Question

Identify the group of elements that corresponds to each of the following generalized electron configurations and indicate the number of unpaired electrons for each: $$ \begin{array}{l}{\text { (a) [noble gas ln }^{2} n p^{5}} \\ {\text { (b) }\left[\text { noble gas } \ln s^{2}(n-1) d^{2}\right.}\\\\{\text { (c) [noble gas } \operatorname{ns}^{2}(n-1) d^{10} n p^{1}} \\ {\text { (d) }[\text { noble gas }] n s^{2}(n-2) f^{6}}\end{array} $$

Short answer

(a) The group 17 element, 1 unpaired electron. (b) The group 4 transition metal, 2 unpaired electrons. (c) The group 13 element, 1 unpaired electron. (d) The second element in the Lanthanide series, 6 unpaired electrons.

Step-by-step solution

(a) Identify the group and unpaired electrons for [noble gas] ns^2 np^5 configuration

For configuration (a) [noble gas] ns^2 np^5, this refers to a group 17 element, as the last electron enters the p orbital and has 5 electrons in it. Since in a p orbital, there are 3 orbitals (px, py, and pz), and since there are 5 electrons, 3 orbitals will have one electron each and one of them will have two electrons. Hence, there will be 1 unpaired electron.

(b) Identify the group and unpaired electrons for [noble gas] ns^2 (n-1)d^2 configuration

In configuration (b) [noble gas] ns^2 (n-1)d^2, this corresponds to a group 4 element in the transition metals, as the last electron enters the d orbital and there are already 2 electrons in the s orbital. Since d orbitals can hold up to a maximum of 10 electrons and this configuration has 2 electrons in it, those 2 electrons will occupy two separate d orbitals. Thus, there will be 2 unpaired electrons.

(c) Identify the group and unpaired electrons for [noble gas] ns^2 (n-1)d^10 np^1 configuration

For configuration (c) [noble gas] ns^2 (n-1)d^10 np^1, this refers to a group 13 element, as 10 electrons are present in the d orbitals and there are already 2 electrons in the s orbital and 1 electron in the p orbital. Since the p orbital can hold 6 electrons and this configuration has only 1 electron in the p orbital (i.e. 1 electron in one of the px, py, or pz orbitals), there will be only 1 unpaired electron.

(d) Identify the group and unpaired electrons for [noble gas] ns^2 (n-2)f^6 configuration

In configuration (d) [noble gas] ns^2 (n-2)f^6, this corresponds to an element in the f-block, specifically the second element in the Lanthanide series. The f orbitals can hold up to a maximum of 14 electrons. In this configuration, there are 6 electrons in the f orbitals. Those 6 electrons will occupy six separate f orbitals. Thus, there will be 6 unpaired electrons.

Key concepts

Group Number

The group number of an element provides valuable insight into its chemical properties and electron configuration. In the periodic table, elements are organized into groups or families, numbered from 1 to 18. These groups correspond to the number of valence electrons in the outermost shell. For instance, in the generalized electron configuration

• **ns**^2 **np**^5
• we find elements in group 17.

This is because the outermost p orbital is filled with five electrons and the s orbital with two, making a total of seven valence electrons. Group 17 elements are known as halogens and are reactive nonmetals. Learning about the group number helps students understand why certain elements behave similarly and react in predictable ways. It also aids in predicting an element's chemical reactivity and bonding patterns.

Unpaired Electrons

Unpaired electrons play a crucial role in the chemical and magnetic properties of an atom. Atoms and ions with unpaired electrons tend to be more reactive and can exhibit magnetic properties known as paramagnetism. For example, consider

• **ns**^2 **np**^5 configuration (group 17): Here, there is only one unpaired electron in the p orbital, contributing to the high reactivity of halogens.
• Conversely, in the **nd**^2 configuration (group 4), we see two unpaired electrons, which indicate that these elements can form covalent bonds.

Unpaired electrons are the ones that do not have a paired partner within their atomic orbital. In chemical reactions, atoms tend to pair these unpaired electrons either by forming bonds with other atoms or by redistributing electrons. This concept is essential for understanding molecular structures and bonding.

Transition Metals

Transition metals span groups 3 to 12 in the periodic table. They are characterized by partially filled d orbitals and exhibit a wide range of oxidation states. This makes them incredibly versatile and useful in various applications, from catalysis to jewelry making.

• In the example of **ns**^2 **(n-1)d**^2, we see elements from group 4, such as titanium and zirconium.

These metals exhibit unique properties such as:

• High melting and boiling points
• Malleability
• Good electrical conductivity

Transition metals often form colorful compounds due to d-d electron transitions. They are also important in biological systems, with metals like iron playing a central role in oxygen transport and electron transfer processes.

F-block Elements

The f-block elements, also known as inner transition metals, include the lanthanides and actinides. These elements have their f orbitals being filled and are found on the separate bottom row of the periodic table.

• The generalized configuration **ns**^2 **(n-2)f**^6 corresponds to elements like neodymium within the lanthanide series.

F-block elements have the following characteristics:

• Complex electron configurations, leading to unique magnetic and optical properties.
• Tend to display +3 oxidation states frequently.
• Highly paramagnetic due to the presence of many unpaired electrons, e.g., 6 in some configurations.

Despite their scarcity, these elements are crucial in modern technologies, playing roles in producing strong magnets, catalysis, and advanced materials. Understanding their electron configurations aids in harnessing their properties for practical applications.