quantization

Examples of quantization in the following topics:

• Wave Nature of Matter Causes Quantization

  • The wave nature of matter is responsible for the quantization of energy levels in bound systems.
  • This is the exact mechanism that causes quantization in atoms.
  • The wave nature of matter is responsible for the quantization of energy levels in bound systems.
  • The angular momentum is $L=m_e v r$, therefore we obtain the quantization of angular momentum:
  • Explain relationship between the wave nature of matter and the quantization of energy levels in bound systems

• Basic Assumptions of the Bohr Model

  • Bohr explained hydrogen's spectrum successfully by adopting a quantization condition and by introducing the Planck constant in his model.
  • We have seen that Planck adopted a new condition of energy quantization to explain the black body radiation, where he introduced the Planck constant $h$ for the first time.
  • Soon after, Einstein resorted to this new concept of energy quantization and used the Planck constant again to explain the photoelectric effects, in which he assumed that electromagnetic radiation interact with matter as particles (later named "photons").
  • Here, Bohr explained the atomic hydrogen spectrum successfully for the first time by adopting a quantization condition and by introducing the Planck constant in his atomic model.
  • Over the period of radical development in the early 20th century, physicists began to realize that it was essential to introduce the notion of "quantization" to explain microscopic worlds.

• Bohr Orbits

  • These "Bohr orbits" have a very important feature of quantization as shown in the following.
  • Assuming circular orbits, Bohr proposed that the angular momentum $L$ of an electron in its orbit is quantized, that is, has only specific, discrete values.
  • Quantization says that this value of $mvr$ can only have discrete values.
  • At the time, Bohr himself did not know why angular momentum should be quantized, but using this assumption he was able to calculate the energies in the hydrogen spectrum, something no one else had done at the time.

• de Broglie and the Bohr Model

  • By assuming that the electron is described by a wave and a whole number of wavelengths must fit, we derive Bohr's quantization assumption.
  • Not all orbits produce constructive interference and thus only certain orbits are allowed (i.e., the orbits are quantized).
  • Rearranging terms, and noting that $L=mvr$ for a circular orbit, we obtain the quantization of angular momentum as the condition for allowed orbits:
  • Bohr's model of electrons traveling in quantized orbits was extended into a more accurate model of electron motion.

• Energy and Momentum

  • Planck theorized that "black bodies" (thermal radiators) and other forms of electromagnetic radiation existed not as spectra, but in discrete, "quantized" form.
  • Energy of a wave is therefore "quantized. "

• Hydrogen Spectra

  • Atomic and molecular emission and absorption spectra have been known for over a century to be discrete (or quantized).
  • Following Einstein's proposal of photons with quantized energies directly proportional to their wavelengths, it became even more evident that electrons in atoms can exist only in discrete orbits.

• General Rules for Assigning Electrons to Atomic Orbitals

  • This separating of electrons into energy units is called quantization of energy because there are only certain quantities of energy that an electron can have in an atom.

• Energy, Mass, and Momentum of Photon

  • Max Planck explained black body radiation using semiclassical models, in which light is still described by Maxwell's equations, but the material objects that emit and absorb light, do so in amounts of energy that are quantized.

• Quantum-Mechanical View of Atoms

  • In 1913, physicist Niels Bohr suggested that the electrons were confined into clearly defined, quantized orbits, and could jump between these, but could not freely spiral inward or outward in intermediate states.

• Particle-Wave Duality

  • Black body radiation: In 1901, to explain the observed spectrum of light emitted by a glowing object, Max Planck assumed that the energy of the radiation in the cavity was quantized, contradicting the established belief that electromagnetic radiation is a wave.