\( \require{cancel} \) \( \newcommand{\xrightleftharpoons}[2]{\overset{#1}{\underset{#2}{\rightleftharpoons}}} \) \( \newcommand{\conc}[1]{\left[\mathrm{#1}\right]} \) \( \newcommand{\chem}[1]{\mathrm{#1}} \) \( \definecolor{green}{RGB}{0,128,0} \) \( \definecolor{blue}{RGB}{0,0,255} \)

Chapter 7

Atomic Structure and Periodicity

Shaun Williams, PhD

Electromagnetic Radiation

  • Different Colored Fireworks

Questions to Consider

  • Why do we get colors?
  • Why do different chemicals give us different colors?
Various colored fireworks bursting over Washington DC landmarks.

Electromagnetic Radiation

$$ c = \lambda \nu $$

Waves

a photograph of waves on the surface of water. A graphic of three waves whose wavelengths start long and then are divided by one-half and then one-half again. As the wavelength is halved, the frequency doubles.

Classification of Electromagnetic Radiation

The breakdown of the electromagnetic radiation into the regions gamma rays, x rays, ultraviolty, visible, infrared, microwaves, and radio waves (from high energy to low energy).

Pickle Light

When electricity is passed through a pickle, it glows with a yellow light.

The Nature of Matter

Energy

The Atomic Spectrum of Hydrogen

Significance

The Bohr Model

Electronic Transitions in the Bohr Model for the Hydrogen Atom

A graphical representation of the first five energy levels in the hydrogen atom. The levels get closer together as the energy increases.
The first five orbits of the hydrogen atom (per the Bohr model) and the electron transition between the 5-to-2, 4-to-2, and 3-to-2 which are responsible for the blue line, green line, and red line in the hydrogen line spectrum.

The Bohr Model Energy Equation

The Bohr Model Analysis

The Quantum Mechanical Model of the Atom

Physical Meaning of a Wave Function \((\Psi)\)

Probability Distribution for the 1s Wave Function

Plots of the 1s orbital with high density at the center and exponentially less as the distance from the center increases.

Radial Probability Distribution

The radial probability distribution with no intensity at the center, rising steeply to a max and the exponentially dropping.

Relative Orbital Size

Quantum Numbers

Quantum Numbers for the First Four Levels of Orbitals in the Hydrogen Atom

\(n\) \(l\) Sublevel
Designation
\(m_l\) Number of
Orbitals
1 0 \(1s\) 0 1
2 0 \(2s\) 0 1
1 \(2p\) -1,0,+1 3
3 0 \(3s\) 0 1
1 \(3p\) -1,0,+1 3
2 \(3d\) -2,-1,0,+1,+2 5
4 0 \(4s\) 0 1
1 \(4p\) -1,0,+1 3
2 \(4d\) -2,-1,0,+1,+2 5
3 \(4f\) -3,-2,-1,0,+1,+2,+3 7

Exercise 1

For principal quantum level \(n = 3\), determine the number of allowed subshells (different values of \(l\)), and give the designation of each.

Exercise 1 - Answer

For principal quantum level \(n = 3\), determine the number of allowed subshells (different values of \(l\)), and give the designation of each.

Number of allowed subshells = 3 (\(l=0,1,2\))

Orbital Shapes and Energies

Three Representations of the Hydrogen \(1s\), \(2s\), and \(3s\) Orbitals

Plots of the three orbitals, density plots, and 3D plots.

The Boundary Surface Representations of All Three \(2p\) Orbitals

A density plot of one of the 2p orbitals and 3D plots of all three 2p orbtials showing the lobe structure of the orbitals.

The Boundary Surfaces of All of the \(3d\) Orbitals

Density plots of three of the 3d orbitals and 3D plots of all five 3d orbtials showing the double lobe structure of the orbitals.

Representation of the \(4f\) Orbitals in Terms of Their Boundary Surfaces

3D plots of all seven 4f orbtials showing the quadruple lobe structure of the orbitals.

Electron Spin and the Pauli Principle

Electron Spin

Polyelectronic Atoms

Penetration Effect

A Comparison of the Radial Probability Distributions of the \(2s\) and \(2p\) Orbitals

The plots of the 2s and 2p orbitals shows the small penetration bump in the 2s that makes the 2s more stable than the 2p.

The Radial Probability Distribution of the \(3s\) Orbital

The radial plot of the 3s orbital shows two small penetration bumps insidethe most probable distance from the nucleus for the 3s orbital.

A Comparison of the Radial Probability Distributions of the \(3s\), \(3p\), and \(3d\) Orbitals

The plots of the 3s, 3p, and 3d orbitals shows the penetration bumps that make the 3s the most stable followed by the 3p.

The History of the Periodic Table

The Aufbau Principle and the Periodic Table

Aufbau Principle

Hund's Rule

Orbital Diagram

Oxygen: \(1s^22s^22p^4\)

\(1s\) \(\phantom{2s}\) \(2s\) \(\phantom{2s}\) \(2p\)
\(\uparrow\downarrow\) \(\phantom{\uparrow\downarrow}\) \(\uparrow\downarrow\) \(\phantom{\uparrow\downarrow}\) \(\uparrow\downarrow\) \(\uparrow\phantom{\downarrow}\) \(\uparrow\phantom{\downarrow}\)

Valence Electrons

The Orbitals Being Filled for Elements in Various Parts of the Periodic Table

The s-block, p-block, d-block, and f-block on the periodic table.

Exercise 2

Determine the expected electron configurations for each of the following.

  1. S
  2. Ba
  3. Eu

Exercise 2 - Answer

Determine the expected electron configurations for each of the following.

  1. S - \(1s^22s^22p^63s^23p^4\) or \([\chem{Ne}]3s^23p^4\)
  2. Ba - \([\chem{Xe}]6s^2\)
  3. Eu - \([\chem{Xe}]6s^24f^7\)

Periodic Trends in Atomic Properties

Periodic Trends

Ionization Energy

\(\chem{Mg\rightarrow Mg^+ + e^-}\) \(I_1=735\,\bfrac{\chem{kJ}}{\chem{mol}}\) (1st IE)
\(\chem{Mg^+\rightarrow Mg^{2+} + e^-}\) \(I_2=1445\,\bfrac{\chem{kJ}}{\chem{mol}}\) (2nd IE)
\(\chem{Mg^{2+}\rightarrow Mg^{3+} + e^-}\) \(I_3=7730\,\bfrac{\chem{kJ}}{\chem{mol}}\) (3rd IE)*

* Core electrons are bound much more tightly than valence electrons.

More on Ionization Energy

The Values of First Ionization Energy for the Elements in the First Six Periods

Plot of the ionizations of the elements in the first six rows showing the trends described on the previous slide.

Successive Ionization Energies (kJ per Mole) for the Elements in Period 3

Element \(I_1\) \(I_2\) \(I_3\) \(I_4\) \(I_5\) \(I_6\) \(I_7\)
Na 495 4560
Mg 735 1445 7730
Al 580 1815 2740 11600
Si 780 1575 3220 4350 16100
P 1060 1890 2905 4950 6270 21200
S 1005 2260 3375 4565 6950 8490 27000
Cl 1255 2295 3850 5160 6560 9360 11000
Ar 1527 2665 3945 5770 7230 8780 12000

Electron Affinity

Atomic Radius

Atomic Radii for Selected Atoms

Plot of the atomic radii of the elements showing the trends described on the previous slide.

Exercise 3

Arrange the elements oxygen, fluorine, and sulfur according to increasing:

Exercise 3 - Answer

Arrange the elements oxygen, fluorine, and sulfur according to increasing:

The Properties of a Group: The Alkali Metals

The Periodic Table - Final Thoughts

  1. It is the number and type of valence electrons that primarily determine an atom's chemistry.
  2. Electron configurations can be determined from the organization of the periodic table.
  3. Certain groups in the periodic table have special names.

Special Names for Groups in the Periodic Table

Group names in the periodic table. Group 1 are the alkali metals, group 2 are the alkaline earth metals, group 17 are the halogens, and group 18 are the noble gases.

The Periodic Table - Final Thoughts (cont.)

  1. Basic division of the elements in the periodic table is into metals and nonmetals.

The nonmetals at above and to the right of the stair-step line. The metals are to the left and below the stair-step line. The metalloids are seven elements that lie on the stair-step line.

The Alkali Metals

/