indicative of the size of an atom's electron cloud.
Two main trends affect atomic size:

• Across a period, atomic size decreases due to the increase in the effective nuclear charge.
• Down a group, atomic size increases with additional electron shells being added.

This concept is crucial when predicting an element’s relative size compared to others. It’s why calcium, in our example question, has a larger covalent radius than titanium, even though both are in the same period. The periodic trends and changes in ENC help understand and predict how atomic size changes across the table.