Graphing Atomic Radius Vs. Atomic Number The graphing calculator can run a program that graphs data such as atomic radius versus atomic number. Graphing the data within the different periods will allow you to discover trends. Go to Appendix \(C\) . If you are using a TI-83 Plus, you can download the program and data sets and run the application as directed. Press the APPS key on your calculator, then choose the application CHEMAPPS. Press 8 then highlight ALL on the screen, press 1 , then highlight LOAD and press 2 to load the data into your calculator. Quit the application, and then run the program RADIUS. For \(\mathrm{L}_{1},\) press 2 \(\mathrm{nd}\) and \(\mathrm{LIST},\) and choose AINUM. For \(\mathrm{L}_{2},\) press 2 \(\mathrm{nd}\) and \(\mathrm{LIST}\) and choose ATRAD. If you are using another calculator, your teacher will provide you with keystrokes and data sets to use. a. Would you expect any atomic number to have an atomic radius of 20 \(\mathrm{pm} ?\) Explain. b. A relationship is considered a function if it can pass a vertical line test. That is if a vertical line can be drawn anywhere on the graph and only pass through one point, the relationship is a function. Does this set of data represent a function? Explain. c. How would you describe the graphical relationship between the atomic numbers and atomic radii?

Step by step solution

01

Understand the instructions

Carefully read the instructions, and make sure you understand how to use your calculator to graph the data. If using a TI-83 plus, download the program and data sets, load them into your calculator, and then run the RADIUS program. If using a different calculator, follow the instructions provided by your teacher.

02

Data graphing

Use the program to graph the atomic radius on the y-axis versus the atomic number on the x-axis. Make sure that you have properly loaded the aforementioned data sets.

03

Interpreting the graph

Study your graph and look for trends. Are there specific atomic numbers that correspond to an atomic radius of 20 pm? If so, list them. If not, provide a reason why you would not expect such a radius.

04

Vertical line test

Apply the vertical line test to check if the data represents a function. To do this, imagine drawing a vertical line anywhere on the graph. If the line passes through more than one point, then the relationship depicted by the graph is not a function. However, if the line only touches one point, then the relationship is a function.

05

Describe the relationship

Finally, based on your observations, describe the general graphical relationship between atomic numbers and atomic radii. Does it seem like there's a direct or inverse relationship? Is the relationship linear or non-linear?

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Atomic Radius

Understanding the concept of atomic radius is essential when exploring the periodic trends. The atomic radius refers to the size of an atom, typically measured from the center of the nucleus to the outer boundary of the surrounding cloud of electrons. However, because of the probabilistic nature of electron locations, the atomic radius isn't a fixed value but rather an average or an estimation.

There are several factors affecting atomic radius, including the number of electron shells and the charge on the nucleus. As the atomic number increases, atoms have more protons in the nucleus, which draws electrons closer, affecting the radius. However, it's important to note that this trend doesn't always increase linearly due to the arrangement of electrons in different shells and subshells.

An easy way to visualize these trends is through graphing—when atomic radius is plotted against atomic number, certain patterns become apparent. This graphical representation helps in understanding the relative sizes of atoms across different elements.

Atomic Number

The atomic number of an element, denoted as 'Z', is a fundamental property found on the periodic table. It represents the total count of protons in the nucleus of an atom. Each element has a unique atomic number, which also determines the element's position on the periodic table.

It is worth mentioning that as the atomic number increases, the number of electrons around the nucleus also increases if the atom is neutral. The arrangement of these electrons in various orbitals, influenced by the increasing positive charge from the protons, creates a complex interplay that impacts the atomic radius, making the study of these numbers relevant for understanding atomic structure.

When students compare atomic radii across the periodic table in a graph, they should remember that they are witnessing the impact of increasing atomic numbers on atomic sizes.

Trends in the Periodic Table

The periodic table is a highly organized chart that illustrates the recurring trends in the properties of elements. These trends are the result of the periodic nature of electron configurations as elements are arranged by increasing atomic number.

Key trends include atomic size, ionization energy, electronegativity, and metallic character. For instance, atomic radius generally decreases from left to right within a period due to an increase in the effective nuclear charge, which pulls electrons closer to the nucleus. In contrast, atomic radius increases down a group as additional electron shells are added, increasing the distance between the nucleus and the outermost electrons.

Recognizing these trends is crucial as they serve as a guide for predicting and explaining the chemical behavior of different elements. Graphs showing the relationship between successive elements' atomic numbers and atomic radii can serve as a visual aid to strengthen the understanding of these periodic trends.

Graphical Data Analysis

Graphical data analysis is a method of visually interpreting data points to identify patterns, correlations, and trends. When graphing atomic radius against atomic number, students can utilize this type of analysis to observe how atomic size varies among different elements.

A well-constructed graph will show pivotal changes in trends—such as the predictable decrease in atomic radius within a period and the increase down a group. By analyzing the shape of the graph, students might notice that it is not a smooth curve, and instead, it portrays 'jumps' in atomic size at certain points. These jumps correspond to entering a new period, where an additional electron shell is added.

The application of graphical data analysis in this context not only helps in digesting complex patterns in atomic structures but also equips students with critical analytical skills that can be applied across various scientific investigations.