Chapter 28: Quantum Physics Key Terms: Photoelectric effect Photons de Broglie wavelength Energy level diagram Wave-particle duality Don t Copy This Except for relativity, everything we have studied up to this point was known by 1900. A spate of discoveries right around 1900 showed that classical physics was incomplete. Experiments found that light sometimes refuses to act as a wave, but electrons sometimes do. These discoveries led to a radical new theory of light and matter called quantum physics. Quantum Physics The rules of quantum physics apply at the scale of atoms and electrons. 1
Photoelectric Effect Experimental evidence that light is made up photons. The photoelectric effect is the emission of electrons (often called photoelectrons) from a substance due to light striking its surface. Characteristics of the Photoelectric Effect 1) There exists a threshold frequency below which there is no photoelectron emission. 2) The emission of the photoelectron is instantaneous. 3) The photoelectrons have a velocity distribution from zero to a certain maximum. 4) The maximum kinetic energy of the photoelectron is dependent upon the frequency of incident radiation and independent of the intensity of the incident radiation. 5) The number of photoelectrons (hence the current) is proportional to the intensity of the radiation. 2
Work Function The minimum amount of energy needed to free an electron from a metal. The maximum KE an electron can leave a metal with is equal to the difference between the energy of the incident photon and the work function. Stopping Potential Don t Copy If the anode is positive in a photoelectric effect experiment, it attracts all electrons and a further increase in potential difference will not increase the current. If the anode is negative, it repels the electrons. However, an electron with sufficient kinetic energy can still reach the anode. As the potential difference is increased, the anode becomes more negative and is able to repel more energetic electrons. Stopping Potential At the stopping potential, all electrons are repelled away from the anode and current ceases to flow. The stopping potential tells us the maximum kinetic energy of the electrons. 3
Einstein s Photoelectric Explanation Electromagnetic radiation is quantized. Light arrives in small bundles or packets of energy. Each quantum of light, now known as a photon has energy related to Planck s constant and the frequency of the photon. Note: Planck s work had explained the energy of vibrating objects; Einstein was the first to take it seriously and apply it elsewhere. Sample Problem #1 (ex. 28.2, page 928) Ultraviolet light at 290 nm does 250 times as much cellular damage as an equal intensity of UV at 310 nm; there is a clear threshold for damage at 300 nm. What is the energy, in ev, of photons with a wavelength of 300 nm? Sample Problem #2 (ex. 28.3, page 930) What are the threshold frequencies and wavelengths from sodium and from aluminum? 4
Sample Problem #3 (ex. 28.4, page 930) What is the maximum electron speed and the stopping potential if sodium is illuminated with light of a wavelength of 300 nm? Photons Light sometimes exhibits wave-like behavior. Diffraction Light sometimes exhibits particle-like behavior. Quantized energy Sample Problem #4 9ex. 28.5, page 932) A 1.0 mw light beam from a laser pointer (λ= 670 nm) shines on a screen. How many photons strike the screen every second? 5
Sample Problem #5 (ex. 28.6, page 932) A red laser pointer and a green laser pointer have the same power. Which one emits a larger number of photons per second? Matter Waves If light waves could exhibit a particle-like nature, why shouldn t material particles have some kind of wave-like nature? With no experimental evidence, Prince Louis-Victor de Broglie reasoned by analogy with E = hf and some ideas of relativity. De Broglie determined that if a material particle of momentum p = mv has a wave-like nature and a wavelength. Sample Problem #6 (ex. 28.8, page 934) What is the de Broglie wavelength of an electron with a kinetic energy of 1.0 ev? 6
Sample Problem #7 (ex. 28.9, page 934) One of the smallest macroscopic particles we could imagine using for an experiment would be a very small smoke or soot particle. These are 1 μm in diameter, too small to see with the naked eye and just barely at the limits of resolution of a microscope. A particle of this size has a mass of about 10-18 kg. Calculate the de Broglie wavelength for a smoke particle moving at the very slow speed of 1 mm/s. The Interference and Diffraction of Matter Though de Broglie made his hypothesis in the absence of experimental data, experimental evidence came soon. Electrons diffract and interfere exactly like x-rays. The Electron Microscope 7
Energy Level Diagrams Useful visual representation of quantized energy of electrons. The lowest rung is called the ground state. Higher rungs are called excited states. Sample Problem #8 (ex. 28. 13, page 940) An electron in a quantum system has allowed energies E 1 = 1.0 ev, E 2 = 4.0 ev, and E 3 = 6.0 ev. What wavelengths are observed in the emission spectrum of this system? More Quantum Quantum Café video 8