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Chapter 28: Quantum Physics

28.A: Quantum Theory

Quantum Theory
The theory that describes the behavior of matter and energy at the atomic and subatomic levels.
Blackbody Radiation
The energy emitted by a blackbody, which follows the Stefan-Boltzmann law: S = σT4.
Wien’s Displacement Law
The law stating that the wavelength at which a blackbody emits most of its energy is inversely proportional to its temperature: λmaxT = 2.8978 × 10–3 m·K.
Planck Radiation Law
A nonclassical equation proposed by Max Planck to describe blackbody radiation: I(λ, T) = (2πc2h/λ5) · (1/(ehc/λkBT – 1)).
Photoelectric Effect
The phenomenon in which electrons are dislodged from a metal by light falling on it.
Photon
A packet of light with a distinct amount of energy, given by E = hf.

Blackbody Radiation

  • Classical physics could not explain blackbody radiation.
  • The rate of energy emitted by a blackbody follows the Stefan-Boltzmann law: S = σT4.
  • A blackbody emits a continuous spectrum of radiation that includes all wavelengths.

Wien’s Displacement Law

  • At higher temperatures, a blackbody emits more radiation at shorter wavelengths with higher frequencies.
  • Wien’s displacement law: λmaxT = 2.8978 × 10–3 m·K.

Planck and Quantized Energy

  • Max Planck proposed the Planck radiation law to explain blackbody radiation.
  • Planck assumed that energy is emitted in discrete values (quanta) proportional to their radiation frequency: E = nhf.

Photoelectric Effect

  • Classical theory predicted that any frequency of light could liberate electrons if it was intense enough.
  • Einstein proposed that light travels in packets called photons with energy E = hf.
  • To eject an electron, the energy of the photon must be greater than the work function (φ) of the metal.
  • The energy of the ejected electron is given by Ke = hf – φ.

Example: Finding the Wavelength

What is the most intense wavelength of light radiated by a blackbody at 7.15 × 103 K?

T = 7.15 × 103 K

λmaxT = 2.8978 × 10–3 m·K

λmax = 2.8978 × 10–3 m·K / T

λmax = 2.8978 × 10–3 m·K / 7.15 × 103 K

λmax = 4.05 × 10–7 m = 405 nm

Example: Finding the Temperature

A red giant star emits a spectrum of light with a maximum intensity at a wavelength of 645 nm. What is the temperature of the star’s photosphere?

λmax = 645 nm = 6.45 × 10–7 m

λmaxT = 2.8978 × 10–3 m·K

T = 2.8978 × 10–3 m·K / λmax

T = 2.8978 × 10–3 m·K / 6.45 × 10–7 m

T = 4.49 × 103 K

Questions for Students

  1. Define quantum theory and its significance.
  2. Explain the concept of blackbody radiation and the Stefan-Boltzmann law.
  3. Describe Wien’s displacement law and provide an example calculation.
  4. What is the Planck radiation law and how does it differ from classical physics?
  5. Describe the photoelectric effect and the role of photons in this phenomenon.