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Chapter-29Particles and Waves This is the central portion of the Eagle Nebula located about 7000 light-years from earth, as seen by the Hubble Space Telescope. Among the topics in this chapter are particle-like entities called photons. As we will see, they play the central role in the process of photo-evaporation, which allows astronomers to peer into the dense star-forming regions of the nebula. A newborn star can be seen on the surface of an EGG, evaporating gaseous globule.
Electron Diffraction The ability to exhibit interference effects is an essential characteristic of waves. One of the most incredible discoveries of twentieth-century physics is that particles can also behave like waves and exhibit interference effects. (a) If electrons behaved as discrete particles with no wave properties, they would pass through one or the other of the two slits and strike the screen, causing it to glow and produce exact images of the slits. (b) In reality, the screen reveals a pattern of bright and dark fringes, similar to the pattern produced when a beam of light is used and interference occurs between the light waves coming from each slit. The electron exhibits a dual nature, with both particle-like characteristics and wave-like characteristics.
The Wave-Particle Duality Scientists now accept the wave-particle duality as an essential part of nature: Waves can exhibit particle-like characteristics, and particles can exhibit wave-like characteristics.
29.2. Blackbody Radiation and Planck's Constant The electromagnetic radiation emitted by a perfect blackbody has an intensity per unit wavelength that varies from wavelength to wavelength, as each curve indicates. At the higher temperature, the intensity per unit wavelength is greater, and the maximum occurs at a shorter wavelength.
Photoelectric Effect Evidence for particle (photon) nature of light comes from a phenomenon called the photoelectric effect, in which electrons are emitted from a metal surface when light shines on it. In the photoelectric effect, light with a sufficiently high frequency ejects electrons from a metal surface. These photoelectrons, as they are called, are drawn to the positive collector, thus producing a current.
Energy of a Photon In 1905 Einstein presented an explanation of the photoelectric effect that took advantage of Planck’s work concerning blackbody radiation. It was primarily for his theory of the photoelectric effect that he was awarded the Nobel Prize in physics in 1921. In his photoelectric theory, Einstein proposed that light of frequency f could be regarded as a collection of discrete packets of energy (photons), each packet containing an amount of energy E given by: (where h is Planck’s constant)
Digital Camera Digital cameras use an array of charge-coupled devices instead of film to capture an image.
Visible Light CCD A CCD array consists of a sandwich of semiconducting silicon, insulating silicon dioxide, and a number of electrodes. The array is divided into many small sections or pixels, sixteen of which are shown in the drawing. Each pixel captures a small part of a picture. Digital cameras for consumers (rather than professionals) have between one and five million pixels, depending on price. The greater the number of pixels, the better is the resolution of the photograph. The blow-up shows a single pixel. Incident photons of visible light strike the silicon and generate electrons via the photoelectric effect. The range of energies of the visible photons is such that one electron is released when a photon interacts with a silicon atom. The electrons are trapped within a pixel because of a positive voltage applied to the electrodes beneath the insulating layer. Thus, the number of electrons that are released and trapped is proportional to the number of photons striking the pixel. In this fashion, each pixel in the CCD array accumulates an accurate representation of the light intensity at that point on the image.
Automatic garage door openers Automatic garage door openers have a safety feature that prevents the door from closing when it encounters an obstruction. A sending unit transmits an invisible (infrared) beam across the opening of the door. The beam is detected by a receiving unit that contains a photodiode. When infrared photons strike the photodiode, electrons bound to the atoms absorb the photons and become liberated. These liberated, mobile electrons cause the current in the photodiode to increase. When a person walks through the beam, the light is momentarily blocked from reaching the receiving unit, and the current in the photodiode decreases. The change in current is sensed by electronic circuitry that immediately stops the downward motion of the door and then causes it to rise up.
Eagle Nebula A giant star-forming region some 7000 light-years from earth. These clouds extend more than a light-year from base to tip and are the birthplace of stars. A star begins to form within a cloud when the gravitational force pulls together sufficient gas to create a high-density “ball.” The process of photoevaporation allows astronomers to see many of the high-density regions where stars are being formed. Photoevaporation is the process in which high-energy, ultraviolet (UV) photons from hot stars outside the cloud heat it up. As photoevaporation proceeds, globules of gas that are denser than their surroundings are exposed. The globules are known as evaporating gaseous globules (EGGs), and they are slightly larger than our solar system.
THE MOMENTUM OF A PHOTON AND THE COMPTON EFFECT The phenomenon in which an X-ray photon is scattered from an electron, with the scattered photon having a smaller frequency than the incident photon, is called the Compton effect.
Compton Effect Compton showed that the difference between the wavelength λ’ of the scattered photon and the wavelength λ of the incident photon is related to the scattering angle θ by:
THE DE BROGLIE WAVELENGTH AND THE WAVE NATURE OF MATTER This photograph shows a highly magnified view of a Drosophila fruit fly, made with a scanning electron microscope. This microscope uses electrons instead of light. The resolution of the fine detail is exceptional because the wavelength of an electron can be made much smaller than that of visible light. (David Scharf/SPL/Photo Researchers, Inc.)
The de Broglie wavelength where h is Planck’s constant and p is the magnitude of the relativistic momentum of the particle.
The De Broglie Wavelength of an Electron and of a Baseball Determine the de Broglie wavelength for (a) an electron (mass = 9.1x 10-31 kg) moving at a speed of 6.0x 106 m/s and (b) a baseball (mass = 0.15 kg) moving at a speed of 13 m/s.
