1. Unit 12: Part 2 Quantum Physics

2. Overview Quantization: Planck’s Hypothesis Quanta of Light: Photons and the Photoelectric Effect Quantum “Particles”: The Compton Effect The Bohr Theory of the Hydrogen Atom A Quantum Success: The Laser

3. Quantization: Planck’s Hypothesis An ideal blackbody absorbs all incoming radiation and re-emits it in a spectrum that depends only on temperature.

4. Quantization: Planck’s Hypothesis The peak wavelength and total power increase with temperature. However, classical theory does not predict this result; instead, it predicts a phenomenon referred to as the “ultraviolet catastrophe.”

5. Quantization: Planck’s Hypothesis Why a catastrophe? The classical theory predicts that the intensity of radiation increases without limit at shorter and shorter wavelengths. This requires an infinite amount of energy and is obviously wrong.

6. Quantization: Planck’s Hypothesis Planck realized that the ultraviolet catastrophe goes away if we assume that the possible values of the energy of electromagnetic radiation are not continuous, but rather come in little “packets,” whose energies are given by: The constant h is called Planck’s constant:

7. Quantization: Planck’s Hypothesis Planck was able to reproduce the correct frequency spectrum using this assumption, but he did not know quite what to make of it.

8. Quanta of Light: Photons and the Photoelectric Effect Einstein proposed that not only must the energy of thermal radiators in a hot substance be quantized, the radiation they emit must be quantized as well. He called these quanta “photons.” Their energy depends on the frequency of the light:

9. Quanta of Light: Photons and the Photoelectric Effect Some metallic materials are photosensitive— they emit electrons when light shines on them. The current produced by these electrons can be measured, as can their kinetic energy.

10. Quanta of Light: Photons and the Photoelectric Effect For a given material and wavelength, increasing the intensity of light increases the current; increasing the voltage does not. The stopping voltage, V 0, indicates the kinetic energy of the emitted electrons:

11. Quanta of Light: Photons and the Photoelectric Effect The maximum kinetic energy increases linearly with the frequency; below a cutoff frequency, characteristic of each material, no electrons will be emitted no matter how intense the light. The wave theory of light cannot explain this; only the photon theory can.

12. Quanta of Light: Photons and the Photoelectric Effect

13. The minimum amount of work required to free an electron is called the work function:

14. Quanta of Light: Photons and the Photoelectric Effect Conservation of energy in the photoelectric effect

15. Quanta of Light: Photons and the Photoelectric Effect The cutoff frequency, below which no electrons will be emitted no matter how intense the light, is given by:

16. Quanta of Light: Photons and the Photoelectric Effect One application of the photoelectric effect: the “electric eye”

17. 3 Quantum “Particles”: The Compton Effect Compton scattering occurs when an X-ray scatters from a material. The scattered ray has a longer wavelength that depends on the scattering angle but not on the material.

18. Quantum “Particles”: The Compton Effect The photon acts as a particle, transferring some of its energy to the electron. Its own energy is less, so the wavelength is longer. is called the Compton wavelength of the electron:

19. The Bohr Theory of the Hydrogen Atom Atoms are observed to emit and absorb photons of particular wavelengths; each type of atom has its own set of wavelengths. An empirical formula was found that gives the four visible spectral lines of hydrogen: R, the Rydberg constant, has a value of 1.097 × 10 –2 nm –1.

20. The Bohr Theory of the Hydrogen Atom In the Bohr model, the electron is in orbit around the nucleus, with the centripetal force being provided by the Coulomb force. This gives possible electron energies of

21. The Bohr Theory of the Hydrogen Atom In order to explain atomic spectra, Bohr then made an assumption about quantization: Bohr assumed that the angular momentum of the electron was quantized and could have only discrete values that were integral multiples of h/2π, where h is Planck’s constant.

22. The Bohr Theory of the Hydrogen Atom We can use this to find the quantized radius and energy:

23. The Bohr Theory of the Hydrogen Atom This leads to an allowed set of orbits and energy levels.

24. The Bohr Theory of the Hydrogen Atom Photons are emitted or absorbed when an electron makes a transition between energy levels. As the energy levels are quantized, the photon wavelengths can only take on certain values.

25. The Bohr Theory of the Hydrogen Atom The energy required for a transition between level n i and level n f is:

26. The Bohr Theory of the Hydrogen Atom This gives the observed series of spectral lines.

27. A Quantum Success: The Laser Some atoms have what are called metastable states: they are excited states, but with relatively long lifetimes. They are responsible for phosphorescence—things that glow in the dark. If an electron is in a metastable state, it may return to a lower state spontaneously; it may also return to a lower state after absorbing a photon of the correct energy. This is called stimulated emission.

28. A Quantum Success: The Laser It is possible to get a material in a condition where there are more electrons in a metastable state than in lower states—this is called a population inversion. In this case, there may be more stimulated emission than absorption.

29. A Quantum Success: The Laser In a helium–neon laser, the helium is first “pumped” into an excited state by collisions with electrons. Then the helium collides with neon atoms, exciting them into the metastable state. A spontaneous emission then excites subsequent stimulated emissions.

30. A Quantum Success: The Laser To make an actual laser, the helium and neon are placed in a tube with a fully reflecting mirror on one end and a partially reflecting mirror on the other.

31. A Quantum Success: The Laser Light from a laser is coherent and monochromatic; this makes it very useful in a number of applications.

32. A Quantum Success: The Laser Holograms use coherent laser light to produce a three-dimensional image.

33. Review Thermal radiation depends only on the temperature of the radiating body. The peak wavelength increases with temperature. Classical theory could not predict the thermal radiation spectrum; Planck did so by assuming that the energies of the atoms in the material were quantized. Einstein explained the photoelectric effect by assuming that light energy is also quantized:

34. Review Light scattering off atomic electrons is called the Compton effect. The scattered light has a longer wavelength: Bohr model of the hydrogen atom: electron is in orbit around proton, centripetal force is provided by Coulomb force. Only certain energy levels are allowed. Electrons making transitions between energy levels emit radiation of particular wavelengths.

35. Review A metastable state is an energy state with a relatively long lifetime. Stimulated emission may occur from a metastable state. A laser uses stimulated emission to produce a beam of monochromatic, coherent light.