Which of the following species are radicals: (a) \(\mathrm{NO}\); (b) \(\mathrm{CH}_{3}^{*}\); (c) \(\mathrm{BF}_{4}\); (d) \(\mathrm{BrO}\) ?

Valence electrons play a pivotal role in chemical bonding and reactions. They are the electrons located in the outermost shell of an atom and are responsible for the chemical properties of the element. For instance, in the provided exercise, to determine if a species is a radical, we first need to count the number of valence electrons. The number of valence electrons for nitrogen and oxygen can be determined from their positions in the periodic table. Nitrogen, being in group 15, has 5 valence electrons, whereas oxygen, found in group 16, has 6.

Understanding the concept of valence electrons is crucial not only for identifying radicals but also for predicting the reactivity of elements and how they combine to form molecules. The interaction of valence electrons between different atoms leads to the formation of chemical bonds, such as ionic or covalent bonds. Therefore, knowing how to count and use valence electrons is an essential skill in chemistry.

Unpaired electrons are single electrons that reside in an atom's valence shell and do not partake in bonding pairs. These electrons are significant because they can give rise to radicals, which are highly reactive species. In the given exercise, CH_3^* is an example of a radical due to the presence of an explicitly indicated unpaired electron, represented by the asterisk. Radicals like this often participate in radical reactions, which are crucial in various chemical processes, such as polymerization and combustion.

To identify unpaired electrons, one must understand electron configuration and the principles of orbital filling, such as Hund's rule, which states that each orbital in a subshell is singly occupied before any orbital is doubly occupied. Electrons will fill the orbitals in a way that maximizes the number of unpaired electrons, which in turn can affect the magnetic properties and reactivity of the atom or molecule.

Molecular radicals are species with at least one unpaired electron in the molecular or ionic state. They are typically formed by homolytic bond cleavage, which means the bond breaks evenly and each atom keeps one of the bonded electrons. This leads to the presence of at least one unpaired electron. As we deduced in the exercise, both NO and BrO are molecular radicals due to having an odd number of valence electrons. Molecular radicals are often reactive and short-lived, but they are central in many natural and industrial processes, like the regulation of circadian rhythms to synthesis of polymers in industry.

Understanding how to determine if a molecule is a radical is essential for students of chemistry, as it allows them to predict reactivity and potential mechanisms in chemical reactions. The significance of radicals extends beyond basic chemistry, influencing fields such as biology, medicine, and material science.