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Lecture 11a

Lecture 11a. Photon Theory of Light & Wave Particle Duality. Chapter 37 Early Quantum Theory and Models of the Atom. Units of Chapter 37. Photon Theory of Light and the Photoelectric Effect Energy, Mass, and Momentum of a Photon Wave – Particle Duality Wave Nature of Matter

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Lecture 11a

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  1. Lecture 11a Photon Theory of Light & Wave Particle Duality

  2. Chapter 37Early Quantum Theory and Models of the Atom

  3. Units of Chapter 37 • Photon Theory of Light and the Photoelectric • Effect • Energy, Mass, and Momentum of a Photon • Wave–Particle Duality • Wave Nature of Matter • Early Models of the Atom • Atomic Spectra: Key to the Structure of the Atom • de Broglie’s Hypothesis Applied to Atoms

  4. 37-2 Photon Theory of Light and the Photoelectric Effect . Einstein suggested that, given the success of Planck’s theory, light must be emitted in small energy packets: These tiny packets, or particles, are called photons.

  5. 37-2 Photon Theory of Light and the Photoelectric Effect The photoelectric effect: if light strikes a metal, electrons are emitted. The effect does not occur if the frequency of the light is too low; the kinetic energy of the electrons increases with frequency.

  6. 37-2 Photon Theory of Light and the Photoelectric Effect • If light is a wave, theory predicts: • Number of electrons and their energy should increase with intensity. • Frequency would not matter.

  7. 37-2 Photon Theory of Light and the Photoelectric Effect • If light is particles, theory predicts: • Increasing intensity increases number of electrons but not energy. • Above a minimum energy required to break atomic bond, kinetic energy will increase linearly with frequency. (Kmax = hf – Wo) • There is a cutoff frequency (fo) below which no electrons will be emitted, regardless of intensity. (hfo = Wo)

  8. 37-2 Photon Theory of Light and the Photoelectric Effect The particle theory assumes that an electron absorbs a single photon. Plotting the kinetic energy vs. frequency: This shows clear agreement with the photon theory, and not with wave theory.

  9. 37-2 Photon Theory of Light and the Photoelectric Effect Example 37-3: Photon energy. Calculate the energy of a photon of blue light, λ = 450 nm in air (or vacuum).

  10. 37-2 Photon Theory of Light and the Photoelectric Effect Example 37-5: Photoelectron speed and energy. What are the kinetic energy and the speed of an electron ejected from a sodium surface whose work function is W0 = 2.28 eV when illuminated by light of wavelength (a) 410 nm and (b) 550 nm?

  11. 37-3 Energy, Mass, and Momentum of a Photon Clearly, a photon must travel at the speed of light. Looking at the relativistic equation for momentum, it is clear that this can only happen if its rest mass is zero. We already know that the energy is hf; we can put this in the relativistic energy-momentum relation and find the momentum:

  12. 37-6 Wave-Particle Duality; the Principle of Complementarity We have phenomena such as diffraction and interference that show that light is a wave, and phenomena such as the photoelectric effect and the Compton effect that show that it is a particle. Which is it? This question has no answer; we must accept the dual wave–particle nature of light.

  13. 37-6 Wave–Particle Duality; the Principle of Complementarity The principle of complementarity states that both the wave and particle aspects of light are fundamental to its nature. Indeed, waves and particles are just our interpretations of how light behaves.

  14. 37-7 Wave Nature of Matter . Just as light sometimes behaves like a particle, matter sometimes behaves like a wave. The wavelength of a particle of matter is This wavelength is extraordinarily small.

  15. 37-7 Wave Nature of Matter Example 37-10: Wavelength of a ball. Calculate the de Broglie wavelength of a 0.20-kg ball moving with a speed of 15 m/s.

  16. 37-7 Wave Nature of Matter Example 37-11: Wavelength of an electron. Determine the wavelength of an electron that has been accelerated through a potential difference of 100 V.

  17. 37-7 Wave Nature of Matter The wave nature of matter becomes more important for very light particles such as the electron. Electron wavelengths can easily be on the order of 10-10 m; electrons can be diffracted by crystals just as X-rays can.

  18. Summary of Chapter 37 . • Light can be considered to consist of photons, each of energy • Photoelectric effect: incident photons knock electrons out of material.

  19. Summary of Chapter 37 . • Wave–particle duality – both light and matter have both wave and particle properties. • Wavelength of an object: • Principle of complementarity: both wave and particle properties are necessary for complete understanding.

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