Chapter 7 - Quantum Theory and the Electronic Structure of Atoms

7.1 - From Classical Physics to Quantum Theory

• We must first grasp the nature of waves to comprehend Planck's quantum theory.
  • A wave is a vibrating disturbance via which energy is conveyed.
• The distance between similar spots on successive waves is measured in wavelength.
• The number of waves that travel through a specific place in one second is known as the frequency v (nu).
  • The vertical distance between a wave's midline and its peak or trough is called amplitude.
• An electromagnetic wave has an electric field component and a magnetic field component, according to Maxwell's theory.
  • The emission and transfer of energy in the form of electromagnetic waves are known as electromagnetic radiation.
• The smallest amount of energy that may be emitted in the form of electromagnetic radiation was given the name quantum by Planck.

7.2 - The Photoelectric Effect

• The photoelectric effect is a process in which electrons are ejected from the surface of certain metals when they are exposed to light with a minimum frequency, known as the threshold frequency.
• The lightwave theory is a hypothesis that describes how light travels through space.
• Einstein, on the other hand, made a remarkable assumption.
  • He proposed that a light beam is a stream of particles. Photons are the new name for these light particles.

7.3 - Bohr’s Theory of the Hydrogen Atom

• Physicists have looked into the properties of emission spectra, or the continuous or line spectra of radiation released by substances.

  • Energizing a sample of the material with thermal energy or another source of energy can reveal a substance's emission spectrum.
  • Light emission at specific wavelengths is represented by line spectra.

  

• When n = 1, which corresponds to the highest stable energy state, the most negative value is reached.

  • This is referred to as the ground state or ground level, and it relates to a system's lowest energy state.

• For n = 2, 3, Each of these levels is referred to as an aroused state or excited level since it is more energetic than the ground state.

7.4 - The Dual Nature of the Electron

• An electron bound to the nucleus, according to de Broglie, acts as a standing wave.
• Some spots on the string, known as nodes, do not move at all, implying that the wave amplitude at these points is 0.

7.5 - Quantum Mechanics

• Werner Heisenberg developed the Heisenberg uncertainty principle, which states: It is impossible to know the momentum p and the position of a particle with certainty at the same time.
  • The wave function of an electron in an atom is known as an atomic orbital.

7.6 - Quantum Numbers

• Three quantum numbers are necessary for quantum mechanics to represent the distribution of electrons in hydrogen and other atoms.
  • These figures are derived from the Schrödinger equation's mathematical solution for the hydrogen atom.
  • The main quantum number, the angular momentum quantum number, and the magnetic quantum number are the three types of quantum numbers.
  • These quantum numbers will be used to characterize atomic orbitals as well as to identify electrons that live within them.

7.7 - Atomic Orbitals

• The p orbitals begin with the primary quantum number n = 2 as should be obvious.
• There is only a 1s orbital if n = 1. The angular momentum quantum number l can only take the value zero if n = 1.
• When l = 2, there are five different ml values, each of which corresponds to a different d orbital. For a d orbital, the lowest value of n is 3.

7.8 - Electron Configuration

• To understand electronic behavior in many-electron atoms, however, we must first understand the atom's electron configuration, or how the electrons are distributed throughout the many atomic orbitals.
• The Pauli exclusion principle is used to determine electron configurations in many-electron atoms.
  • No two electrons in an atom may have the same set of four quantum numbers, according to this concept.
  • The term "paramagnetic" refers to materials that have net unpaired spins and are attracted to a magnet.
  • Diamagnetic materials have no net unpaired spins and are somewhat repelled by magnets.

7.9 - The Building-Up Principle

• According to the Aufbau principle, as protons are added one by one to the nucleus to form the elements, electrons are similarly added to the atomic orbitals.
• Except for hydrogen and helium, the electron configurations of all elements are represented by a noble gas core
  • which displays in brackets the noble gas element that most nearly precedes the element in question, followed by the symbol for the highest filled subshells in the outermost shells.
• Transition metals either have partially full d subshells or quickly produce cations with partially filled d subshells.