Section Summary

Section Summary

12.1 Quantization of Energy

  • The first indication that energy is sometimes quantized came from blackbody radiation, which is the emission of EM radiation by an object with an emissivity of 1.
  • Planck recognized that the energy levels of the emitting atoms and molecules were quantized, with only the allowed values of E=n+12hf,E=n+12hf, size 12{E= left (n+ { { size 8{1} } over { size 8{2} } } right ) ital "hf"} {} where nn size 12{n} {} is any non-negative integer (0, 1, 2, 3, …).
  • hh size 12{h} {} is Planck’s constant, whose value is h=6.626× 10–34 J s.h=6.626× 10–34 J s. size 12{h = 6 "." "626" times " 10" rSup { size 8{"–34"} } " J " cdot " s"} {}
  • Thus, the oscillatory absorption and emission energies of atoms and molecules in a blackbody could increase or decrease only in steps of size ΔE=hfΔE=hf size 12{ΔE = ital "hf"} {} where ff size 12{f} {} is the frequency of the oscillatory nature of the absorption and emission of EM radiation.
  • Another indication of energy levels being quantized in atoms and molecules comes from the lines in atomic spectra, which are the EM emissions of individual atoms and molecules.

12.2 The Photoelectric Effect

  • The photoelectric effect is the process in which EM radiation ejects electrons from a material.
  • Einstein proposed photons to be quanta of EM radiation having energy E=hfE=hf size 12{E = ital "hf"} {}, where ff size 12{f} {} is the frequency of the radiation.
  • All EM radiation is composed of photons. As Einstein explained, all characteristics of the photoelectric effect are due to the interaction of individual photons with individual electrons.
  • The maximum kinetic energy KEeKEe size 12{"KE" rSub { size 8{e} } } {} of ejected electrons (photoelectrons) is given by KE e=hf – BEKE e=hf – BE size 12{"KE "= ital "hf"" – BE"} {}, where hfhf size 12{ ital "hf"} {} is the photon energy and BE is the binding energy (or work function) of the electron to the particular material.

12.3 Photon Energies and the Electromagnetic Spectrum

  • Photon energy is responsible for many characteristics of EM radiation, being particularly noticeable at high frequencies.
  • Photons have both wave and particle characteristics.

12.4 Photon Momentum

  • Photons have momentum, given by p=hλp=hλ size 12{p = { {h} over {λ} } } {}, where λλ size 12{λ} {} is the photon wavelength.
  • Photon energy and momentum are related by p=Ecp=Ec size 12{p = { {E} over {c} } } {}, where E=hf=hc/λE=hf=hc/λ size 12{E = ital "hf"= ital "hc"/λ } {} for a photon.

12.5 The Wave Nature of Matter

  • Particles of matter also have a wavelength, called the de Broglie wavelength, given by λ=hpλ=hp size 12{λ = { {h} over {p} } } {}, where pp size 12{p} {} is momentum.
  • Matter is found to have the same interference characteristics as any other wave.

12.6 Probability: The Heisenberg Uncertainty Principle

  • Matter is found to have the same interference characteristics as any other wave.
  • There is now a probability distribution for the location of a particle rather than a definite position.
  • Another consequence of the wave character of all particles is the Heisenberg uncertainty principle, which limits the precision with which certain physical quantities can be known simultaneously. For position and momentum, the uncertainty principle is ΔxΔphΔxΔph size 12{ΔxΔp >= { {h} over {4π} } } {}, where ΔxΔx size 12{Δx} {} is the uncertainty in position and ΔpΔp size 12{Δp} {} is the uncertainty in momentum.
  • For energy and time, the uncertainty principle is ΔEΔthΔEΔth size 12{ΔEΔt >= { {h} over {4π} } } {} where ΔEΔE size 12{ΔE} {} is the uncertainty in energy and ΔtΔt size 12{Δt} {} is the uncertainty in time.
  • These small limits are fundamentally important on the quantum-mechanical scale.

12.7 The Particle-Wave Duality Reviewed

  • The particle-wave duality refers to the fact that all particles—those with mass and those without mass—have wave characteristics.
  • This is a further connection between mass and energy.