| <Previous | January | February | March | April | May | Next> |
Lecture 13: Beyond Classical Physics: Photons and Wave-Particle Duality
March 6, 2025
Reading Assignment
- Read: Supplementary Reading Ch 2
Objectives
- (Continuing objective) Describe applications of the concepts of induction, waves, and light to everyday “real life” situations.
- Describe the failures of classical physics in resolving the ultraviolet catastrophe, the stability of atoms, and the atomic spectra.
- Calculate any of these photon properties, given one of the others: energy, momentum, frequency, and wavelength. Solve problems relating light intensity, the number of photons per second, the energy per photon, and the frequency or wavelength of the associated wave.
- Explain how photons resolve the ultraviolet catastrophe, and calculate the number of photons in modes of a cavity in thermal equilibrium at temperature \(T\).
- Describe how light interacts with matter in the form of photons, and how this explains the photoelectric effect, ionizing radiation, and radiation-induced chemical reactions. Relate the photon energy, binding energy, and final kinetic energies of any freed electrons.
- Calculate the de Broglie wavelength for photons and for non-relativistic particles. Conversely, calculate the momentum or kinetic energy of a non-relativistic particle from the de Broglie wavelength.
Homework
- Friday's Assigned Problems:
Supp CH 2: 1, 3, 4, 5, 6, 7, 9, 10, 13, 14
Notes: For Supp CH 2 #5, answer in both eV/c and kg$\cdot$m/s.
- Monday's Hand-In Problems: A47, A105; CH 32: 18, 48; Supp CH 1: 8; Supp CH 2: 2, 8, 11, 12, 15
Lecture Materials
- Click here for the Lecture overheads. Answers: CT1 - 2; CT2 - 6; CT3 - 6
- Video of the electron double slit experiment.
- PheT simulation of the photoelectric effect (requires java).
Videos of example problems
To see the problem statement, click on the link below. To play the video example, click on the underlined words "Video Demonstration" near the top of the page with the problem statement.- Example with electron microscope -- de Broglie's relation and diffraction limits
- Example of calculating how many photons are in a laser beam.
- Example of photons breaking apart something (in this case, breaking apart a molecule of water, similar to photoelectric effect problems.
- Example of using the Equipartition theorem to determine how many photons should be in a box, similar to the UV Catastrophe probelems.
Pre-Class Entertainment
- Music from Ghana, in recognition of the Independence Day of Ghana.
Assigned Problems Guide
- Supp 2-1: (a) quick, using the expression for $E_\text{ph}$. (b) longer. Use the de Broglie relation to get momentum $p$ from $\lambda$, and then use $K = \frac{1}{2} mv^2$. Probably easiest to use SI units.
- Supp 2-3: quick. The cutoff frequency happens when the photon energy is just exactly equal to the binding energy (if the photons have more energy, electrons can come off, if they have less, the electrons can't come off).
- Supp 2-4: (a) a result of single-slit interference is that we need wavelengths at least as small as the object we're looking at to be able to resolve them. So that's it for part (a). (b) Use this wavelength and the de Broglie relation to get an electron energy.
- Supp 2-5: medium quick. The de Broglie relation uses a wavelength, so turn the frequency into a wavelegth.
- Supp 2-6: medium quick. Classic photoelectric effect problem using Eq. (2.9)
- Supp 2-7: medium quick. Use the photon energy expression.
- Supp 2-9: medium. Use your standing wave analysis skills to find the wavelength, and then turn it into a frequency.
- Supp 2-10: medium long. This is a symbols problem, not one with numbers. Like in lecture: use the photon frequency to find the photon energy, and then with $\frac{1}{2}k_BT$ as the energy, find the number of photons and interpret your answer.
- Supp 2-13: medium. This is a lot like the photoelectric effect. The electron is bound to a hydrogen atom by the binding energy $13.6\,\text{eV}$.
- Supp 2-14: medium quick. The reason this experiment is so mind blowing is that in one experiment electrons act like both waves and particles.