Periodic Trends

 

Introduction

Electrons are held in an atom or ion by the electrostatic attraction between the positively charged nucleus and the negatively charged electrons. In multi-electron species, the electrons do not experience the full positive charge of the nucleus due to shielding by electrons which lie between the electron of interest and the nucleus. The amount of positive charge that actually acts on an electron is called the effective nuclear charge.

Effective Nuclear Charge

The concept of effective nuclear charge (Z*) is important to understanding periodic properties. The effective nuclear charge is that portion of the total nuclear charge that a given electron in an atom experiences. This is equal to the atomic number (Z) minus the amount (σ) that other electrons in the atom shield the given atom from the nucleus.

Z* = Z-σ

Example: Lithium has three protons and an electron configuration of 1s22s1. The electron in the 2s orbital is shielded from the full attraction of the protons by the electrons of the 1s orbital (Figure 1). Thus, Z* felt by the 2s electron should be one rather than three. However, lithium's 2s electron does not behave as if it is experiencing exactly a +1 charge (Z* is actually about 1.3 charge units). This can be explained by the fact that the 2s orbital has two maxima in its radial probability function (Figure 1), and the lesser maxima penetrates within the maximum of the inner 1s electron. Although lithium's 2s electron spends most of its time in the outer lobe of that orbital feeling a nuclear charge of +1, some of the time it is inside the 1s orbital experiencing the full nuclear charge of +3. Thus, Z* is somewhat greater than +1.

Slater's Rules for Determining σ

In 1930, J.S. Slater formulated the following set of empirical rules for determining the values of the shielding constant σ.

Slater's Rules
  1. Write out the electronic configuration of the element and group the orbitals in the following order:

    (1s)(2s, 2p)(3s, 3p)(3d)(4s, 4p)(4d)(4f)(5s, 5p)........

  2. To establish the screening constant for any electron, sum up the following contributions:
    1. Electrons in groups outside (to the right) of the one being considered do not contribute to the shielding.
    2. Electrons in the same group contribute 0.35 to the shielding (except the 1s group, where a contribution of 0.30 is used
    3. For s or p electrons being observed, each electron in the (n-1) shell contributes 0.85 to the shielding and each electron in the (n-2), (n-3), ... shells contribute 1.00 to the shielding
    4. For d or f electrons being observed, each electron in an underlying group contributes 1.00 to the shielding.

 

Example

Example: Calculate Z* for a 4s and a 3d electron in Zn

Determine the electron configuration for Zn
(1s)2(2s, 2p)8(3s, 3p)8(3d)10(4s)2

For a 4s electron:
Establish the screening constant for the 4s electron
σ = (1 x 0.35) + (18 x 0.85) + (10x1.00) = 25.65

Calculate the effective nuclear charge
Z*= Z-σ = 30-25.65 = 4.35

For a 3d electron:
Establish the screening constant for the 3d electron

Calculate the effective nuclear charge

From this example, you can see that the 3d electrons experience a much greater positive charge than the 4s electron and would be held more tightly. Thus, the 4s electrons will be the first removed when Zn is ionized.

 

PROBLEMS
  1. Using Slater's rules, calculate a value for the effective nuclear charge felt by (a) an electron being added to the 3s orbital of a neon atom and (b) an electron being ionized from the 2p orbital of the neon atom. Comment on your results relative to the stability of the electron configuration of the neon atom.
  2. Calculate Z* for the valence electrons in the atoms Li to Ne using (a) the assumption that σ equals the number of inner-shell electrons and (b) Slater's rules. Plot both sets of results on the same graph and discuss.
  3. Recall why the energy of an ns orbital is less than that of an np orbital. Use this information to discuss the assumption that these orbitals are always considered as a group (ns, np) in Slater's rules.

  4. Plot of the probability of finding 3s, 3p, 3d and 4s electrons as a function of the radial distance from the nucleus can be viewed here. Discuss these probabilities relative to rules 2c and 2d of Slater's rules.

You can access a spreadsheet for calculating effective nuclear charges here. If you need assistance in using Excel for plotting data, try this tutorial.

 

The Periodic Table

You have used the periodic table throughout your study of chemistry. Read more about the periodic table here. Mendeleev was one of the early chemists to recognize that the properties of the elements were periodic in nature. Read from Mendeleev's original publication.

 

Periodic Trends

In the remainder of this module, you will be analyzing the periodic trends that exist among the elements. Start your investigation by viewing this movie on periodic trends.

Atomic Radius

There are several ways to define the atomic radius of an atom:

  • covalent radius (rcov), the half-distance between the nuclei of two atoms joined in a covalent bond
  • van der Waals radius (rvdw), the half-distance between the nuclei of two atoms of neighboring molecules
  • metallic radius (rmet), for metallic elements, the half-distance between the nuclei of two neighboring atoms in the solid metal

The difference between covalent radius and van der Waals radius is shown in Figure 2.

 

PROBLEMS
  1. Plot the values of radii vs. atomic number for the Group 1A elements and the Period 2 elements. you will find the data that you need in this Excel spreadsheet of physical property data for the elements (right clicking on the link will allow you to save the file).
  2. Use the concept of effective nuclear charge to rationalize the trend in radii values for the Group 1A elements.
  3. Use the concept of effective nuclear charge to rationalize the trend in radii values for the Period 2 elements.
You can see a short movie depicting what you should have concluded here.

Ionization Energy

Recall that the ionization energy (actually the first ionization energy) is the energy required to remove an electron from the outermost occupied orbital of a gaseous atom.

PROBLEMS
  1. Plot the ionization energies for the first 86 elements of the periodic table versus atomic number.Display your plot as both a normal graph and as a bar graph. Explain the general trends that occur across a period and down a family using the concept of effective nuclear charge. In each period an anomaly to the general trend occurs with the Group 3A element and the Group 6A element. Explain this anomalous behavior.
  2. Using Slater's rules, calculate the Z* for Al, Al+, Al2+, and Al3+. Discuss the results relative to the expected ionization energies for these species.
  3. Calculate the Z* for the valence ns electron of lithium, sodium, and potassium using the assumption that σ equals the number of inner-shell electrons. Are your results consistent with the trends in ionization energy for these elements? Discuss why or why not.

Electron Affinity

Electron affinity is the change in energy that occurs when an electron is added to a neutral, gaseous atom.

PROBLEMS
Plot the electron affinity for Main Group elements ( Group 1A-8A) versus atomic number.Display your plot as both a normal graph and as a bar graph. Explain the general trends that occur across a period and down a family using the concept of effective nuclear charge. An anomaly to the general trend occurs in a period in going from the Group 1A element to the Group 2A element and in going from the Group 4A to Group 5A. An anomaly can also be found between rows 2 and 3 in going down a period. Give an explanation for each of these anomalies.

Electronegativity

Electronegativity is the ability of an atom in a molecule to draw electrons to itself.

PROBLEMS

Sketch a periodic table, indicating the trend of electronegativities from lowest to highest. Relate these trends to effective nuclear charge and atomic size.

Other Trends

There are many properties for which you can investigate periodic trends. There is a nice Excel spreadsheet that allows you to look at the trends for various properties in 3-D. Download the spreadsheet. This spreadsheet uses macros for accessing the plots. If you get a message that the macros have not downloaded because of the security setting, reset the security setting for Excel using the tools menu. You will need to enable editing and if asked, make it a trusted document.