Conceptual Physics Fundamentals Chapter 15: QUANTUM THEORY This lecture will help you understand: The Photoelectric Effect Absorption Spectra Fluorescence Incandescence Lasers Wave-Particle Duality Particles as Waves: Electron Diffraction Quantum Mechanics Uncertainty Principle Correspondence Principle The Photoelectric Effect I think it is safe to say that no one understands quantum mechanics. Richard P. Feynman 1
The Photoelectric Effect Quantization the idea that the natural world is granular rather than smoothly continuous Quantum any elemental particle that makes up matter or carries energy The Photoelectric Effect The photoelectric effect A model for how matter radiates hypothesized by Max Planck, a German theoretical physicist in early 1900s warm bodies emit radiant energy (light) in individualized bundles (quanta) energy in each quantum is proportional to the frequency of radiation E ~ f, or with Planck s constant h, E = hf The Photoelectric Effect The photoelectric effect (continued) 2
The Photoelectric Effect The photoelectric effect (continued) The Photoelectric Effect The photoelectric effect Einstein s view on light as a stream of particles, bundles of energy (photons) photons interact with matter one at a time high-energy photons dislodge electrons from certain metals The Photoelectric Effect CHECK YOUR NEIGHBOR In the photoelectric effect, the brighter the illuminating light on a photosensitive surface, the greater the A. velocity of ejected electrons. B. number of ejected electrons. C. both A and B D. none of the above 3
The Photoelectric Effect In the photoelectric effect, the brighter the illuminating light on a photosensitive surface, the greater the A. velocity of ejected electrons. B. number of ejected electrons. C. both A and B D. none of the above The Photoelectric Effect CHECK YOUR NEIGHBOR In the photoelectric effect, the higher the frequency of the illuminating light on a photosensitive surface, the greater the A. velocity of ejected electrons. B. number of ejected electrons. C. both A and B D. none of the above The Photoelectric Effect In the photoelectric effect, the higher the frequency of the illuminating light on a photosensitive surface, the greater the A. velocity of ejected electrons. B. number of ejected electrons. C. both A and B D. none of the above 4
When energy is imparted to an element, an electron may be boosted to a higher energy level. The atom is said to be excited. Excitation The frequency of an emitted photon ~ energylevel difference in de-exciting. E = hf CHECK YOUR NEIGHBOR Which has less energy per photon? A. red light B. green light C. blue light D. all have the same 5
Which has less energy per photon? A. red light B. green light C. blue light D. all have the same Explanation: In accord with E ~ f, the lowest frequency light has the lowest energy per photon. CHECK YOUR NEIGHBOR Excitation is the process in which A. electrons are boosted to higher energy levels in an atom. B. atoms are charged with light energy. C. atoms are made to shake, rattle, and roll. D. none of the above Excitation is the process in which A. electrons are boosted to higher energy levels in an atom. B. atoms are charged with light energy. C. atoms are made to shake, rattle, and roll. D. none of the above 6
Spectroscope arrangement of slit, focusing lenses, and prism or diffraction grating to see emission spectrum of light from glowing element When an electron is at a higher energy level, atom is excited and temporarily loses the acquired energy when it returns to a lower level and emits radiant energy. Spectral lines forms an image of the slit on the screen using a spectroscope each component of color is focused at a definite position according to frequency Spectral lines of hydrogen more orderly than other elements successive lines get closer until the lines merge Swedish physicist and mathematician Johannes Rydberg discovered that the sum of the frequencies of two lines often equals the frequency of a third line. 7
Ritz combination principle Rydberg s discovery called the Ritz Combination Principle: The spectral lines of any element include frequencies that are either the sum or the difference of the frequencies of two other lines. Absorption spectra Atoms in a gas absorb light of the same frequency they emit. A spectroscope can detect dark lines in an otherwise continuous spectrum. CHECK YOUR NEIGHBOR Most of what we know about atoms is gained by investigating the A. masses of elements. B. electric charge of elements. C. periodic table of the elements. D. light they emit. 8
Most of what we know about atoms is gained by investigating the A. masses of elements. B. electric charge of elements. C. periodic table of the elements. D. light they emit. Explanation: Light emitted by atoms, their atomic spectra, are considered to be the fingerprints of atoms. Fluorescence Fluorescence Many materials excited by ultraviolet light emit visible light upon de-excitation. Fluorescent lamps Fluorescence UV emitted by excited gas strikes phosphor material that emits white light. 9
Fluorescence CHECK YOUR NEIGHBOR An atom that absorbs a photon can then emit one A. only at the same energy. B. of any energy depending on the situation. C. only at a higher energy. D. only at the same or lower energy. Fluorescence An atom that absorbs a photon can then emit one A. only at the same energy. B. of any energy depending on the situation. C. only at a higher energy. D. only at the same or lower energy. Incandescence Incandescence The frequency of radiation emitted by a hot body is proportional to the temperature of the hot body. f ~ T Radiation curve of brightness versus frequency for emitted light. 10
Incandescence Incandescence (continued) Isolated bells ring with a distinct frequency (as atoms in a gas do). Sound from a box of bells crowded together is discordant (like light from an incandescent solid). Incandescence CHECK YOUR NEIGHBOR Which lamp is more efficient for emitting light? A. incandescent lamp B. fluorescent lamp C. both the same for the same wattage D. none of the above Incandescence Which lamp is more efficient for emitting light? A. incandescent lamp B. fluorescent lamp C. both the same for the same wattage D. none of the above 11
Lasers Lasers incoherent light (many frequencies and out of phase) Lasers (continued) Lasers monochromatic light out of phase Lasers Lasers (continued) coherent light of identical frequencies in phase 12
Lasers Lasers (continued) a device that produces a beam of coherent light many types and many ranges of light not a source of energy (as is sometimes thought) Wave-Particle Duality Wave-particle duality A photon behaves as a particle when emitted by an atom or absorbed by photographic film or other detectors. But it behaves as a wave in traveling from a source to the place where it is detected. In this sense, light can be both a wave and a particle! Wave-Particle Duality Wave-particle duality (continued) This image is built up photon by photon. 13
Wave-Particle Duality Double-slit experiment The light passing through two slits, a, forms an interference pattern, b, shown graphically in c. Particles as Waves: Electron Diffraction Particles as waves: electron diffraction Every particle of matter is associated with a corresponding wave. According to Louis de Broglie, a particle s wavelength is related to its momentum. wavelength = h momentum Particles as Waves: Electron Diffraction CHECK YOUR NEIGHBOR When we speak of de Broglie waves, we re speaking of the wave nature of A. transverse waves. B. longitudinal waves. C. particles. D. quantum uncertainties. 14
Particles as Waves: Electron Diffraction When we speak of de Broglie waves, we re speaking of the wave nature of A. transverse waves. B. longitudinal waves. C. particles. D. quantum uncertainties. Particles as Waves: Electron Diffraction Electron diffraction Interference patterns of beams of light and electrons compared Particles as Waves: Electron Diffraction Electron waves Electrons orbiting an atomic nucleus form standing waves. 15
Particles as Waves: Electron Diffraction Electron waves Hence the discrete energy levels in atoms! Quantum Mechanics The fundamental equation of quantum mechanics is Schrödinger s wave equation, which is: (Details of this equation are beyond the scope of this course.) Quantum Mechanics Quantum Mechanics In Schrödinger s wave equation, the thing that waves is the nonmaterial matter wave amplitude a mathematical entity called a wave function, represented by the symbol ψ (the Greek letter psi). All the information about the matter waves is contained in the wave function. 16
Quantum Mechanics Progression from the Bohr model of the atom to the modified model with de Broglie waves to the Schrödinger model. Quantum Mechanics CHECK YOUR NEIGHBOR As to why electrons orbit in only certain orbits, a compelling explanation views orbital electrons as A. particles that morph into waves. B. standing waves. C. planetary particles. D. quantum particles. Quantum Mechanics As to why electrons orbit in only certain orbits, a compelling explanation views orbital electrons as A. particles that morph into waves. B. standing waves. C. planetary particles. D. quantum particles. Explanation: Standing waves are stable and close in on themselves in phase. (See Figure 15.31). 17
Uncertainty Principle Uncertainty principle The act of observing something as tiny as an electron probes the electron and, in so doing, produces a considerable uncertainty in either its position or its motion. Uncertainty Principle Uncertainty principle (continued) German physicist Werner Heisenberg called this the uncertainty principle. When the uncertainties in measurements of momentum p and position x for a particle are multiplied together, the product must be equal to or greater than Planck s constant, h, divided by 2π, which is represented as h (called h-bar). p x h Uncertainty Principle Uncertainty principle (continued) The is uncertainty in measurement of : p is uncertainty in measurement of p and x the uncertainty in position. The product of uncertainties must be equal to or greater than ( ) the size of h. 18
Uncertainty Principle Uncertainty principle (continued) Applies to uncertainties of measurements of energy and time. The uncertainty in knowledge of energy, E, and the duration taken to measure the energy, t, are related by the expression: E t h. Uncertainty Principle Uncertainty principle (continued) Heisenberg s uncertainty principle applies only to quantum mechanics. it does not apply to uncertainties of macroscopic laboratory measurements a shield of nature s secrets the notion that science is basically uncertain Uncertainty Principle To which of these does Heisenberg s uncertainty principle apply? A. measuring room temperature with a thermometer B. momentum and distances of a high-speed bullet C. a public opinion survey D. none of the above 19
Uncertainty Principle To which of these does Heisenberg s uncertainty principle apply? A. measuring room temperature with a thermometer B. momentum and distances of a high-speed bullet C. a public opinion survey D. none of the above Explanation: Heisenberg s uncertainty principle involves the unavoidable interaction between nature at the atomic level and the means by which we probe it. Correspondence Principle Correspondence principle The correspondence principle, first stated by Niels Bohr is: If a new theory is valid, it must account for the verified results of the old theory. New theory and old must correspond; that is, they must overlap and agree in the region where the results of the old theory have been fully verified. Correspondence Principle CHECK YOUR NEIGHBOR To which of these does the correspondence principle apply? A. The Schrödinger equation leads to Newton s equations for orbital motion of satellites. B. The energy of a particle can be expressed as E = mc 2. C. Diffraction can be explained with either particles or photons. D. all of the above 20
Correspondence Principle To which of these does the correspondence principle apply? A. The Schrödinger equation leads to Newton s equations for orbital motion of satellites. B. The energy of a particle can be expressed as E = mc 2. C. Diffraction can be explained with either particles or photons. D. all of the above Explanation: Unlike Heisenberg s uncertainty principle, the correspondence principle is a general rule. Old and new theory must overlap where both are valid. Complementarity Complementarity Wholeness often means accepting alternate explanations for natural phenomena. Opposite ideas can complement one another (light can be both a wave and a particle). Bohr chose the yin-yang diagram to illustrate complementarity. 21