Electronic Structure and Waves

• The chapter is about electronic structure, the way electrons are arranged, and their energy levels.
• Extremely small particles possess wave-like properties.

Waves

• Electromagnetic radiation moves as waves through space at the speed of light.
• Wavelength (λ) refers to the distance between corresponding points on adjacent waves.
• Frequency (v) refers to the number of waves passing a given point per unit of time.
• Longer wavelengths mean smaller frequencies, if the velocity is the same.
• All electromagnetic radiation travels at the same velocity with the speed of light being 3.00 × 108 m/s and the equation being c = λν.
• There are many types of electromagnetic radiation, that have different wavelengths and energies.

Electronic Properties

• Three observed properties associated with how atoms interact with electromagnetic radiation are:
  • The emission of light from hot objects (blackbody radiation).
  • The emission of electrons from metal surfaces on which light is shone (the photoelectric effect).
  • Emission of light from electronically excited gas atoms (emission spectra).

Nature of Energy

• The wave nature of light does not explain how an object glows when its temperature increases.
• Max Planck explained that energy comes in packets called quanta.

Photoelectric effect

• Einstein used quanta to explain the photoelectric effect.
• Each metal has a different energy at which it ejects electrons; at lower energy, electrons are not emitted.
• Energy is proportional to frequency: E = hv, where h is Planck's constant, 6.626 × 10-34 J.s.

Atomic Emissions

• Emission spectra observed from energy emitted by atoms and molecules in the early twentieth century.
• For atoms and molecules, continuous spectrums ("rainbows") are not observed like from a white light source.
• Only a line spectrum of discrete wavelengths is observed. Each element has a unique line spectrum.
• Johann Balmer (1885) discovered a simple formula relating the four lines to integers.
• Johannes Rydberg advanced this formula; RH is called the Rydberg constant.
• Neils Bohr explained why this mathematical relationship works.

Bohr Model

• Niels Bohr adopted Planck's assumption and explained these phenomena:
  • Only orbits of certain radii, corresponding to specific energies, are permitted for the electron in a hydrogen atom.
  • An electron in a permitted orbit is in an "allowed" energy state and does not radiate energy and spiral into the nucleus.
  • Energy is emitted or absorbed by the electron only as the electron changes from one energy state to another; absorbed as a photon that has energy E = hv.
• Electrons in the lowest energy state are in the ground state.
• If any energy is higher than ground state then is an excited state.
• Transitions from one energy level to another can be calculated since each orbit has a specific value compared to RH.
• A positive ΔΕ means energy is absorbed which occurs if n₁ > n₁.
• A negative ΔΕ means energy is released which happens if n₁ < n₁.
• The Bohr Model:
• Only works for hydrogen.
• Classical physics would result in an electron falling into the positively charged nucleus, which is based on pure assumption.
• Circular motion is not wave-like in nature.
• Bohr Model's important ideas in the current atomic model:
  • Electrons exist only in certain discrete energy levels, described by quantum numbers.
  • Energy is involved in the transition of an electron from one level to another.

Wave Nature of Matter

• Louis de Broglie theorized with if light can have material properties, matter should exhibit wave properties.
• He demonstrated the relationship between mass and wavelength was λ = h/mv.
• Heisenberg showed that the more precisely the momentum of a particle is known, the less precisely its position is known: (∆x) (Δmv) ≥ h/4π.

Quantum Mechanics

• Erwin Schrödinger developed a mathematical treatment that incorporates both the wave and particle nature of matter.
• The solution of Schrödinger's wave equation for hydrogen yields wave functions for the electron.
• The square of the wave function gives the electron density, or probability of where an electron is likely to be at any given time.
• Solving the wave equation gives a set of wave functions, or orbitals, and their corresponding energies.
• Each orbital describes a spatial distribution of electron density.
• An orbital is described by a set of three quantum numbers.

Quantum Numbers

• The principal quantum number, n, describes the energy level on which the orbital resides.
• The values of n are integers ≥ 1, corresponding to the values in the Bohr model.
• The quantum number defines the shape of the orbital.
• Allowed values of / are integers ranging from 0 to n - 1.
• Letter designate the different values of /.
• The magnetic quantum number describes the three-dimensional orientation of the orbital.
  • Allowed values of m, are integers ranging from -/ to / including 0: -I ≤ m₁ ≤ 1
  • Consequently:on any given energy level, there can be up to 1 s orbital, 3 p orbitals, 5 d orbitals, and 7 f orbitals.
• Orbitals with the same value of n form an electron shell.
• Different orbital types within a shell are subshells.
• The value of / for s orbitals is 0; they are spherical in shape; and the radius of the sphere increases with the value of n.
• For an ns orbital, the number of peaks is n.
• For an ns orbital, the number of nodes (where there is zero probability of finding an electron) is n - 1.
• As n increases, the electron density is more spread out and there is a greater probability of finding an electron further from the nucleus.
• The value of / for p orbitals is 1, and they have two lobes with a node between them.
• The value of / for a d orbital is 2.
• Four of the five d orbitals have four lobes; the other resembles a p orbital with a doughnut around the center.
• F orbitals: Very complicated shapes and seven equivalent orbitals in a sublevel with /= 3.
• For a one-electron hydrogen atom, orbitals on the same energy level have the same energy.
• The chemists call these degenerate orbitals.
• As the number of electrons increases, so does the repulsion between them.
• Therefore, in atoms with more than one electron, not all orbitals on the same energy level are degenerate.
• Orbital sets in the same sublevel are still degenerate.
• Energy levels start to overlap in energy (e.g., 4s is lower in energy than 3d.)
• In the 1920s, the spin quantum number (ms) was discovered to mean that two electrons in the same orbital do not have exactly the same energy.
• The spin of an electron describes its magnetic field, which affects its energy; has only two allowed values, +1/2 and -1/2.
• Pauli Exclusion Principle: No two electrons in the same atom can have the same set of four quantum numbers.
• No two electrons in the same atom can have the exact same energy.
• Every electron in an atom must differ by at least one of the four quantum number values: n, I, m₁, and ms.
• The way electrons are distributed in an atom is it its electron configuration.
• The most stable organization is the lowest possible energy, called the ground state.
• Each component consists of a number denoting the energy level, a letter denoting the type of orbital, and a superscript denoting the number of electrons in those orbitals.
• Diagrams are used to represent one orbital and the direction of the arrow that represents the electrons and the relative spin of the electron.
• Hund's Rule: For a set of orbitals in the same sublevel, there must be one electron in each orbital before pairing and the electrons have the same spin, as much as possible.

Electron Configurations

• Elements in the same group of the periodic table have the same number of electrons in the outermost shell, which are the valence electrons.
• The filled inner shell electrons called core electrons include completely filled d or f sublevels.
• A shortened version of electron configuration is written with brackets around a noble gas symbol and listing only valence electrons.
• The Argon ends period 3. Its electron configuration is 1s22s22p63s23p6.
• Potassium might be expected to have electrons in 3d but 4s fills next.
• The transition metals follow the filling of 4s by filling 3d in the 4th period.
• The elements which fill the f orbitals have special names as a portion of a period.
• The lanthanide elements (atomic numbers 57 to 70) have electrons entering the 4f sublevel.
• The actinide elements (including Uranium, at. no. 92, and Plutonium, at. no. 94) have electrons entering the 5f sublevel
• Orbitals are filled in increasing order of energy.
• Different blocks on the periodic table correspond to different types of orbitals: s = blue, p = pink (s and p are representative elements); d = orange (transition elements); f = tan (lanthanides and actinides, or inner transition elements).
• The s and p blocks are called the main-group elements.
• The periodic table is followed directly when determining the electron configuration for MOST elements.
• Some irregularities occur when there are enough electrons to half-fill s and d orbitals on a given row.
• For instance, the electron configuration is [Ar] 4s1 3d5 rather than the expected [Ar] 4s² 3d4 for chromium.
• This occurs because the 4s and 3d orbitals are very close in energy, and the anomalies occur in f-block atoms with f and d orbitals, as well.