5.3: quantum mechanics and the wave nature of matter

the wave nature of matter

• Louis De Broglie theorized that if light can have material properties, matter should exhibit wave properties, developing the slit experiment to create a new model of the atom
• electrons move trough “slits”
  • a particle can only move through one slit at a time
  • a wave can move through multiple slits at a time

the quantum mechanical model of the atom

• electronic structure: the structure of electrons within an atom

• Louis De Broglie, Edward Schrödinger, and Werner Heisenberg were on the front line of the development of quantum mechanics

• quantum mechanics (aka wave mechanics) was a completely new approach to the atomic model

quantum mechanics

• Schrödinger’s equation: Ĥψ = Eψ
  • ψ = wave function
  • E = total energy of the atom
• each solution to Schrödinger’s equation is a probability of where an electron could be found in space
• the wave function is a function of the coordinates x, y, and z
• orbital: a solution to the wave function
  • orbitals are not the same as Bohr orbits
  • 1s orbital: the wave function corresponding to the lowest energy for the hydrogen atom
  • s orbital: a spherical orbital contained by every energy level → volume changes by level but shape does not
  • p orbital: an orbital consisting of two lobes contained by the second energy level and up
  • d orbital: an orbital that generally contains four lobes contained by the third energy level and up
• orbitals are essentially regions of space in which the probability of finding an electron is ≥ 90%
• heavily correlated to nuclear charge and ionization energy
  • nuclear charge is determined by the size of ions and properties of the atom
  • ionization energy describes the minimum amount of energy required to remove an electron from the ground state of a gaseous atom or ion, and requires more energy to remove each successive electron from the atom
  • ground state: the lowest-energy state of an atom
  • excited state: higher-energy states of an atom (n ≥ 2)

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