Write the condensed electron configurations for the following atoms and indicate how many unpaired electrons each has: (a) \(\mathrm{Mg},(\mathbf{b}) \mathrm{Ge}\) (c) \(\mathrm{Br}\) (d) \(V\), (e) Y, (f) Lu.

The periodic table is a comprehensive chart that organizes all known elements according to their chemical properties and atomic structures. Importantly, each element's position is determined by its atomic number, which incrementally increases from one element to the next.

Elements in the same column, or group, have similar properties and the same number of electrons in their outermost shell, which greatly influences their chemical behavior. Understanding the layout of the periodic table is crucial when learning to write electron configurations, as it helps to identify the energy levels (shells) and orbitals types (s, p, d, f) that an element’s electrons occupy.

As we delve into electron configurations, we find patterns, such as the alkali metals all having one electron in their outer shell or noble gases having full outer shells. These configurations reveal much about the reactivity and bonding of each element.

Unpaired electrons are the electrons in an atom that do not have a corresponding electron with opposite spin in the same orbital. These electrons play a pivotal role in determining the magnetic properties and chemical reactivity of an element.

For instance, elements with unpaired electrons are typically paramagnetic, meaning they are attracted by magnetic fields, because these unpaired electrons can align their spins in the direction of the field. Here's an easy way to picture this: think of unpaired electrons as little magnets themselves, without a partner to neutralize their magnetic field.

Understanding how to identify the number of unpaired electrons as part of determining the electron configuration is not only important for predicting chemical and physical behavior but also crucial in fields such as quantum chemistry and spectroscopy, where the electronic structure of an atom is fundamental.

The atomic number is perhaps the most crucial piece of information on the periodic table for each element. Simply put, the atomic number tells us the number of protons in the nucleus of an atom, which also equals the number of electrons in a neutral atom.

Thus, as the atomic number increases, so does the electron count, since it fundamentally defines an element's identity and position in the periodic table. This makes it the starting point for writing electron configurations.

For example, referring back to our exercise, magnesium (Mg) has the atomic number 12, meaning it has 12 protons and, in its neutral state, 12 electrons. Therefore, when writing its electron configuration, we begin by filling the orbitals starting from the lowest energy level up to the 12th electron. This methodical filling leads to the arrangement of electrons around an atom and can be predicted using the periodic table.