Conceptual Physics 11th Edition Chapter 31: LIGHT QUANTA

This lecture will help you understand: Birth of Quantum Theory Quantization and Planck’s Constant Photoelectric Effect Wave–Particle Duality Double-Slit Experiment Particles as Waves: Electron Diffraction Uncertainty Principle Complementarity

Birth of Quantum Theory There has been a long historical debate about the nature of light: Some believed it to be particle-like. Others believed it to be wavelike. Young’s double-slit experiment in 1801 proved that light was a wave. Max Planck in 1900 hypothesized that radiant energy was emitted in discrete bundles, each of which he called a quantum.

Quantization and Planck’s Constant Quantum physics states that in the microworld of the atom, the amount of energy in any system is quantized—not all values of energy are possible. Example: The energy in a beam of laser light, which is a whole-number multiple of a single lowest value of energy—one quantum The quanta of light, and of electromagnetic radiation in general, are the photons. Energy of a quanta: E = hf where h is Planck’s constant

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 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 Light shining on the negatively charged, photosensitive metal surface liberates electrons. The liberated electrons are attracted to the positive plate and produce a measurable current. If we instead charge this plate with just enough negative charge that it repels electrons, the current can be stopped. We can then calculate the energies of the ejected electrons from the easily measured potential difference between the plates.

The Photoelectric Effect The photoelectric effect (continued)

The Photoelectric Effect The photoelectric effect (continued)

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. number of ejected electrons. Both A and B. None of the above. B. number of ejected electrons.

The Photoelectric Effect CHECK YOUR ANSWER In the photoelectric effect, the brighter the illuminating light on a photosensitive surface, the greater the A. velocity of ejected electrons. number of ejected electrons. Both A and B. None of the above. B. number of ejected electrons.

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. number of ejected electrons. Both A and B. None of the above. A. velocity of ejected electrons.

The Photoelectric Effect CHECK YOUR ANSWER In the photoelectric effect, the higher the frequency of the illuminating light on a photosensitive surface, the greater the A. velocity of ejected electrons. number of ejected electrons. Both A and B. None of the above. A. velocity of ejected electrons.

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.

Double-Slit Experiment Monochromatic light passing through two slits, a, forms an interference pattern, b, shown graphically in c.

Double-Slit Experiment Suppose we dim our light source so that, in effect, only one photon at a time reaches the barrier with the thin slits. If film behind the barrier is exposed to the light for a very short time, the film gets exposed as shown below. Each spot represents the place where the film has been exposed by a photon. If the light is allowed to expose the film for a longer time, a pattern of fringes begins to emerge

Double-Slit Experiment If we cover one slit so that photons striking the photographic film can pass only through a single slit, the tiny spots on the film accumulate to form a single-slit diffraction pattern. We find that photons hit the film at places they would not hit if both slits were open.

Double-Slit Experiment How do photons traveling through one slit “know” that the other slit is open and avoid certain regions, proceeding only to areas that will ultimately fill to form an interference pattern? Each single photon has wave properties as well as particle properties. The photon displays different aspects at different times. A photon behaves as a particle when it is being emitted by an atom or absorbed by photographic film or other detectors, and behaves as a wave in traveling from a source to the place where it is detected. So the photon strikes the film as a particle but travels to its position as a wave that interferes constructively.

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. momentum Wavelength  h

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. longitudinal waves. particles. quantum uncertainties. C. particles.

Particles as Waves: Electron Diffraction CHECK YOUR ANSWER When we speak of de Broglie waves, we’re speaking of the wave nature of A. transverse waves. longitudinal waves. particles. quantum uncertainties. C. particles.

Particles as Waves: Electron Diffraction Interference patterns of beams of light (left) and electrons (right) compared

Particles as Waves: Electron Diffraction Electron microscope uses the wave nature of electrons to create images similar to the image of the mosquito shown here.

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 2, which is represented as (called h-bar). px 

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 .

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  .

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.

To which of these does Heisenberg’s uncertainty principle apply? CHECK YOUR ANSWER To which of these does Heisenberg’s uncertainty principle apply? A. Measuring room temperature with a thermometer Momentum and distances of a high-speed bullet A public opinion survey None of the above. D. None of these.

To which of these does Heisenberg’s uncertainty principle apply? CHECK YOUR ANSWER To which of these does Heisenberg’s uncertainty principle apply? A. Measuring room temperature with a thermometer Momentum and distances of a high-speed bullet A public opinion survey 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. D. None of these.

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.