Describe the changes in properties (from metals to nonmetals or from nonmetals to metals) as we move (a) down a periodic group and (b) across the periodic table.

Understanding the metallic character is crucial when navigating the periodic table. Metallic character refers to the set of chemical properties associated with elements that are metals. These properties include shininess, malleability, ductility, and most notably, the ease at which they can lose electrons to form positive ions (cations).

When you move down a group in the periodic table, the atomic radius increases as additional electron shells are added. This larger atomic radius tends to decrease the effective nuclear charge experienced by the valence electrons because there is more shielding by the inner electrons. As a result, these outer electrons are less tightly held and can be lost more easily, which enhances the metallic character. Elements also exhibit lower ionization energies and electronegativities, contributing to their higher metallic nature.

The atomic radius is a fundamental concept in understanding periodic trends. It's essentially the distance from an atom's nucleus to the boundary of its surrounding cloud of electrons. Since we cannot measure the edges of these electron clouds precisely, the atomic radius is often calculated as half the distance between the nuclei of two identical atoms bonded together.

As we move down a group, each element has more electron shells, making the atom larger; therefore, the atomic radius increases. Conversely, from left to right across a period, protons are added to the nucleus, increasing the positive charge, which draws electrons closer to the nucleus. This leads to a smaller atomic radius. Smaller atomic radii increase the attraction on valence electrons, affecting properties like ionization energy and electronegativity.

Ionization energy is the energy required to remove an electron from an atom or ion in its gaseous state. It's indicative of how strongly an atom's nucleus holds onto its valence electrons. High ionization energy means that an atom does not lose its electrons easily, which is typical for nonmetals.

As you go down a group, the ionization energy decreases because the atomic radius is larger, and the valence electrons are further from the nucleus and less tightly held. This makes it easier for the atom to lose electrons. Conversely, moving across a period, the ionization energy increases as the atoms have a stronger attraction towards the valence electrons due to a smaller atomic radius and a higher nuclear charge.

Electronegativity is a measure of an atom's ability to attract and hold onto electrons within a chemical bond. It is an important concept for predicting the nature of chemical bonds; elements with high electronegativity tend to form negative ions (anions) and are more likely to accept electrons.

Across a period, electronegativity increases. This is because atoms are smaller due to a larger nuclear charge pulling the electrons closer to the nucleus. Meanwhile, as we move down a group, electronegativity decreases due to increased atomic radius and electron shielding which reduces the pull on bonding electrons. Hence, the elements at the top right of the periodic table (excluding noble gases) are typically the most electronegative, such as fluorine, while those at the bottom left are the least electronegative.