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Analyzing the Periodic
Properties of Elements

Introduction

The periodic table is organized rather strangely, at first sight. There is a big gap at the top. There is a whole section excerpted and stuck at the bottom. There seems to be a pattern in atomic numbers for the start of a new row, but it does not work for the first row and stops working after the third row. The reason for the weird appearance of the table lies deep in the inner workings of the atoms. There are underlying patterns and we will use our knowledge of basic quantum mechanics, that is, electron configuration, to explore a few of those patterns. In this activity we will use patterns in electron configuration combined with an understanding of the role of the atomic nucleus to describe and explain trends in effective nuclear charge, atomic radius, and first ionization energies.

It will be useful to have a few definitions. First, the effective nuclear charge (Zeff) is the charge due to the nucleus that is not shielded by electrons in shells closer to the nucleus. For example, the electron configuration of lithium (Li) is 1s22s1. The 2s electron is attracted by a +3 charge from the nucleus but repelled by each 1s electron by a –1 charge, each. The net effect is that the nuclear charge is reduced: +3 + (–2) = +1 so that the effective nuclear charge on the valence electron of lithium is +1. Valence electons are the electrons in the electron configuration of the ground state of an atom that are in the shell with the highest value of n, the principal quantum number. These are easy to figure for elements in groups 1, 2, and 13 - 18 (the s-block and p-block elements). The valence electrons are those in the highest s- and/or p-subshells. Core electrons are all electrons in shells with lower value of n. For s-block and p-block elements the core electrons are equivalent to the noble gas core. For d-block or transition metal elements we count as core electrons the ones found in the nd subshell in addition to those in the noble gas core. The only valence electrons are in the (n + 1)s subshell. For example, the element titanium (Ti) has the electron configuration 1s22s22p63s23p63d24s2. Titanium has only two valence electrons, those designated 4s2. The 3d2 electrons are considered core electrons along with the 18 electrons in the argon-core, [Ar], making a total of 20 core electrons. As you go from one element to the next in the d-block you add an additional proton and an additional core electron, making effective nuclear charge constant across a row. (In reality it increases slightly, but for this activity we will make this simplifying assumption.)

Atomic radius is a simple-enough idea. Picturing the atoms as spheres, what are their radiuses? This can be measured in a lab by various methods, including deviation from the ideal gas law to calculate the empirical van der Waals radius. We will use a theoretically calculated atomic radius, based on quantum mechanics. In this activity one goal is to build an understanding of the trends in atomic radius based on electron configuration and the effective nuclear charge felt by valence electrons.

The ionization energy is the energy needed to remove an electron from an atom. The first ionization energy is the energy required to remove the highest-potential-energy electron from an atom. As a chemical equation, this looks like:
X + energy → X+ + e–

It may seem odd at first to say that we are removing the electron with the highest potential energy. Remember, potential energy increases as you get farther from the nucleus. Far away from the nucleus the electron is taken to have zero potential energy. As an electron goes from far away down into the quantum shells of an atom it gives up energy by radiating photons until it ends up at a position with negative potential energy. From here, in order to be ionized, the electron must absorb energy. The farther down inside the atom the electron is found, the more energy will be required to ionize it. And the farther an electron is from the nucleus, the less energy will be required to ionize it.

The first ionization always removes the highest-energy electron: the electron removed will always have the highest value of n and l in the ground state electron configuration of the element. For example, the electron ionized from titanium (Ti) is a 4s subshell electron, not the 3d. Another example is that the 2p electron is the one ionized from boron (B), not a 2s electron.


Objective

Explore a few trends in the atomic properties of the elements as they vary from element to element in the periodic table. Specifically, you will explore:

  1. Effective Nuclear Charge
  2. Atomic Radius
  3. First Ionization Energy


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Procedure

Getting Started

  1. Open a new Google Doc and attach it to the assignment on Google Classroom. Copy and paste the questions from the Analysis section into your document.
  2. Open the spreadsheet and make a copy for yourself. Attach it to the Google Classroom assignment.
  3. Fill in the columns marked Core Electrons, Valence Electrons, and Effective Nuclear Charge. Use formulas to make it easier to do quickly. Note that the sheet has been color-coded in a way that is meant to suggest patterns. Refer to the introduction for some important information about Zeff for transition metals.

Graph Number 1, Z vs. Zeff

  1. Create a graph showing how Effective Nuclear Charge (Zeff) changes as a function of Atomic Number (Z). On the Insert Menu, choose Chart. Make sure Atomic Number is on the x-axis! You should have one series listed under Setup in the Chart Editor. You want a Line Chart with sharp, not smoothed angles. In the Chart Editor, under Customize, alter the Series to have Points that are 7 px in size. Add a Chart Title and Axis Titles to make this graph readable and meaningful.
  2. Find the problem in the Analysis that asks for this graph. Copy it from the spreadsheet into the appropriate location in your doc.

Graph Number 2, Z vs. Atomic Radius

  1. Create a graph showing how Atomic Radius changes as a function of Atomic Number (Z). On the Insert Menu, choose Chart. You want a Line Chart with sharp, not smoothed angles. Add points and titles as before.
  2. Find the problem in the Analysis that asks for this graph. Copy it from the spreadsheet into the appropriate location in your doc.

Graph Number 3, Zeff vs. Atomic Radius for Period 2

  1. Create a graph showing how Atomic Radius changes as a function of Effective Nuclear Charge (Zeff). Only graph the data for elements 3 - 10 (Li - Ne). On the Insert Menu, choose Chart. You want a Line Chart with sharp, not smoothed angles. Add points and titles as before.
  2. Find the problem in the Analysis that asks for this graph. Copy it from the spreadsheet into the appropriate location in your doc.

Graph Number 4, Zeff vs. Inverse Atomic Radius for Period 2

  1. Copy the cells which contain the Zeff and Atomic Radius values for elements 3 - 10 (Li - Ne). Paste these cells in a free area on the spreadsheet or on its own tab, if you wish.
  2. Use a formula in a spreadsheet cell next to the atomic radius of lithium to calculate the inverse of the atomic radiuses. Then copy that formula so that you have a column of inverse radius values.
  3. Create a graph showing Inverse Atomic Radius as a function of Effective Nuclear Charge (Zeff). On the Insert Menu, choose Chart. You want a Scatter Chart with data points only and no lines. Add titles as before.
  4. In the Chart Editor under Customize, find the Series section. Check the box for Trendline. In the drop-down menu called Label that appears, change “None” to “Use Equation”.
  5. Find the problem in the Analysis that asks for this graph. Copy it from the spreadsheet into the appropriate location in your doc.

Graph Number 5, Z vs. First Ionization Energy

  1. Create a graph showing how First Ionization Energy changes as a function of Atomic Number (Z). On the Insert Menu, choose Chart. You want a Line Chart with sharp, not smoothed angles. Add points and titles as before.
  2. Find the problem in the Analysis that asks for this graph. Copy it from the spreadsheet into the appropriate location in your doc.

Graph Number 6, Zeff vs. Ionization Energy for Period 2

  1. Create a graph showing how Ionization Energy changes as a function of Effective Nuclear Charge (Zeff) for period two elements. Only graph the data for elements 3 - 10 (Li - Ne). On the Insert Menu, choose Chart. You want a Line Chart with sharp, not smoothed angles. Add points and titles as before.
  2. Find the problem in the Analysis that asks for this graph. Copy it from the spreadsheet into the appropriate location in your doc.


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Analysis

In your Google doc answer the following questions. Copy and paste the questions from this online document so that they are easy to answer.

Exploring Effective Nuclear Charge

  1. Insert graph number 1, Z vs. Zeff
  2. What is the trend for how Zeff changes with increasing atomic number for the s-block and p-block elements?
  3. Why does the trend reset back to 1 repeatedly in this graph?
  4. Using the concepts you learned in studying electron configuration, explain the s-block and p-block trend for effective nuclear charge.
  5. What is the trend for how Zeff changes with increasing atomic number for the d-block elements?
  6. Explain the d-block elements trend using the definitions of effective nuclear charge along with your understanding of electron configuration.

Exploring Atomic Radius

  1. Insert graph number 2, Z vs. Atomic Radius
  2. What are the electron configurations of the following six elements?
    He and Li, Ne and Na, Ar and K
  3. Compare the radius of each of these six elements to one another within each pair. What do you notice?
  4. Using what you know about electron configuration and effective nuclear charge, explain the pattern you just described.
  5. Atomic radius steadily decreases from sodium (Na) to argon (Ar), as you can see in your graph. Explain this trend using what you know about electron configuration and effective nuclear charge.
  6. Atomic radius only changes very gradually from scandium (Sc) to zinc (Zn). Explain this trend using what you know about core and valence electrons in addition to the usual things.
  7. The highest values for atomic radius are all elements in group 1: Li, Na, K, Rb, and Cs. Explain why these elements are always the ones with largest radius in their row of the periodic table.
  8. Compare the height of the radius measurement for each of the group 1 elements. What pattern do you see in the radius of these elements as you go from the top to the bottom of this group? Please explain this trend.
  9. Insert graph number 3, Zeff vs. Atomic Radius for Period 2
  10. This graph should appear to be a classic example of a simple type of proportion. Explain how you know whether it is a direct or inverse proportion.
  11. If you graph Zeff vs. the inverse of the radius values (1/r), what would you expect it to look like? Why?
  12. Insert graph number 4, Zeff vs. Inverse Atomic Radius for Period 2
  13. Is this a direct or inverse proportion now that we have graphed the inverse of radius against Zeff? What does that say about the type of proportion shown in graph number 3?
  14. Explain this proportion between effective nuclear charge and atomic radius using the concepts of electron configuration, core electrons, and valence electrons.

Exploring Ionization Energy

  1. Insert graph number 5, Z vs. First Ionization Energy
  2. Which elements are always at the highest ionization energy values for their rows of the periodic table? Explain why.
  3. Which elements are always at the lowest ionization energy values for their rows of the periodic table? Thinking not just about Zeff but also atomic radius, explain why these elements have the lowest ionization energies for their row.
  4. Why is there generally a very steep increase in the ionization energy of elements for Li - Ne and for Na - Ar?
  5. Why is there generally a very gradual increase in the ionization energy of elements from Sc to Zn and from Y to Cd?
  6. Consider the ionization energies for the noble gases, group 18 (He, Ne, Ar, Kr, and Xe). What is the trend for ionization energies for these elements? Explain this trend.
  7. Insert graph number 6, Zeff vs. Ionization Energy for Period 2
  8. This graph shows the generally steep increase in ionization energy noted for the s-block and p-block elements. But there are two places where the general trend is broken. Which two elements are bucking the trend?
  9. Give the electron configuration for Be and for B.
  10. Despite having a larger effective nuclear charge, why does B have a lower ionization energy than Be? Consider the relative potential energies of subshells within the same quantum shell in your answer.
  11. Give the electron configuration for N and for O.
  12. Despite having a larger effective nuclear charge, why does O have a lower ionization energy than N? Consider the change in the potential energy experienced by electrons when they are forced to pair up with opposite spins in a single orbital vs. when they can remain in separate orbitals with the same spin.
Data for atomic radius are from Wikipedia (https://en.wikipedia.org/wiki/Atomic_radii_of_the_elements_(data_page)).
Data regarding first ionization energies are from PubChem (https://pubchem.ncbi.nlm.nih.gov/ptable/ionization-energy/).

Last updated: Dec 18, 2024 Home