Based on what you have learned so far in this course, predict the relationship between \(\mathrm{IE}_{1}\) and atomic number by making a rough graph of \(\mathrm{IE}_{1}\) vs. atomic number. Discuss possible ideas with your team and decide which one you think makes the most sense. DO NOT PROCEED TO THE NEXT PAGE UNTIL YOU HAVE MADE YOUR PREDICTED GRAPH.

In chemistry, understanding periodic trends is crucial to predict properties of elements, such as their ionization energy. These trends arise due to the repeated patterns in the electronic structure of atoms as one moves across or down the periodic table.

As a fundamental concept, students often learn that elements are arranged in the periodic table in order of increasing atomic number. Along periods (horizontal rows), elements experience a gradual change in properties, while groups (vertical columns) contain elements with similar chemical properties. This arrangement helps in uncovering patterns among various elemental properties, including atomic radius, electronegativity, and of course, ionization energy.

When we discuss ionization energy, we often reference its trend across a period—generally increasing from left to right due to a stronger attraction between electrons and the nucleus. Conversely, ionization energy trends typically decrease as we move down a group because of the increased distance between the nucleus and the outermost electron.

The concept of atomic structure details how an atom is configured, understanding which is vital for predicting the behavior of atoms during chemical reactions. Atoms consist of a nucleus containing protons and neutrons, surrounded by electrons that occupy different energy levels or shells.

Understanding the atomic number, which defines the number of protons in the nucleus and consequently the number of electrons in a neutral atom, sets the stage for understanding ionization energy. The arrangement of electrons across the various shells and subshells is governed by quantum mechanical principles, resulting in specific configurations that determine the chemical characteristics of the element.

The effect of adding protons to the nucleus and electrons to the corresponding shells, as we move across the periodic table, influences the ionization energy, as the positive charge of the nucleus attracts the negatively charged electrons with more force.

Focusing on ionization energy (IE1) itself, this is the energy required to remove the outermost electron from a gaseous atom or ion. The first ionization energy, IE1, is significant because it offers insight into the reactivity of an element and its tendency to form bonds.

Higher ionization energies suggest a greater attraction between the atom's nucleus and its outermost electron, typically indicating less reactivity. As we consider the relationship between atomic number and IE1, it's understood that ionization energy tends to increase with an increasing atomic number within a period due to decreasing atomic radius and greater nuclear charge. However, the solution's steps rightly point out that there are exceptions to this trend, notably at the start of a new period or a new electron shell and where electron pairing occurs, leading to 'dips' in the graph.

The exercise of graphing atomic properties like IE1 as a function of atomic number is an illustrative way to visualize these periodic trends. Such a graph provides a tangible representation of the concepts we're exploring.

To construct an accurate graph, we start by plotting the atomic number on the x-axis and IE1 values on the y-axis. The general rising slope of the line reflects the overall increasing trend of ionization energy. Upon this, we add the noted fluctuations to demonstrate the decrease in IE1 at the start of each new period and where electron pairing within the shells occurs. This graphical representation aids in making the abstract notion of periodic trends more concrete and provides a tool for predicting the properties of unknown elements or ions.