Chapter 10 – Summary

10.1 Electromagnetic Radiation

Light and other forms of electromagnetic radiation move through a vacuum with a constant speed, c, of 2.998 × 10⁸ m s⁻¹. This radiation shows wavelike behaviour, which can be characterized by a frequency (ν) and a wavelength (λ)such that c = λν. Each particle of EMR spectrum has a quantum of energy associated with it and is called a photon. The energy of a photon is proportional to its frequency, and inversely proportional to its wavelength. Light demonstrates both wavelike and particle-like behaviour is known as wave-particle duality. All forms of electromagnetic radiation share these properties, although various forms including X-rays, visible light, microwaves, and radio waves interact differently with matter and have very different practical applications.

10.3 Wave Nature of Matter

An electron possesses both particle and wave properties. The modern model for the electronic structure of the atom is based on recognizing that an electron possesses particle and wave properties, the so-called wave–particle duality. Louis de Broglie showed that the wavelength of  particle is equal to Planck’s constant divided by the mass times the velocity of the particle. He argued that Bohr’s assumption of quantization can be explained if the electron is considered not as a particle, but rather as a circular standing wave such that only an integer number of wavelengths could fit exactly within the orbit. Thus, it appears that while electrons are small localized particles, their motion does not follow the equations of motion implied by classical mechanics, but instead it is governed by some type of a wave equation that governs a probability distribution even for a single electron’s motion. Thus the wave–particle duality first observed with photons is actually a fundamental behaviour intrinsic to all quantum particles.

Werner Heisenberg considered the limits of how accurately we can measure properties of an electron or other microscopic particles. He determined that there is a fundamental limit to how accurately one can measure both a particle’s position and its momentum simultaneously. The more accurately we measure the momentum of a particle, the less accurately we can determine its position at that time, and vice versa. This is summed up in what we now call the Heisenberg uncertainty principle: It is fundamentally impossible to determine simultaneously and exactly both the momentum and the position of a particle.

10.4 Quantum-Mechanical Model of the Atom

Macroscopic objects act as particles. Microscopic objects (such as electrons) have properties of both a particle and a wave. Their exact trajectories cannot be determined. The quantum mechanical model of atoms describes the three-dimensional position of the electron in a probabilistic manner according to a mathematical function called a wavefunction, often denoted as ψ. Atomic wavefunctions are also called orbitals. The squared magnitude of the wavefunction describes the distribution of the probability of finding the electron in a particular region in space. Therefore, atomic orbitals describe the areas in an atom where electrons are most likely to be found.

An atomic orbital is characterized by three quantum numbers. The principal quantum number, n, can be any positive integer. The general region for value of energy of the orbital and the average distance of an electron from the nucleus are related to n. Orbitals having the same value of n are said to be in the same shell. The angular momentum quantum number, l, can have any integer value from 0 to n – 1. This quantum number describes the shape or type of the orbital. Orbitals with the same principle quantum number and the same l value belong to the same subshell. The magnetic quantum number, m_l, with 2l + 1 values ranging from –l to +l, describes the orientation of the orbital in space. The forth quantum number is spin quantum number. Each electron has a spin quantum number, m_s, that can be equal to ([latex]\pm \frac{1}{2}[/latex]). No two electrons in the same atom can have the same set of values for all the four quantum numbers. An orbital can be empty or it can contain one or two electrons, but never more than two. If two electrons occupy the same orbital, they must have opposite spins.

In summary, electrons occupy orbitals, which are probability fields or spaces around the nucleus of an atom where an electron is likely to be found. Important criteria was established in defining the modern atomic theory:

1. Atoms have a series of energy levels called principal energy levels, which are designated by whole numbers (n = 1, 2, 3, ….).
2. The energy of the level increases as the value of n increases.
3. Each principal energy level contains one or more types of orbitals, called subshells.
4. The number of subshells present in a given principal energy level equals n.
   1. For example: Principal energy level 4 (n = 4) has 4 subshells including s, p, d and f
5. The n value is always used to label the orbitals of a given principal level and is followed by a letter that indicates the type (shape) of the orbital (For example: 1s, 2p, 3d ….).
6. An orbital can be empty or it can contain one or two electrons, but never more than two. If two electrons occupy the same orbital, they must have opposite spins.
7. The shape of an orbital does not indicate the specific details of electron movement (how it moves in a given orbital). It gives the probability distribution for where an electron is most likely to be found in that orbital.
8. The total number of orbitals in a given shell (principal energy level) is 2n and the maximum number of electrons in each shell (principal energy level) is 2n².

10.5 Atomic Structures of the First 20 Elements and the Periodic Table

The relative energy of the subshells determine the order in which atomic orbitals are filled (1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, and so on). Electron configurations and orbital diagrams can be determined by applying the Pauli exclusion principle (no two electrons can have the same set of four quantum numbers) and Hund’s rule (whenever possible, electrons retain unpaired spins in degenerate orbitals). The orbital filling diagram and the periodic table can be used as tools to help determine the electron filling order when writing electron configurations and orbital diagrams. Full electron configuration or noble gas configurations can be used to represent the number of electrons in a parent atom. For ions, electron configurations and orbital diagrams can also be used to illustrate the electrons in an ion.

Electrons in the outermost orbitals, called valence electrons, are responsible for most of the chemical behaviour of elements. In the periodic table, elements with analogous valence electron configurations usually occur within the same group. There are some exceptions to the predicted filling order, particularly when half-filled or completely filled orbitals can be formed. The periodic table can be divided into three categories based on the orbital in which the last electron to be added is placed: main group elements (s and p orbitals), transition elements (d orbitals), and inner transition elements (f orbitals).

10.6 Atomic Properties and Periodic Table Trends

Electron configurations allow us to understand many periodic trends. Covalent radius increases as we move down a group because the n level (orbital size) increases. Covalent radius mostly decreases as we move left to right across a period because the effective nuclear charge experienced by the electrons increases, and the electrons are pulled in tighter to the nucleus. Anionic radii are larger than the parent atom, while cationic radii are smaller, because the number of valence electrons has changed while the nuclear charge has remained constant. Ionization energy (the energy associated with forming a cation) decreases down a group and mostly increases across a period because it is easier to remove an electron from a larger, higher-energy orbital. Electron affinity (the energy associated with forming an anion) is more favourable (exothermic) when electrons are placed into lower energy orbitals, closer to the nucleus. Therefore, electron affinity becomes increasingly negative as we move left to right across the periodic table and decreases as we move down a group. For both IE and electron affinity data, there are exceptions to the trends when dealing with completely filled or half-filled subshells.

Attribution & References

Except where otherwise noted, this page is adapted by Jackie MacDonald from:

• “Chapter 3” In General Chemistry 1 & 2 by Rice University, a derivative of Chemistry (Open Stax) by Paul Flowers, Klaus Theopold, Richard Langley & William R. Robinson and is licensed under CC BY 4.0. ​Access for free at Chemistry (OpenStax)​ / Key concepts/summaries from sections 3.1-3.5 extracted for reuse here.
• “6.3 Development of Quantum Theory” In Chemistry 2e (Open Stax) by Paul Flowers, Klaus Theopold, Richard Langley & William R. Robinson is licensed under CC BY 4.0. Access for free at Chemistry 2e (Open Stax)
• “Chapter 6 Summary” In Chemistry 2e (Open Stax) by Paul Flowers, Klaus Theopold, Richard Langley & William R. Robinson is licensed under CC BY 4.0. Access for free at Chemistry 2e (Open Stax) . / Adaptations to content and addition of examples and exercises to optimize student comprehension.